mrf_train {mrf}

Multiresolution Forecast

Description

Creates a multiresolution forecast model which can be used for forecasting with method 'mrf_forecast' based on the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_train(Data, Horizon=1, Aggregation="auto", Method = "r",
TimeSteps4ModelSelection=2, crit="AIC", InSample=FALSE, Threshold="hard",
Lambda=0.05, NumClusters=1, itermax=1)

Arguments

Data

[1:n] Numerical vector with n values from the training data.

Horizon

Number indicating forecast horizon. Horizon = 1 means one-step forecast and Horizon > 1 means a one-step forecast and all multi-step forecasts from horizon 2 to 'Horizon'. Default: Horizon = 1.

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. Default: Aggregation = "auto".

Method

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

TimeSteps4ModelSelection

Number of time steps of data (newest part) on which a model selection is performed. Default: TimeSteps4ModelSelection = 2.

crit

String with criterion. Available criterions: "AIC" = Akaikes Info. Crit. "MAE" = Mean Abs. Error. "MRE" = Mean Root Error. Default: crit = "AIC".

InSample

Boolean, deciding if in-sample-forecast based on rolling forecasting origin is computed or not. TRUE = Computation of in-sample-forecast. FALSE = No computation. Default: InSample = FALSE

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.

NumClusters

Number of clusters used for parallel computing. Default: NumClusters = 1.

itermax

Number of iterations used in the differential evolutionary optimization algorithm. Default: itermax = 1.

Value

List with

Data

[1:n] Numerical vector with n values from the training data.

Method

String indicating which method to use.

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.

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.

Horizon

Number indicating forecast horizon. Horizon = 1 means one-step forecast and Horizon > 1 means a one-step forecast and all multi-step forecasts from horizon 2 to 'Horizon'.

ModelError

[1:TimeSteps4ModelSelection, 1:Horizon] Numerical matrix with one-/multi-steps in columns and the time steps rowwise. The error is according to the scheme of a rolling forecasting origin. The length depends on the minimum required length for constructing the wavelet model and the length of data. The newer part of the data is used for the model fit truncating the oldest data according to the minimum required length for constructing the model.

ModelMAE

Integer: Mean Absolute Error (MAE) computed for the in-sample-forecast resulting from a rolling forecasting origin.

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)
Data = as.vector(AirPassengers)
len_data = length(Data)
Train = Data[1:(len_data-2)]
Test = Data[(len_data-1):len_data]
# One-step forecast (Multiresolution Forecast)
model = mrf_train(Train)
one_step = mrf_forecast(model, Horizon=1)
Error = one_step$Forecast - Test[1]
# Multi-step forecast (Multiresolution Forecast)
# Horizon = 2 => Forecast with Horizon 1 and 2 as vector
model = mrf_train(Train, Horizon=2)
multi_step = mrf_forecast(model, Horizon=2)
Error = multi_step$Forecast - Test