mrf_multi_step_forecast {mrf}

Multiresolution Forecast

Description

This function creates a multi step forecast for all horizons from 1 to steps based on the manuscript [Stier et al., 2021] which is currently in press. The deployed forecast method can be an autoregression or a neural network (multilayer perceptron with one hidden layer). Multi step forecasts are computed recursively.

Usage

mrf_multi_step_forecast(UnivariateData, Horizon, Aggregation,
CoefficientCombination=NULL, Method = "r", Threshold="hard", Lambda=0.05)

Arguments

UnivariateData

[1:n] Numerical vector with n values.

Horizon

Number indicating horizon for forecast from 1 to horizon.

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.

Method

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

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.

Value

List of

multistep

[1:Horizon] Numerical vector with forecast of horizon according to its index.

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)
len_data = length(array(AirPassengers))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
# One-step forecast (Multiresolution Forecast)
one_step = mrf_multi_step_forecast(UnivariateData = UnivariateData,
                                    Horizon = 2,
                                    CoefficientCombination = c(1,1,1),
                                    Aggregation = c(2,4),
                                    Method="r")
# Multi-step forecast (Multiresolution Forecast)
# Horizon = 2 => Forecast with Horizon 1 and 2 as vector
multi_step = mrf_multi_step_forecast(UnivariateData = UnivariateData,
                                      Horizon = 2,
                                      CoefficientCombination = c(1,1,1),
                                      Aggregation = c(2,4),
                                      Method="r")