mrf_rolling_forecasting_origin {mrf}

Rolling forecasting origin for Multiresolution Forecasts

Description

This function computes a rolling forecasting origin for one- or multi-step forecasts with a specific method based on the manuscript [Stier et al., 2021] which is currently in press. Multi-step forecasts are computed recursively with the one step forecast method.

Usage

mrf_rolling_forecasting_origin(UnivariateData, Aggregation,
CoefficientCombination=NULL, Horizon = 2, Window = 3, Method = "r",
NumClusters = 1,
Threshold="hard", Lambda=0.05)

Arguments

UnivariateData

[1:n] Numerical vector with n values.

CoefficientCombination

[1:Scales+1] Numerical vector with numbers which are associated with wavelet levels. The last number is associated with the smooth level. Each number determines the number of coefficient used per level. The selection follows a specific scheme.

Aggregation

[1:Scales] Numerical vector carrying numbers whose index is associated with the wavelet level. The numbers indicate the number of time in points used for aggregation from the original time series.

Horizon

Number indicating horizon for forecast from 1 to horizon.

Window

Number indicating how many points are used for cross validation.

Method

String indicating which method to use. Available methods: 'r' = Autoregression. 'nn' = Neural Network. 'elm' = Extreme Learning Machine. 'nnetar' = forecast::nnetar. Default: Method="r".

NumClusters

Number of clusters used for parallel computing.

Threshold

Character indicating if Thresholding is done on the wavelet decomposition or not. Default: Threshold="hard". Possible entries: Threshold="hard" for hard thresholding. Threshold="soft" for soft thresholding. Any other input indicates no thresholding.

Lambda

Numeric value indicating the threshold for computing a hard or soft threshold on the wavelet decomposition.

Details

Thus, h-step forecast for h = 1,..., horizon for window_size many steps can be computed. The forecasting method can be an autoregression or a neural network (multilayer perceptron). The CoefficientCombination parameter controls the number of coefficients chosen for each wavelet and smooth part level individually. The NumClusters parameter determines the number of cluster used for parallel computation. NumClusters = 1 performs a non parallel version. NumClusters is constrained by the maximum number of clusters available minus one to prevent the machine to be overchallenged.

Value

List of

Error

[1:Window,1:Horizon] Numerical Matrix with 'Window' many row entries indicating one time point with 'Horizon' many forecast errors.

Forecast

[1:Window,1:Horizon] Numerical Matrix with 'Window' many row entries indicating one time point with 'Horizon' many forecasts.

Author(s)

Quirin Stier

References

[Stier et al., 2021] Stier, Q.,Gehlert, T. and Thrun, M. C.: Multiresolution Forecasting for Industrial Applications, Processess, 2021.

Examples

data(AirPassengers)
UnivariateData=as.vector(array(AirPassengers))
res = mrf_rolling_forecasting_origin(UnivariateData,
                                 CoefficientCombination = c(10,10,10),
                                 Aggregation = c(2,4),
                                 Horizon = 2, Window = 3, Method = "r",
                                 NumClusters = 1)
Error = res$Error
Forecast = res$Forecast