Package 'TSPred'

Description

Functions for time series pre(post)processing, decomposition, modelling, prediction and accuracy assessment. The generated models and its yielded prediction errors can be used for benchmarking other time series prediction methods and for creating a demand for the refinement of such methods. For this purpose, benchmark data from prediction competitions may be used.

Author(s)

Rebecca Pontes Salles

Maintainer: [email protected]

Description

The an() function normalizes data of the provided time series to bring values into the range [0,1]. The function applies the method of Adaptive Normalization designed for non-stationary heteroscedastic (with non-uniform volatility) time series. an.rev() reverses the normalization.

Usage

an(data, max = NULL, min = NULL, byRow = TRUE, outlier.rm = TRUE, alpha = 1.5)

an.rev(data, max, min, an)

Arguments

Value

data normalized between 0 and 1. max and min are returned as attributes, as well as the mean values of each row (sliding window) in data (an).

Author(s)

Rebecca Pontes Salles

References

E. Ogasawara, L. C. Martinez, D. De Oliveira, G. Zimbrao, G. L. Pappa, and M. Mattoso, 2010, Adaptive Normalization: A novel data normalization approach for non-stationary time series, Proceedings of the International Joint Conference on Neural Networks.

See Also

Other normalization methods: minmax()

Examples

data(CATS)
swin <- sw(CATS[,1],5)
d <- an(swin, outlier.rm=FALSE)
x <- an.rev(d, max=attributes(d)$max, min=attributes(d)$min, an=attributes(d)$an)
all(round(x,4)==round(swin,4))

Description

Constructors for the modeling class representing a time series modeling and prediction method based on a particular model.

Usage

ARIMA(train_par = list(), pred_par = list(level = c(80, 95)))

ETS(train_par = list(), pred_par = list(level = c(80, 95)))

HW(train_par = list(), pred_par = list(level = c(80, 95)))

TF(train_par = list(), pred_par = list(level = c(80, 95)))

NNET(
  size = 5,
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = size + 1),
  proc = list(MM = MinMax())
)

RFrst(
  ntree = 500,
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = 6),
  proc = list(MM = MinMax())
)

RBF(
  size = 5,
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = size + 1),
  proc = list(MM = MinMax())
)

SVM(
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = 6),
  proc = list(MM = MinMax())
)

MLP(
  size = 5,
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = size + 1),
  proc = list(MM = MinMax())
)

ELM(
  train_par = list(),
  pred_par = list(),
  sw = SW(window_len = 6),
  proc = list(MM = MinMax())
)

Tensor_CNN(
  train_par = NULL,
  pred_par = list(level = c(80, 95)),
  sw = SW(window_len = 6),
  proc = list(MM = MinMax())
)

Tensor_LSTM(
  train_par = NULL,
  pred_par = list(batch_size = 1, level = c(80, 95)),
  sw = SW(window_len = 6),
  proc = list(MM = MinMax())
)

Arguments

Value

An object of class modeling.

Linear models

ARIMA: ARIMA model. train_func set as auto.arima and pred_func set as forecast.

ETS: Exponential Smoothing State Space model. train_func set as ets and pred_func set as forecast.

HW: Holt-Winter's Exponential Smoothing model. train_func set as hw and pred_func set as forecast.

TF: Theta Forecasting model. train_func set as thetaf and pred_func set as forecast.

Machine learning models

NNET: Artificial Neural Network model. train_func set as nnet and pred_func set as predict.

RFrst: Random Forest model. train_func set as randomForest and pred_func set as predict.

RBF: Radial Basis Function (RBF) Network model. train_func set as rbf and pred_func set as predict.

SVM: Support Vector Machine model. train_func set as tune.svm and pred_func set as predict.

MLP: Multi-Layer Perceptron (MLP) Network model. train_func set as mlp and pred_func set as predict.

ELM: Extreme Learning Machine (ELM) model. train_func set as elm_train and pred_func set as elm_predict.

Tensor_CNN: Convolutional Neural Network - TensorFlow. train_func based on functions from tensorflow and keras, and pred_func set as predict.

Tensor_LSTM: Long Short Term Memory Neural Networks - TensorFlow. train_func based on functions from tensorflow and keras, and pred_func set as predict.

Author(s)

Rebecca Pontes Salles

See Also

Other constructors: LT(), MSE_eval(), evaluating(), modeling(), processing(), tspred()

Description

The function predicts nonconsecutive blocks of N unknown values of a single time series using the arimapred function and an interpolation approach.

Usage

arimainterp(
  TimeSeries,
  n.ahead,
  extrap = TRUE,
  xreg = NULL,
  newxreg = NULL,
  se.fit = FALSE
)

Arguments

Details

In order to avoid error accumulation, when possible, the function provides the separate prediction of each half of the blocks of unknown values using their past and future known values, respectively. If extrap is TRUE, this strategy is not possible for the last of the blocks of unknown values, for whose prediction the function uses only its past values. By default the function omits any missing values found in TimeSeries.

Value

A vector of time series of predictions, or if se.fit is TRUE, a vector of lists, each one with the components pred, the predictions, and se, the estimated standard errors. Both components are time series. See the predict.Arima function in the stats package and the function arimapred.

Author(s)

Rebecca Pontes Salles

References

H. Cheng, P.-N. Tan, J. Gao, and J. Scripps, 2006, "Multistep-Ahead Time Series Prediction", In: W.-K. Ng, M. Kitsuregawa, J. Li, and K. Chang, eds., Advances in Knowledge Discovery and Data Mining, Springer Berlin Heidelberg, p. 765-774.

See Also

arimapred, marimapred

Examples

data(CATS)
arimainterp(CATS[,c(2:3)],n.ahead=20,extrap=TRUE)

Description

The function returns the parameters of a fitted ARIMA model, including non-seasonal and seasonal orders and drift.

Usage

arimaparameters(fit)

Arguments

Details

The fit object could possibly be the result of auto.arima or Arima of the forecast package, or arima of the stats package.

Value

A list giving the number of AR, MA, seasonal AR and seasonal MA coefficients, plus the period and the number of non-seasonal and seasonal differences of the provided ARIMA model. The value of the fitted drift constant is also presented.

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestArima,arimapred

Examples

data(SantaFe.A)
arimaparameters(forecast::auto.arima(SantaFe.A[,1]))

Description

The function predicts and returns the next n consecutive values of a time series using an automatically fitted ARIMA model. It may also plot the predicted values against the actual ones using the function plotarimapred.

Usage

arimapred(
  timeseries,
  timeseries.cont = NULL,
  n.ahead = NULL,
  na.action = stats::na.omit,
  xreg = NULL,
  newxreg = NULL,
  se.fit = FALSE,
  plot = FALSE,
  range.p = 0.2,
  ylab = NULL,
  xlab = NULL,
  main = NULL
)

Arguments

Details

The ARIMA model used for time series prediction is automatically fitted by the auto.arima function in the forecast package. In order to avoid drift errors, the function introduces an auxiliary regressor whose values are a sequence of consecutive integer numbers starting from 1. The fitted ARIMA model is used for prediction by the predict.Arima function in the stats package. For more details, see the auto.arima function in the forecast package and the predict.Arima function in the stats package.

Value

A time series of predictions, or if se.fit is TRUE, a list with the components pred, the predictions, and se, the estimated standard errors. Both components are time series. See the predict.Arima function in the stats package.

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

auto.arima, predict.Arima, plotarimapred, marimapred

Examples

data(SantaFe.A,SantaFe.A.cont)
arimapred(SantaFe.A[,1],SantaFe.A.cont[,1])
arimapred(SantaFe.A[,1],n.ahead=100)

Description

The BCT() function returns a transformation of the provided time series using a Box-Cox transformation. BCT.rev() reverses the transformation. Wrapper functions for BoxCox and InvBoxCox of the forecast package, respectively.

Usage

BCT(x, lambda = NULL, ...)

BCT.rev(x, lambda, ...)

Arguments

Details

If lambda is not 0, the Box-Cox transformation is given by

$f_\lambda(x) =\frac{x^\lambda - 1}{\lambda}$

If $\lambda=0$, the Box-Cox transformation is given by

$f_0(x)=\log(x)$

.

Value

A vector of the same length as x containing the transformed values.

Author(s)

Rebecca Pontes Salles

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211–246.

See Also

DIF,detrend, MAS, LT, PCT

Examples

data(CATS)
BCT(CATS[,1])

Description

benchmark is a generic function for benchmarking results based on particular metrics. The function invokes particular methods which depend on the class of the first argument.

Usage

benchmark(obj, ...)

## S3 method for class 'tspred'
benchmark(obj, bmrk_objs, rank.by = c("MSE"), ...)

Arguments

Details

The function benchmark.tspred benchmarks a time series prediction process defined by a tspred object based on a particular metric. The metrics resulting from its execution are compared against the ones produced by other time series prediction processes (defined in a list of tspred objects).

Value

A list containing:

Author(s)

Rebecca Pontes Salles

See Also

[tspred()] for defining a particular time series prediction process.

Examples

#Obtaining objects of the processing class
proc1 <- subsetting(test_len=20)
proc2 <- BoxCoxT(lambda=NULL)
proc3 <- WT(level=1, filter="bl14")

#Obtaining objects of the modeling class
modl1 <- ARIMA()

#Obtaining objects of the evaluating class
eval1 <- MSE_eval()
eval2 <- MAPE_eval()

#Defining a time series prediction process
tspred_1 <- tspred(subsetting=proc1,
                   processing=list(BCT=proc2,
                                   WT=proc3),
                   modeling=modl1,
                   evaluating=list(MSE=eval1,
                                   MAPE=eval2)
                  )
summary(tspred_1)

#Obtaining objects of the processing class
proc4 <- SW(window_len = 6)
proc5 <- MinMax()

#Obtaining objects of the modeling class
modl2 <- NNET(size=5,sw=proc4,proc=list(MM=proc5))

#Defining a time series prediction process
tspred_2 <- tspred(subsetting=proc1,
                   processing=list(BCT=proc2,
                                   WT=proc3),
                   modeling=modl2,
                   evaluating=list(MSE=eval1,
                                   MAPE=eval2)
                  )
summary(tspred_2)

data("CATS")
data <- CATS[3]

tspred_1_run <- workflow(tspred_1,data=data,prep_test=TRUE,onestep=TRUE)
tspred_2_run <- workflow(tspred_2,data=data,prep_test=TRUE,onestep=TRUE)

b <- benchmark(tspred_1_run,list(tspred_2_run),rank.by=c("MSE"))

Description

A univariate artificial time series presenting 5 non-consecutive blocks of 20 unknown points.

Usage

CATS

Format

A data frame with 980 observations on the following 5 variables.

V1

a numeric vector containing the known points 1-980 of the CATS time series.

V2

a numeric vector containing the known points 1001-1980 of the CATS time series.

V3

a numeric vector containing the known points 2001-2980 of the CATS time series.

V4

a numeric vector containing the known points 3001-3980 of the CATS time series.

V5

a numeric vector containing the known points 4001-4980 of the CATS time series.

Details

The CATS Competition presented an artificial time series with 5,000 points, among which 100 are unknown. The competition proposed that the competitors predicted the 100 unknown values from the given time series, which are grouped into five non-consecutive blocks of 20 successive values (CATS.cont). The unknown points of the series are the 981-1000, 1981-2000, 2981-3000, 3981-4000 and 4981-5000. The performance evaluation done by the CATS Competition was based on the MSEs computed on the 100 unknown values (E1) and on the 80 first unknown values (E2). The E2 error was considered relevant because some of the proposed methods used interpolation techniques, which cannot be applied in the case of the fifth set of unknown points.

References

A. Lendasse, E. Oja, O. Simula, M. Verleysen, and others, 2004, Time Series Prediction Competition: The CATS Benchmark, In: IJCNN'2004-International Joint Conference on Neural Networks

A. Lendasse, E. Oja, O. Simula, and M. Verleysen, 2007, Time series prediction competition: The CATS benchmark, Neurocomputing, v. 70, n. 13-15 (Aug.), p. 2325-2329.

See Also

CATS.cont

Examples

data(CATS)
str(CATS)
plot(ts(CATS["V5"]))

Description

A dataset of providing the 5 blocks of 20 unknown points of the univariate time series in CATS

Usage

CATS.cont

Format

A data frame with 20 observations on the following 5 variables.

V1

a numeric vector containing the unknown points 981-1000 of the CATS time series in CATS

V2

a numeric vector containing the unknown points 1981-2000 of the CATS time series in CATS

V3

a numeric vector containing the unknown points 2981-3000 of the CATS time series in CATS

V4

a numeric vector containing the unknown points 3981-4000 of the CATS time series in CATS

V5

a numeric vector containing the unknown points 4981-5000 of the CATS time series in CATS

Details

Contains the 100 unknown observations which were to be predicted of the CATS time series in (CATS) as demanded by the CATS Competition.

Source

A. Lendasse, E. Oja, O. Simula, M. Verleysen, and others, 2004, Time Series Prediction Competition: The CATS Benchmark, In: IJCNN'2004-International Joint Conference on Neural Networks

References

A. Lendasse, E. Oja, O. Simula, and M. Verleysen, 2007, Time series prediction competition: The CATS benchmark, Neurocomputing, v. 70, n. 13-15 (Aug.), p. 2325-2329.

See Also

CATS

Examples

data(CATS.cont)
str(CATS.cont)
plot(ts(CATS.cont["V5"]))

Description

The detrend() function performs a detrending transformation and removes a trend from the provided time series. detrend.rev() reverses the transformation.

Usage

detrend(x, trend)

Arguments

Value

A vector of the same length as x containing the residuals of x after trend removal.

Author(s)

Rebecca Pontes Salles

References

R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, New York, NY, 4 edition, 2017.

See Also

DIF,BCT, MAS, LT, PCT

Examples

data(CATS,CATS.cont)
fpoly <- fittestPolyR(CATS[,1],h=20)
trend <- fitted(fpoly$model)

residuals <- detrend(CATS[,1],trend)
x <- detrend.rev(residuals,trend)

Description

The Diff() function returns a simple or seasonal differencing transformation of the provided time series. Diff.rev() reverses the transformation. Wrapper functions for diff and diffinv of the stats package, respectively.

Usage

Diff(
  x,
  lag = ifelse(type == "simple", 1, stats::frequency(x)),
  differences = NULL,
  type = c("simple", "seasonal"),
  ...
)

Diff.rev(
  x,
  lag = ifelse(type == "simple", 1, stats::frequency(x)),
  differences = 1,
  xi,
  type = c("simple", "seasonal"),
  addinit = TRUE
)

Arguments

Value

x if differences is automatically selected, and is not set as greater than 0. Same as diff otherwise.

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

Other transformation methods: LogT(), WaveletT(), emd(), mas(), mlm_io(), outliers_bp(), pct(), train_test_subset()

Examples

data(CATS)
d <- Diff(CATS[,1], differences = 1)
x <- Diff.rev(as.vector(d), differences = attributes(d)$differences, xi = attributes(d)$xi)
all(round(x,4)==round(CATS[,1],4))

Description

The function automatically applies an empirical mode decomposition to a provided univariate time series. Wrapper function for emd of the Rlibeemd package. It also allows the automatic selection of meaningful IMFs using fittestEMD. emd.rev() reverses the transformation.

Usage

emd(
  x,
  num_imfs = 0,
  S_number = 4L,
  num_siftings = 50L,
  meaningfulImfs = NULL,
  h = 1,
  ...
)

emd.rev(pred)

Arguments

Value

A list containing the meaningful IMFs of the empirical mode decomposition of x. A vector indicating the indices of the meaningful IMFs and the number of IMFs produced are passed as attributes named "meaningfulImfs" and "num_imfs", respectively.

Author(s)

Rebecca Pontes Salles

References

Kim, D., Paek, S. H., & Oh, H. S. (2008). A Hilbert-Huang transform approach for predicting cyber-attacks. Journal of the Korean Statistical Society, 37(3), 277-283.

See Also

fittestEMD, fittestWavelet

Other transformation methods: Diff(), LogT(), WaveletT(), mas(), mlm_io(), outliers_bp(), pct(), train_test_subset()

Examples

data(CATS)
e <- emd(CATS[,1])
x <- emd.rev(e)
all(round(x,4)==round(CATS[,1],4))

Description

The EUNITE Competition main dataset composed of a set of univariate time series of half-an-hour electrical loads measured between 1997 and 1998.

Usage

EUNITE.Loads

Format

A data frame with 730 observations on the following 48 variables.

X00.30

a numeric vector with loads measured in the period 00:00-00:30 of 1997-1998.

X01.00

a numeric vector with loads measured in the period 00:30-01:00 of 1997-1998.

X01.30

a numeric vector with loads measured in the period 01:00-01:30 of 1997-1998.

X02.00

a numeric vector with loads measured in the period 01:30-02:00 of 1997-1998.

X02.30

a numeric vector with loads measured in the period 02:00-02:30 of 1997-1998.

X03.00

a numeric vector with loads measured in the period 02:30-03:00 of 1997-1998.

X03.30

a numeric vector with loads measured in the period 03:00-03:30 of 1997-1998.

X04.00

a numeric vector with loads measured in the period 03:30-04:00 of 1997-1998.

X04.30

a numeric vector with loads measured in the period 04:00-04:30 of 1997-1998.

X05.00

a numeric vector with loads measured in the period 04:30-05:00 of 1997-1998.

X05.30

a numeric vector with loads measured in the period 05:00-05:30 of 1997-1998.

X06.00

a numeric vector with loads measured in the period 05:30-06:00 of 1997-1998.

X06.30

a numeric vector with loads measured in the period 06:00-06:30 of 1997-1998.

X07.00

a numeric vector with loads measured in the period 06:30-07:00 of 1997-1998.

X07.30

a numeric vector with loads measured in the period 07:00-07:30 of 1997-1998.

X08.00

a numeric vector with loads measured in the period 07:30-08:00 of 1997-1998.

X08.30

a numeric vector with loads measured in the period 08:00-08:30 of 1997-1998.

X09.00

a numeric vector with loads measured in the period 08:30-09:00 of 1997-1998.

X09.30

a numeric vector with loads measured in the period 09:00-09:30 of 1997-1998.

X10.00

a numeric vector with loads measured in the period 09:30-10:00 of 1997-1998.

X10.30

a numeric vector with loads measured in the period 10:00-10:30 of 1997-1998.

X11.00

a numeric vector with loads measured in the period 10:30-11:00 of 1997-1998.

X11.30

a numeric vector with loads measured in the period 11:00-11:30 of 1997-1998.

X12.00

a numeric vector with loads measured in the period 11:30-12:00 of 1997-1998.

X12.30

a numeric vector with loads measured in the period 12:00-12:30 of 1997-1998.

X13.00

a numeric vector with loads measured in the period 12:30-13:00 of 1997-1998.

X13.30

a numeric vector with loads measured in the period 13:00-13:30 of 1997-1998.

X14.00

a numeric vector with loads measured in the period 13:30-14:00 of 1997-1998.

X14.30

a numeric vector with loads measured in the period 14:00-14:30 of 1997-1998.

X15.00

a numeric vector with loads measured in the period 14:30-15:00 of 1997-1998.

X15.30

a numeric vector with loads measured in the period 15:00-15:30 of 1997-1998.

X16.00

a numeric vector with loads measured in the period 15:30-16:00 of 1997-1998.

X16.30

a numeric vector with loads measured in the period 16:00-16:30 of 1997-1998.

X17.00

a numeric vector with loads measured in the period 16:30-17:00 of 1997-1998.

X17.30

a numeric vector with loads measured in the period 17:00-17:30 of 1997-1998.

X18.00

a numeric vector with loads measured in the period 17:30-18:00 of 1997-1998.

X18.30

a numeric vector with loads measured in the period 18:00-18:30 of 1997-1998.

X19.00

a numeric vector with loads measured in the period 18:30-19:00 of 1997-1998.

X19.30

a numeric vector with loads measured in the period 19:00-19:30 of 1997-1998.

X20.00

a numeric vector with loads measured in the period 19:30-20:00 of 1997-1998.

X20.30

a numeric vector with loads measured in the period 20:00-20:30 of 1997-1998.

X21.00

a numeric vector with loads measured in the period 20:30-21:00 of 1997-1998.

X21.30

a numeric vector with loads measured in the period 21:00-21:30 of 1997-1998.

X22.00

a numeric vector with loads measured in the period 21:30-22:00 of 1997-1998.

X22.30

a numeric vector with loads measured in the period 22:00-22:30 of 1997-1998.

X23.00

a numeric vector with loads measured in the period 22:30-23:00 of 1997-1998.

X23.30

a numeric vector with loads measured in the period 23:00-23:30 of 1997-1998.

X24.00

a numeric vector with loads measured in the period 23:30-24:00 of 1997-1998.

Details

The EUNITE Competition proposed the prediction of maximum daily electrical loads based on half-an-hour loads and average daily temperatures of 1997-1998 (EUNITE.Temp). The holidays with respect to this period were also provided (EUNITE.Reg) and the use of data on average daily temperatures of 1995-1996 was allowed. The dataset present considerable seasonality due to properties of electrical load demand, climate influence and holiday effects, among other reasons. Competitors were asked to predict the 31 values corresponding to the daily maximum electrical loads of January 1999 (EUNITE.Loads.cont). The performance evaluation done by the EUNITE Competition was based on the MAPE error and on the MAXIMAL error of prediction found by the competitors.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Loads.cont, EUNITE.Reg, EUNITE.Temp

Examples

data(EUNITE.Loads)
str(EUNITE.Loads)
plot(ts(EUNITE.Loads["X24.00"]))

Description

A dataset of univariate time series providing 31 points beyond the end of the time series in EUNITE.Loads containing half-an-hour electrical loads measured in January 1999.

Usage

EUNITE.Loads.cont

Format

A data frame with 31 observations on the following 48 variables.

X00.30

a numeric vector containing further observations of X00.30 in EUNITE.Loads relative to January 1999.

X01.00

a numeric vector containing further observations of X01.00 in EUNITE.Loads relative to January 1999.

X01.30

a numeric vector containing further observations of X01.30 in EUNITE.Loads relative to January 1999.

X02.00

a numeric vector containing further observations of X02.00 in EUNITE.Loads relative to January 1999.

X02.30

a numeric vector containing further observations of X02.30 in EUNITE.Loads relative to January 1999.

X03.00

a numeric vector containing further observations of X03.00 in EUNITE.Loads relative to January 1999.

X03.30

a numeric vector containing further observations of X03.30 in EUNITE.Loads relative to January 1999.

X04.00

a numeric vector containing further observations of X04.00 in EUNITE.Loads relative to January 1999.

X04.30

a numeric vector containing further observations of X04.30 in EUNITE.Loads relative to January 1999.

X05.00

a numeric vector containing further observations of X05.00 in EUNITE.Loads relative to January 1999.

X05.30

a numeric vector containing further observations of X05.30 in EUNITE.Loads relative to January 1999.

X06.00

a numeric vector containing further observations of X06.00 in EUNITE.Loads relative to January 1999.

X06.30

a numeric vector containing further observations of X06.30 in EUNITE.Loads relative to January 1999.

X07.00

a numeric vector containing further observations of X07.00 in EUNITE.Loads relative to January 1999.

X07.30

a numeric vector containing further observations of X07.30 in EUNITE.Loads relative to January 1999.

X08.00

a numeric vector containing further observations of X08.00 in EUNITE.Loads relative to January 1999.

X08.30

a numeric vector containing further observations of X08.30 in EUNITE.Loads relative to January 1999.

X09.00

a numeric vector containing further observations of X09.00 in EUNITE.Loads relative to January 1999.

X09.30

a numeric vector containing further observations of X09.30 in EUNITE.Loads relative to January 1999.

X10.00

a numeric vector containing further observations of X10.00 in EUNITE.Loads relative to January 1999.

X10.30

a numeric vector containing further observations of X10.30 in EUNITE.Loads relative to January 1999.

X11.00

a numeric vector containing further observations of X11.00 in EUNITE.Loads relative to January 1999.

X11.30

a numeric vector containing further observations of X11.30 in EUNITE.Loads relative to January 1999.

X12.00

a numeric vector containing further observations of X12.00 in EUNITE.Loads relative to January 1999.

X12.30

a numeric vector containing further observations of X12.30 in EUNITE.Loads relative to January 1999.

X13.00

a numeric vector containing further observations of X13.00 in EUNITE.Loads relative to January 1999.

X13.30

a numeric vector containing further observations of X13.30 in EUNITE.Loads relative to January 1999.

X14.00

a numeric vector containing further observations of X14.00 in EUNITE.Loads relative to January 1999.

X14.30

a numeric vector containing further observations of X14.30 in EUNITE.Loads relative to January 1999.

X15.00

a numeric vector containing further observations of X15.00 in EUNITE.Loads relative to January 1999.

X15.30

a numeric vector containing further observations of X15.30 in EUNITE.Loads relative to January 1999.

X16.00

a numeric vector containing further observations of X16.00 in EUNITE.Loads relative to January 1999.

X16.30

a numeric vector containing further observations of X16.30 in EUNITE.Loads relative to January 1999.

X17.00

a numeric vector containing further observations of X17.00 in EUNITE.Loads relative to January 1999.

X17.30

a numeric vector containing further observations of X17.30 in EUNITE.Loads relative to January 1999.

X18.00

a numeric vector containing further observations of X18.00 in EUNITE.Loads relative to January 1999.

X18.30

a numeric vector containing further observations of X18.30 in EUNITE.Loads relative to January 1999.

X19.00

a numeric vector containing further observations of X19.00 in EUNITE.Loads relative to January 1999.

X19.30

a numeric vector containing further observations of X19.30 in EUNITE.Loads relative to January 1999.

X20.00

a numeric vector containing further observations of X20.00 in EUNITE.Loads relative to January 1999.

X20.30

a numeric vector containing further observations of X20.30 in EUNITE.Loads relative to January 1999.

X21.00

a numeric vector containing further observations of X21.00 in EUNITE.Loads relative to January 1999.

X21.30

a numeric vector containing further observations of X21.30 in EUNITE.Loads relative to January 1999.

X22.00

a numeric vector containing further observations of X22.00 in EUNITE.Loads relative to January 1999.

X22.30

a numeric vector containing further observations of X22.30 in EUNITE.Loads relative to January 1999.

X23.00

a numeric vector containing further observations of X23.00 in EUNITE.Loads relative to January 1999.

X23.30

a numeric vector containing further observations of X23.30 in EUNITE.Loads relative to January 1999.

X24.00

a numeric vector containing further observations of X24.00 in EUNITE.Loads relative to January 1999.

Details

Contains the 31 values corresponding to the daily maximum electrical loads of January 1999 which were to be predicted of EUNITE.Loads as demanded by the EUNITE Competition.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Loads, EUNITE.Reg, EUNITE.Temp

Examples

data(EUNITE.Loads.cont)
str(EUNITE.Loads.cont)
plot(ts(EUNITE.Loads.cont["X24.00"]))

Description

The EUNITE Competition dataset containing a set of variables serving as regressors for the electrical loads measured between 1997 and 1998 in EUNITE.Loads.

Usage

EUNITE.Reg

Format

A data frame with 730 observations on the following 2 variables.

Holiday

a numeric vector containing daily data on the holidays for the time period 1997-1998. Composed of binary values where 1 represents a holiday and 0 a common day.

Weekday

a numeric vector containing daily data on the weekdays for the time period 1997-1998. Composed of integer values where 1 represents a Sunday, 2 a Monday, 3 a Tuesday, 4 a Wednesday, 5 a Thursday, 6 a Friday and 7 a Saturday.

Details

The EUNITE Competition proposed the prediction of maximum daily electrical loads based on half-an-hour loads (EUNITE.Loads) and average daily temperatures of 1997-1998 (EUNITE.Temp). Competitors were asked to predict the 31 values corresponding to the daily maximum electrical loads of January 1999 (EUNITE.Loads.cont). For the posed prediction problem, it is useful to consider as regressors the holidays and the weekdays with respect to this period in EUNITE.Reg, which are expected to have a considerable impact on the electrical consumption.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Reg.cont, EUNITE.Loads, EUNITE.Temp

Examples

data(EUNITE.Reg)
str(EUNITE.Reg)

Description

A dataset of regressor variables for electrical loads measured in January 1999, providing 31 points beyond the end of the data in EUNITE.Reg.

Usage

EUNITE.Reg.cont

Format

A data frame with 31 observations on the following 2 variables.

Holiday

a numeric vector containing further data of the variable Holiday in EUNITE.Reg relative to January 1999.

Weekday

a numeric vector containing further data of the variable Weekday in EUNITE.Reg relative to January 1999.

Details

Contains the 31 values of the regressors used for the prediction of the daily maximum electrical loads of January 1999 from EUNITE.Loads as demanded by the EUNITE Competition.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Reg, EUNITE.Loads, EUNITE.Temp

Examples

data(EUNITE.Reg.cont)
str(EUNITE.Reg.cont)

Description

The EUNITE Competition dataset composed of a univariate time series of average daily temperatures measured between 1995 and 1998.

Usage

EUNITE.Temp

Format

A data frame with 1461 observations on the following variable.

Temperature

a numeric vector with average daily temperatures measured in the period 1995-1998.

Details

The EUNITE Competition proposed the prediction of maximum daily electrical loads based on half-an-hour loads (EUNITE.Loads) and average daily temperatures of 1997-1998, where the latter is used as a regressor. Competitors were asked to predict the 31 values corresponding to the daily maximum electrical loads of January 1999 (EUNITE.Loads.cont). For the posed prediction problem, the average daily temperatures of January 1999 must also be predicted and for that, the use of data on average daily temperatures of 1995-1996 was allowed.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Temp.cont, EUNITE.Loads, EUNITE.Reg

Examples

data(EUNITE.Temp)
str(EUNITE.Temp)
plot(ts(EUNITE.Temp))

Description

A dataset with a univariate time series providing 31 points beyond the end of the time series in EUNITE.Temp containing average daily temperatures measured in January 1999.

Usage

EUNITE.Temp.cont

Format

A data frame with 31 observations on the following variable.

Temperature

a numeric vector containing further observations of Temperature in EUNITE.Temp relative to January 1999.

Details

Contains the 31 values corresponding to the average daily temperatures of January 1999 which were to be predicted of EUNITE.Temp as demanded by the EUNITE Competition.

Source

EUNITE 1999, Electricity Load Forecast using Intelligent Adaptive Technology: The EUNITE Network Competition. URL: http://www.eunite.org/knowledge/Competitions/1st_competition/1st_competition.htm.

References

B.-J. Chen, M.-W. Chang, and C.-J. Lin, 2004, Load forecasting using support vector Machines: a study on EUNITE competition 2001, IEEE Transactions on Power Systems, v. 19, n. 4 (Nov.), p. 1821-1830.

See Also

EUNITE.Temp, EUNITE.Loads, EUNITE.Reg

Examples

data(EUNITE.Temp.cont)
str(EUNITE.Temp.cont)
plot(ts(EUNITE.Temp.cont))

Description

evaluate is a generic function for evaluating the quality of time series prediction or modeling fitness based on a particular metric defined in an evaluating object. The function invokes particular methods which depend on the class of the first argument.

Usage

evaluate(obj, ...)

## S3 method for class 'evaluating'
evaluate(obj, test, pred, ...)

## S3 method for class 'fitness'
evaluate(obj, mdl, test = NULL, pred = NULL, ...)

## S3 method for class 'error'
evaluate(obj, mdl = NULL, test = NULL, pred = NULL, ..., fitness = FALSE)

Arguments

Value

A list containing obj and the computed metric values.

Author(s)

Rebecca Pontes Salles

See Also

Other evaluate: evaluate.tspred()

Examples

data(CATS,CATS.cont)
mdl <- forecast::auto.arima(CATS[,1])
pred <- forecast::forecast(mdl, h=length(CATS.cont[,1]))

evaluate(MSE_eval(), test=CATS.cont[,1], pred=pred$mean)
evaluate(MSE_eval(), mdl, fitness=TRUE)
evaluate(AIC_eval(), mdl)

Evaluate method for tspred objects

Description

Evaluates the modeling fitness and quality of time series prediction of the trained models and predicted time series data contained in a tspred class object, respectively, based on a particular metric. Each metric is defined by an evaluating object in the list contained in the tspred class object.

Usage

## S3 method for class 'tspred'
evaluate(obj, fitness = TRUE, ...)

Arguments

Details

The function evaluate.tspred calls the method evaluate on each evaluating object contained in obj. It uses each trained model, the testing set and the time series predictions contained in obj to compute the metrics. Finally, the produced quality metrics are introduced in the structure of the tspred class object in obj.

Value

An object of class tspred with updated structure containing computed quality metric values.

Author(s)

Rebecca Pontes Salles

See Also

[tspred()] for defining a particular time series prediction process, and [MSE_eval()] for defining a time series prediction/modeling quality metric.

Other evaluate: evaluate()

Examples

data(CATS)

#Obtaining objects of the processing class
proc1 <- subsetting(test_len=20)
proc2 <- BoxCoxT(lambda=NULL)
proc3 <- WT(level=1, filter="bl14")

#Obtaining objects of the modeling class
modl1 <- ARIMA()

#Obtaining objects of the evaluating class
eval1 <- MSE_eval()

#Defining a time series prediction process
tspred_1 <- tspred(subsetting=proc1,
                   processing=list(BCT=proc2,
                                   WT=proc3),
                   modeling=modl1,
                   evaluating=list(MSE=eval1)
)
summary(tspred_1)

tspred_1 <- subset(tspred_1, data=CATS[3])
tspred_1 <- preprocess(tspred_1,prep_test=FALSE)
tspred_1 <- train(tspred_1)
tspred_1 <- predict(tspred_1, onestep=TRUE)
tspred_1 <- postprocess(tspred_1)
tspred_1 <- evaluate(tspred_1)

Description

Constructor for the evaluating class representing a time series prediction or modeling fitness quality evaluation based on a particular metric. The evaluating class has two specialized subclasses fitness and error reagarding fitness criteria and prediction/modeling error metrics, respectively.

Usage

evaluating(eval_func, eval_par = NULL, ..., subclass = NULL)

fitness(eval_func, eval_par = NULL, ..., subclass = NULL)

error(eval_func, eval_par = NULL, ..., subclass = NULL)

Arguments

Value

An object of class evaluating. A list usually containing at least the following elements:

Author(s)

Rebecca Pontes Salles

See Also

Other constructors: ARIMA(), LT(), MSE_eval(), modeling(), processing(), tspred()

Examples

e <- error(eval_func=TSPred::NMSE, eval_par=list(train.actual=NULL),
           method="Normalised Mean Squared Error", subclass="NMSE")
summary(e)

f <- fitness(eval_func=stats::AIC, method="Akaike's Information Criterion", subclass="AIC")
summary(f)

Description

The function predicts and returns the next n consecutive values of a univariate time series using an automatically best fitted ARIMA model. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.

Usage

fittestArima(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  na.action = stats::na.omit,
  level = c(80, 95),
  ...
)

Arguments

Details

The ARIMA model is automatically fitted by the auto.arima function and it is used for prediction by the forecast function both in the forecast package.

The fitness criteria AICc, AIC (AIC), BIC (BIC) and log-likelihood (logLik) are extracted from the fitted ARIMA model. Also, the prediction accuracy of the model is computed by means of MSE (MSE), NMSE (NMSE), MAPE (MAPE), sMAPE (sMAPE) and maximal error (MAXError) measures.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestArimaKF, fittestLM, marimapred

Examples

data(CATS,CATS.cont)
fArima <- fittestArima(CATS[,1],CATS.cont[,1])
#predicted values
pred <- fArima$pred$mean
#model information
cbind(AICc=fArima$AICc, AIC=fArima$AIC, BIC=fArima$BIC,
 logLik=fArima$logLik, MSE=fArima$MSE, NMSE=fArima$NMSE, 
 MAPE=fArima$MSE, sMAPE=fArima$MSE, MaxError=fArima$MaxError)

#plotting the time series data
plot(c(CATS[,1],CATS.cont[,1]),type='o',lwd=2,xlim=c(960,1000),ylim=c(0,200),
 xlab="Time",ylab="ARIMA")
#plotting the predicted values
lines(ts(pred,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(fArima$pred$upper[,2],start=981),lwd=2,col='light blue')
lines(ts(fArima$pred$lower[,2],start=981),lwd=2,col='light blue')

Description

The function predicts and returns the next n consecutive values of a univariate time series using the best evaluated ARIMA model automatically fitted with Kalman filter. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.

Usage

fittestArimaKF(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  na.action = stats::na.omit,
  level = 0.9,
  filtered = TRUE,
  initQ = NULL,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness"),
  ...
)

Arguments

Details

A best ARIMA model is automatically fitted by the auto.arima function in the forecast package. The coefficients of this model are then used as initial parameters for optimization of a state space model (SSModel) using the Kalman filter and functions of the KFAS package (see SSMarima and artransform).

If initQ is NULL, it is automatically set as either log(var(timeseries)) or 0. For that, a set of candidate ARIMA state space models is generated by different initial parameterization of initQ during the model optimization process. The value option which generates the best ranked candidate ARIMA model acoording to the criteria in rank.by is selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate models are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the candidate models are fitted and fitness criteria are calculated based on all observations in timeseries.

If rank.by is set as "errors" or "fitness", the candidate models are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate models. The rank.position.sum criterion is calculated as the sum of the rank positions of a model (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestArima, fittestLM, marimapred

Examples

data(CATS,CATS.cont)
fArimaKF <- fittestArimaKF(CATS[,2],CATS.cont[,2])
#predicted values
pred <- fArimaKF$pred

#extracting Kalman filtered and smoothed time series from the best fitted model
fs <- KFAS::KFS(fArimaKF$model,filtering=c("state","mean"),smoothing=c("state","mean"))
f <- fitted(fs, filtered = TRUE) #Kalman filtered time  series
s <- fitted(fs) #Kalman smoothed time  series
#plotting the time series data
plot(c(CATS[,2],CATS.cont[,2]),type='o',lwd=2,xlim=c(960,1000),ylim=c(200,600),
 xlab="Time",ylab="ARIMAKF")
#plotting the Kalman filtered time series
lines(f,col='red',lty=2,lwd=2)
#plotting the Kalman smoothed time series
lines(s,col='green',lty=2,lwd=2)
#plotting predicted values
lines(ts(pred$mean,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(pred$upper,start=981),lwd=2,col='light blue')
lines(ts(pred$lower,start=981),lwd=2,col='light blue')

Description

The function automatically applies an empirical mode decomposition to a provided univariate time series. The resulting components of the decomposed series are used as base for predicting and returning the next n consecutive values of the provided univariate time series using also automatically fitted models. It also evaluates fitness and prediction accuracy of the produced models.

Usage

fittestEMD(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  num_imfs = 0,
  S_number = 4L,
  num_siftings = 50L,
  level = 0.95,
  na.action = stats::na.omit,
  model = c("ets", "arima"),
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "errors")
)

Arguments

Details

The function produces an empirical mode decomposition of timeseries. See the emd function. The Intrinsic Mode Functions (IMFs) and residue series resulting from the decomposition are separately used as base for model fitting and prediction. The set of predictions for all IMFs and residue series are then reversed transformed in order to produce the next h consecutive values of the provided univariate time series in timeseries. See the emd.rev function.

The function automatically selects the meaningful IMFs of a decomposition. For that, the function produces models for different selections of meaningful IMFs according to the possible intervals i:num_imfs for i=1,...,(num_imfs-1), where num_imfs is the number of IMFs in a decomposition. The options of meaningful IMFs of a decomposition which generate the best ranked model fitness/predictions acoording to the criteria in rank.by are selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate empirical mode decompositions are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the component series of the candidate decompositions are modeled and model fitness criteria are calculated based on all observations in timeseries. In particular, the fitness criteria calculated for ranking the candidate decompositions correspond to the models produced for the IMFs.

If rank.by is set as "errors" or "fitness", the candidate decompositions are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate decompositions. The rank.position.sum criterion is calculated as the sum of the rank positions of a decomposition (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

Kim, D., Paek, S. H., & Oh, H. S. (2008). A Hilbert-Huang transform approach for predicting cyber-attacks. Journal of the Korean Statistical Society, 37(3), 277-283.

See Also

fittestWavelet, fittestMAS

Examples

data(CATS)

femd <- fittestEMD(CATS[,1],h=20)

Description

The function automatically evaluates and returns the fittest linear model among ARIMA and polynomial regression, with and without Kalman filtering, for prediction of a given univariate time series. Wrapper for the fittestArima, fittestArimaKF, fittestPolyR and fittestPolyRKF functions for automatic time series prediction, whose results are also returned.

Usage

fittestLM(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  level = 0.95,
  na.action = stats::na.omit,
  filtered = TRUE,
  order = NULL,
  minorder = 0,
  maxorder = 5,
  raw = FALSE,
  initQ = NULL,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness"),
  ...
)

Arguments

Details

The results of the best evaluated models returned by fittestArima, fittestArimaKF, fittestPolyR and fittestPolyRKF are ranked and the fittest linear model for prediction of the given univariate time series is selected based on the criteria in rank.by.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). See fittestArima, fittestArimaKF, fittestPolyR or fittestPolyRKF.

If rank.by is set as "errors" or "fitness", the candidate models are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate models. The rank.position.sum criterion is calculated as the sum of the rank positions of a model (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

See Also

fittestArima, fittestArimaKF, fittestPolyR, fittestPolyRKF

Examples

data(CATS,CATS.cont)
fittest <- fittestLM(CATS[,1],CATS.cont[,1])

#fittest model information
fittest$rank[1,]

#predictions of the fittest model
fittest$ranked.results[[1]]$pred

Description

The function uses an automatically produced moving average smoother as base for predicting and returning the next n consecutive values of the provided univariate time series using an also automatically fitted model (ets/stlf or arima). It also evaluates the fitness and prediction accuracy of the produced model.

Usage

fittestMAS(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  order = NULL,
  minorder = 1,
  maxorder = min(36, length(ts(na.action(timeseries)))/2),
  model = c("ets", "arima"),
  level = 0.95,
  na.action = stats::na.omit,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness"),
  ...
)

Arguments

Details

The function produces a moving average smoother of timeseries with order order and uses it as base for model fitting and prediction. If model="arima", an arima model is used and automatically fitted using the auto.arima function. If model="ets", the function fits an [forecast]ets model (if timeseries is non-seasonal or the seasonal period is 12 or less) or stlf model (if the seasonal period is 13 or more).

For producing the prediction of the next h consecutive values of the provided univariate time series, the function mas.rev is used.

If order is NULL, it is automatically selected. For that, a set with candidate models constructed for moving average smoothers of orders from minorder to maxorder is generated. The default value of maxorder is set based on code from the sma function of smooth package. The value option of order which generate the best ranked candidate model acoording to the criteria in rank.by is selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate models are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the candidate models are fitted and fitness criteria are calculated based on all observations in timeseries.

If rank.by is set as "errors" or "fitness", the candidate models are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate models. The rank.position.sum criterion is calculated as the sum of the rank positions of a model (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestEMD, fittestWavelet

Examples

data(CATS)

fMAS <- fittestMAS(CATS[,1],h=20,model="arima")

#automatically selected order of moving average
mas.order <- fMAS$order

Description

The function predicts and returns the next n consecutive values of a univariate time series using the best evaluated automatically fitted polynomial regression model. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.

Usage

fittestPolyR(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  order = NULL,
  minorder = 0,
  maxorder = 5,
  raw = FALSE,
  na.action = stats::na.omit,
  level = 0.95,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness")
)

Arguments

Details

A set with candidate polynomial regression models of order order is generated with help from the dredge function from the MuMIn package. The candidate models are ranked acoording to the criteria in rank.by and the best ranked model is returned by the function.

If order is NULL, it is automatically selected. For that, the candidate polynomial regression models generated receive orders from minorder to maxorder. The value option of order which generate the best ranked candidate polynomial regression model acoording to the criteria in rank.by is selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate models are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the candidate models are fitted and fitness criteria are calculated based on all observations in timeseries.

If rank.by is set as "errors" or "fitness", the candidate models are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate models. The rank.position.sum criterion is calculated as the sum of the rank positions of a model (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestPolyRKF, fittestLM

Examples

data(CATS,CATS.cont)
fPolyR <- fittestPolyR(CATS[,3],CATS.cont[,3])
#predicted values
pred <- fPolyR$pred

#plotting the time series data
plot(c(CATS[,3],CATS.cont[,3]),type='o',lwd=2,xlim=c(960,1000),ylim=c(-100,300),
xlab="Time",ylab="PR")
#plotting predicted values
lines(ts(pred$mean,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(pred$lower,start=981),lwd=2,col='light blue')
lines(ts(pred$upper,start=981),lwd=2,col='light blue')

Description

The function predicts and returns the next n consecutive values of a univariate time series using the best evaluated polynomial regression model automatically fitted with Kalman filter. It also evaluates the fitness of the produced model, using AICc, AIC, BIC and logLik criteria, and its prediction accuracy, using the MSE, NMSE, MAPE, sMAPE and maximal error accuracy measures.

Usage

fittestPolyRKF(
  timeseries,
  timeseries.test = NULL,
  h = NULL,
  na.action = stats::na.omit,
  level = 0.9,
  order = NULL,
  minorder = 0,
  maxorder = 5,
  initQ = NULL,
  filtered = TRUE,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness")
)

Arguments

Details

The polynomial regression model produced and returned by the function is generated and represented as state space model (SSModel) based on code from the dlmodeler package. See dlmodeler.polynomial. The model is optimized using the Kalman filter and functions of the KFAS package (see fitSSM).

If order is NULL, it is automatically selected. For that, a set of candidate polynomial regression state space models of orders from minorder to maxorder is generated and evaluated. Also, if initQ is NULL, it is automatically set as either log(stats::var(timeseries)) or 0. For that, candidate models receive different initial parameterization of initQ during the model optimization process. The value options of order and/or initQ which generate the best ranked candidate polynomial regression model acoording to the criteria in rank.by are selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate models are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the candidate models are fitted and fitness criteria are calculated based on all observations in timeseries.

If rank.by is set as "errors" or "fitness", the candidate models are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate models. The rank.position.sum criterion is calculated as the sum of the rank positions of a model (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

fittestPolyR, fittestLM ~

Examples

data(CATS,CATS.cont)
fPolyRKF <- fittestPolyRKF(CATS[,1],CATS.cont[,1])
#predicted values
pred <- fPolyRKF$pred

#extracting Kalman filtered and smoothed time series from the best fitted model
fs <- KFAS::KFS(fPolyRKF$model,filtering=c("state","mean"),smoothing=c("state","mean"))
f <- fitted(fs, filtered = TRUE) #Kalman filtered time  series
s <- fitted(fs) #Kalman smoothed time  series
#plotting the time series data
plot(c(CATS[,1],CATS.cont[,1]),type='o',lwd=2,xlim=c(960,1000),ylim=c(0,200),
 xlab="Time",ylab="PRKF")
#plotting the Kalman filtered time series
lines(f,col='red',lty=2,lwd=2)
#plotting the Kalman smoothed time series
lines(s,col='green',lty=2,lwd=2)
#plotting predicted values
lines(ts(pred$mean,start=981),lwd=2,col='blue')
#plotting prediction intervals
lines(ts(pred$lower,start=981),lwd=2,col='light blue')
lines(ts(pred$upper,start=981),lwd=2,col='light blue')

Description

The function automatically applies a maximal overlap discrete wavelet transform to a provided univariate time series. The resulting components of the decomposed series are used as base for predicting and returning the next n consecutive values of the provided univariate time series using also automatically fitted models (ets or arima). It also evaluates fitness and prediction accuracy of the produced models.

Usage

fittestWavelet(
  timeseries,
  timeseries.test = NULL,
  h = 1,
  filters = c("haar", "d4", "la8", "bl14", "c6"),
  n.levels = NULL,
  maxlevel = NULL,
  boundary = "periodic",
  model = c("ets", "arima"),
  conf.level = 0.95,
  na.action = stats::na.omit,
  rank.by = c("MSE", "NMSE", "MAPE", "sMAPE", "MaxError", "AIC", "AICc", "BIC",
    "logLik", "errors", "fitness"),
  ...
)

Arguments

Details

The function produces a maximal overlap discrete wavelet transform of timeseries. It performs a time series decomposition of level n.levels using the wavelet filter filters. See the modwt function. Each component series resulting from the decomposition (n.levels wavelet coefficients series and n.levels scaling coefficients series) is separately used as base for model fitting and prediction. If model="arima", arima models are used and automatically fitted using the auto.arima function. If model="ets", the function fits [forecast]ets models. The set of predictions for all component series are then reversed transformed in order to produce the next h consecutive values of the provided univariate time series in timeseries. See the imodwt function.

If length(filters)>1 or filters=NULL, it is automatically selected. For that, a set of candidate wavelet decompositions with different options of filters is generated and used for model fitting and prediction. Also, if n.levels is NULL, it is automatically set as a value within the interval 1:maxlevel (if maxlevel is not provided, it is calculated according to the wavelet filter based on code from modwt). For that, candidate decompositions are specified with different levels. The options of filter and/or level of decomposition which generate the best ranked model fitness/predictions acoording to the criteria in rank.by are selected.

The ranking criteria in rank.by may be set as a prediction error measure (such as MSE, NMSE, MAPE, sMAPE or MAXError), or as a fitness criteria (such as AIC, AICc, BIC or logLik). In the former case, the candidate wavelet decompositions are used for time series prediction and the error measures are calculated by means of a cross-validation process. In the latter case, the component series of the candidate decompositions are modeled and model fitness criteria are calculated based on all observations in timeseries. In particular, the fitness criteria calculated for ranking the candidate decomposition correspond to the model produced for the n.levelsth scaling coefficients series as it can be considered the main component of a decomposition of level n.levels (Conejo,2005).

If rank.by is set as "errors" or "fitness", the candidate decompositions are ranked by all the mentioned prediction error measures or fitness criteria, respectively. The wheight of the ranking criteria is equally distributed. In this case, a rank.position.sum criterion is produced for ranking the candidate decompositions. The rank.position.sum criterion is calculated as the sum of the rank positions of a decomposition (1 = 1st position = better ranked model, 2 = 2nd position, etc.) on each calculated ranking criteria.

Value

A list with components:

Author(s)

Rebecca Pontes Salles

References

A. J. Conejo, M. A. Plazas, R. Espinola, A. B. Molina, Day-ahead electricity price forecasting using the wavelet transform and ARIMA models, IEEE Transactions on Power Systems 20 (2005) 1035-1042.

T. Joo, S. Kim, Time series forecasting based on wavelet filtering, Expert Systems with Applications 42 (2015) 3868-3874.

C. Stolojescu, I. Railean, S. M. P. Lenca, A. Isar, A wavelet based prediction method for time series. In Proceedings of the 2010 International Conference Stochastic Modeling Techniques and Data Analysis, Chania, Greece (pp. 8-11) (2010).

See Also

fittestEMD, fittestMAS ~

Examples

data(CATS)

fW <- fittestWavelet(CATS[,1],h=20,model="arima")

#plot wavelet transform/decomposition
plot(fW$WT)

Description

The Institute of Applied Economic Research of Brazil (Ipea) (Ipea, 2017) is a public institution of Brazil that provides support to the federal government with regard to public policies: fiscal, social, and economic. Ipea provides public datasets derived from real economic and financial data of the world.

Usage

ipeadata_d

Format

The ipeadata_d dataset contains 12 time series of 901 to 8154 observations. The 12 time series are provided as the following variables of a data frame.

GM366_IBVSP366

Stock Index: Sao Paulo Stock Exchange - closed - BM&FBovespa.

GM366_ERC366

Exchange rate - R$ / US$ - commercial - purchase - mean - R$ - Bacen Outras/SGS.

GM366_EREURO366

Euro area - exchange rate - euro / US$ - mean - Euro - Bacen Outras/SGS.

GM366_ERPV366

Exchange rate - R$ / US$ - parallel - selling - mean - R$ - Economic value.

GM366_ERV366

Exchange rate - R$ / US$ - commercial - selling - mean - R$ - Bacen Outras/SGS.

GM366_TJOVER366

Interest Rate: Over / Selic - (% p.a.) - Bacen Outras/SGS.

GM366_TJTR366

Interest rate - TR - (% p.m.) - Bacen Outras/SGS.

SECEX366_MVTOT366

Imports - weekly mean - US$ - MDIC/Secex.

SECEX366_XVTOT366

Exports - weekly mean - US$ - MDIC/Secex.

JPM366_EMBI366

EMBI + Risco-Brasil - JP Morgan.

BM366_TJOVER366

Interest rate - Selic - fixed by Copom - (% p.a.) - Bacen/Boletim/M. Finan..

GM366_TJOVERV366

Interest Rate: Over / Selic - Ipea.

Details

The ipeadata_d dataset is provided by Ipea. It comprehends the most requested time series collected in daily rates. The ipeadata_d dataset comprehend observations of exchange rates (R$/US$), exports/imports prices, interest rates, and more, measured from 1962 to September of 2017.

The data had missing data removed by the function na.omit.

ipeadata_d.cont provide 30 points beyond the end of the time series in ipeadata_d. Intended for use as testing set.

Source

Ipea, Ipeadata. Macroeconomic and regional data, Technical Report, http://www.ipeadata.gov.br, 2017. The "Most request series" section and filtered by "Frequency" equal to "Daily".

References

Ipea, Ipeadata. Macroeconomic and regional data, Technical Report, http://www.ipeadata.gov.br, 2017.

See Also

ipeadata_m ~

Examples

data(ipeadata_d)
str(ipeadata_d)
plot(ts(ipeadata_d[1]))

Description

The Institute of Applied Economic Research of Brazil (Ipea) (Ipea, 2017) is a public institution of Brazil that provides support to the federal government with regard to public policies: fiscal, social, and economic. Ipea provides public datasets derived from real economic and financial data of the world.

Usage

ipeadata_m

Format

The ipeadata_m dataset contains 23 time series of 156 to 1019 observations. The 23 time series are provided as the following variables of a data frame.

BM12_ERC12

Exchange rate - Brazilian real (R$) / US dollar (US$) - purchase - average - R$ - Bacen / Boletim / BP.

BM12_ERV12

Exchange rate - Brazilian real (R$) / US dollar (US$) - selling - average - R$ - Bacen / Boletim / BP.

IGP12_IGPDI12

IGP-DI - general price index domestic supply (aug 1994 = 100) - FGV/Conj. Econ. - IGP.

FUNCEX12_MDPT12

Imports - prices - index (average 2006 = 100) - Funcex.

FUNCEX12_XPT12

Exports - prices - index (average 2006 = 100) - Funcex.

PRECOS12_INPC12

INPC - national consumer price index (dec 1993 = 100) - IBGE/SNIPC.

PRECOS12_INPCBR12

INPC - national consumer price index - growth rate - (% p.m.) - IBGE/SNIPC.

PRECOS12_IPCA12

IPCA - extended consumer price index (dec 1993 = 100) - IBGE/SNIPC.

SEADE12_TDAGSP12

Unemployment rate - open - RMSP - (%) - Seade/PED.

SEADE12_TDOTSP12

Unemployment rate - hidden - RMSP - (%) - Seade/PED.

SEADE12_TDOPSP12

Unemployment rate - hidden - precarious - RMSP - (%) - Seade/PED.

GAC12_SALMINRE12

Real minimum wage - R$ - Ipea.

IGP12_IGPM12

IGP-M - general price index at market prices (aug 1994 = 100) - FGV/Conj. Econ. - IGP.

PRECOS12_IPCAG12

IPCA - extended consumer price index - growth rate - (% p.m.) - IBGE/SNIPC.

IGP12_IGPDIG12

IGP-DI - general price index domestic supply - growth rate - (% p.m.) - FGV/Conj. Econ. - IGP.

IGP12_IGPMG12

IGP-M - general price index at market prices - growth rate - (% p.m.) - FGV/Conj. Econ. - IGP.

IGP12_IGPOGG12

IGP-OG - general price index overall supply - growth rate - (% p.m.) - FGV/Conj. Econ. - IGP.

PRECOS12_IPCA15G12

IPCA 15 - extended consumer price index - growth rate - (% p.m.) - IBGE/SNIPC.

[BM12_PIB12

GDP - R$ - Bacen / Boletim / Ativ. Ec..

MTE12_SALMIN12

Minimum wage - R$ - MTE.

BM12_TJOVER12

Interest rate - Overnight/Selic - (% p.m.) - Bacen/Boletim/M. Finan..

SEADE12_TDTGSP12

Unemployment rate - Sao Paulo - (%) - Seade/PED.

PMEN12_TD12

Unemployment rate - reference: 30 days - RMs - (%) - IBGE/PME - obs: PME closed in 2016-mar.

Details

The ipeadata_m dataset is provided by Ipea. It comprehends the most requested time series collected in monthly rates. The ipeadata_m dataset comprehend observations of exchange rates (R$/US$), exports/imports prices, interest rates, minimum wage, unemployment rate, and more, measured from 1930 to September of 2017.

The data had missing data removed by the function na.omit.

ipeadata_m.cont provide 12 points beyond the end of the time series in ipeadata_m. Intended for use as testing set.

Source

Ipea, Ipeadata. Macroeconomic and regional data, Technical Report, http://www.ipeadata.gov.br, 2017. The "Most request series" section and filtered by "Frequency" equal to "Monthly".

References

Ipea, Ipeadata. Macroeconomic and regional data, Technical Report, http://www.ipeadata.gov.br, 2017.

See Also

ipeadata_d ~

Examples

data(ipeadata_m)
str(ipeadata_m)
plot(ts(ipeadata_m[1]))

Description

The LogT() function returns a logarithmic transformation of the provided time series. A natural log is returned by default. LogT.rev() reverses the transformation.

Usage

LogT(x, base = exp(1))

LogT.rev(x, base = exp(1))

Arguments

Value

A vector of the same length as x containing the transformed values.

Author(s)

Rebecca Pontes Salles

References

R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, New York, NY, 4 edition, 2017.

See Also

Other transformation methods: Diff(), WaveletT(), emd(), mas(), mlm_io(), outliers_bp(), pct(), train_test_subset()

Examples

data(NN5.A)
LogT(NN5.A[,10])

Description

Constructors for the processing class representing a time series processing method based on a particular time series transformation.

Usage

LT(base = exp(1))

BoxCoxT(lambda = NULL, prep_par = NULL, postp_par = NULL, ...)

WT(
  level = NULL,
  filter = NULL,
  boundary = "periodic",
  prep_par = NULL,
  postp_par = NULL,
  ...
)

subsetting(train_perc = 0.8, test_len = NULL)

SW(window_len = NULL)

NAS(na.action = stats::na.omit, prep_par = NULL)

MinMax(min = NULL, max = NULL, byRow = TRUE)

AN(min = NULL, max = NULL, byRow = TRUE, outlier.rm = TRUE, alpha = 1.5)

DIFF(
  lag = NULL,
  differences = NULL,
  type = "simple",
  postp_par = list(addinit = FALSE)
)

MAS(order = NULL, prep_par = NULL, postp_par = list(addinit = FALSE))

PCT(postp_par = NULL)

EMD(num_imfs = 0, meaningfulImfs = NULL, prep_par = NULL)

Arguments

Value

An object of class processing.

Mapping-based nonstationary transformation methods

LT: Logarithmic transform. prep_func set as LogT and postp_func set as LogT.rev.

BoxCoxT: Box-Cox transform. prep_func set as BCT and postp_func set as BCT.rev.

DIFF: Differencing. prep_func set as Diff and postp_func set as Diff.rev.

MAS: Moving average smoothing. prep_func set as mas and postp_func set as mas.rev.

PCT: Percentage change transform. prep_func set as pct and postp_func set as pct.rev.

Splitting-based nonstationary transformation methods

WT: Wavelet transform. prep_func set as WaveletT and postp_func set as WaveletT.rev.

EMD: Empirical mode decomposition. prep_func set as emd and postp_func set as emd.rev.

Data subsetting methods

subsetting: Subsetting data into training and testing sets. prep_func set as train_test_subset and postp_func set to NULL.

SW: Sliding windows. prep_func set as sw and postp_func set to NULL.

Methods for handling missing values

NAS: Missing values treatment. prep_func set as parameter na.action and postp_func set to NULL.

Normalization methods

MinMax: MinMax normalization. prep_func set as minmax and postp_func set to minmax.rev.

AN: Adaptive normalization. prep_func set as an and postp_func set to an.rev.

Author(s)

Rebecca Pontes Salles

References

R. Salles, K. Belloze, F. Porto, P.H. Gonzalez, and E. Ogasawara. Nonstationary time series transformation methods: An experimental review. Knowledge-Based Systems, 164:274-291, 2019.

See Also

Other constructors: ARIMA(), MSE_eval(), evaluating(), modeling(), processing(), tspred()

Description

The function calculates the MAPE error between actual and predicted values.

Usage

MAPE(actual, prediction)

Arguments

Value

A numeric value of the MAPE error of prediction.

Author(s)

Rebecca Pontes Salles

References

Z. Chen and Y. Yang, 2004, Assessing forecast accuracy measures, Preprint Series, n. 2004-2010, p. 2004-10.

See Also

sMAPE, MSE, NMSE, MAXError

Examples

data(SantaFe.A,SantaFe.A.cont)
pred <- marimapred(SantaFe.A,n.ahead=100)
MAPE(SantaFe.A.cont[,1], pred)

Description

The function returns the parameters of a set of automatically fitted ARIMA models, including non-seasonal and seasonal orders and drift. Based on multiple application of the arimapar function.

Usage

marimapar(timeseries, na.action = stats::na.omit, xreg = NULL)

Arguments

Details

See the arimapar function.

Value

A list of numeric vectors, each one giving the number of AR, MA, seasonal AR and seasonal MA coefficients, plus the period and the number of non-seasonal and seasonal differences of the automatically fitted ARIMA models. It is also presented the value of the fitted drift constants.

References

See the arimapar function.

See Also

arimapar, arimapred, marimapred

Description

The function predicts and returns the next n consecutive values of a set of time series using automatically fitted ARIMA models. Based on multiple application of the arimapred function.

Usage

marimapred(
  TimeSeries,
  TimeSeriesCont = NULL,
  n.ahead = NULL,
  na.action = stats::na.omit,
  xreg = NULL,
  newxreg = NULL,
  se.fit = FALSE,
  plot = FALSE,
  range.p = 0.2,
  ylab = NULL,
  xlab = NULL,
  main = NULL
)

Arguments

Details

See the arimapred function.

Value

A vector of time series of predictions, if the number of consecutive values predicted of each time series in TimeSeries is the same, otherwise a list of time series of predictions.

If se.fit is TRUE, a vector of lists, each one with the components pred, the predictions, and se, the estimated standard errors. Both components are time series. See the predict.Arima function in the stats package and the function arimapred.

Author(s)

Rebecca Pontes Salles

References

See the arimapred function. the literature/web site here ~

See Also

arimapred ~

Examples

data(SantaFe.A,SantaFe.A.cont)
marimapred(SantaFe.A,SantaFe.A.cont)

Description

The mas() function returns a simple moving average smoother of the provided time series. mas.rev() reverses the transformation(smoothing) process.

Usage

mas(x, order, ...)

mas.rev(xm, xi, order, addinit = TRUE)

Arguments

Details

The moving average smoother transformation is given by

$(1/k) * ( x[t] + x[t+1] + ... + x[t+k-1] )$

where k=order, t assume values in the range 1:(n-k+1), and n=length(x). See also the ma of the forecast package.

Value

Numerical time series of length length(x)-order+1 containing the simple moving average smoothed values.

Author(s)

Rebecca Pontes Salles

References

R.H. Shumway and D.S. Stoffer, 2010, Time Series Analysis and Its Applications: With R Examples. 3rd ed. 2011 edition ed. New York, Springer.

See Also

Other transformation methods: Diff(), LogT(), WaveletT(), emd(), mlm_io(), outliers_bp(), pct(), train_test_subset()

Examples

data(CATS)

m <- mas(CATS[,1],order=5)

#automatically select order of moving average
m <- mas(CATS[,1],order=NULL,h=20)


x <- mas.rev(m, attributes(m)$xi, attributes(m)$order)

all(round(x,4)==round(CATS[,1],4))

Description

The function calculates the maximal error between actual and predicted values.

Usage

MAXError(actual, prediction)

Arguments

Value

A numeric value of the maximal error of prediction.

Author(s)

Rebecca Pontes Salles

See Also

sMAPE, MAPE

Examples

data(SantaFe.A,SantaFe.A.cont)
pred <- marimapred(SantaFe.A,n.ahead=100)
MAXError(SantaFe.A.cont[,1], pred)

Description

The minmax() function normalizes data of the provided time series to bring values into the range [0,1]. minmax.rev() reverses the normalization.

Usage

minmax(data, max = NULL, min = NULL, byRow = FALSE)

minmax.rev(data, max, min)

Arguments

Details

Ranging is done by using:

$X' = \frac{(x - x_{min})}{(x_{max} - x_{min})}$

.

Value

data normalized between 0 and 1. If byRow is TRUE, the function returns data normalized by rows (sliding windows). max and min are returned as attributes.

Author(s)

Rebecca Pontes Salles

References

R.J. Hyndman and G. Athanasopoulos, 2013, Forecasting: principles and practice. OTexts.

E. Ogasawara, L. C. Martinez, D. De Oliveira, G. Zimbrao, G. L. Pappa, and M. Mattoso, 2010, Adaptive Normalization: A novel data normalization approach for non-stationary time series, Proceedings of the International Joint Conference on Neural Networks.

See Also

Other normalization methods: an()

Examples

data(CATS)
d <- minmax(CATS[,1])
x <- minmax.rev(d, max = attributes(d)$max, min = attributes(d)$min)
all(round(x,4)==round(CATS[,1],4))

d <- minmax(sw(CATS[,1],5), byRow = TRUE)
x <- minmax.rev(d, max = attributes(d)$max, min = attributes(d)$min)
all(round(x,4)==round(sw(CATS[,1],5),4))

Description

Constructor for the modeling class representing a time series modeling and prediction method based on a particular model. The modeling class has two specialized subclasses linear and MLM reagarding linear models and machine learning based models, respectively.

Usage

modeling(
  train_func,
  train_par = NULL,
  pred_func = NULL,
  pred_par = NULL,
  ...,
  subclass = NULL
)

MLM(
  train_func,
  train_par = NULL,
  pred_func = NULL,
  pred_par = NULL,
  sw = NULL,
  proc = NULL,
  ...,
  subclass = NULL
)

linear(
  train_func,
  train_par = NULL,
  pred_func = NULL,
  pred_par = NULL,
  ...,
  subclass = NULL
)

Arguments

Value

An object of class modeling.

Author(s)

Rebecca Pontes Salles

See Also

Other constructors: ARIMA(), LT(), MSE_eval(), evaluating(), processing(), tspred()

Examples

forecast_mean <- function(...){
   do.call(forecast::forecast,c(list(...)))$mean
}
  
l <- linear(train_func = forecast::auto.arima, pred_func = forecast_mean,
            method="ARIMA model", subclass="ARIMA")
summary(l)

m <- MLM(train_func = nnet::nnet, train_par=list(size=5),
      pred_func = predict, sw=SW(window_len = 6), proc=list(MM=MinMax()),
      method="Artificial Neural Network model", subclass="NNET")
summary(m)

Description

The function calculates the MSE error between actual and predicted values.

Usage

MSE(actual, prediction)

Arguments

Value

A numeric value of the MSE error of prediction.

Author(s)

Rebecca Pontes Salles

References

Z. Chen and Y. Yang, 2004, Assessing forecast accuracy measures, Preprint Series, n. 2004-2010, p. 2004-10.

See Also

NMSE,MAPE,sMAPE, MAXError

Examples

data(SantaFe.A,SantaFe.A.cont)
pred <- marimapred(SantaFe.A,n.ahead=100)
MSE(SantaFe.A.cont[,1], pred)

Description

Constructors for the evaluating class representing a time series prediction or modeling fitness quality evaluation based on particular metrics.

Usage