mrf_model_selection {mrf}

Model selection for Multiresolution Forecasts

Description

Evaluates the best coefficient combination for a given aggregation scheme based on a rolling forecasting origin based on the manuscript [Stier et al., 2021] which is currently in press.

Usage

mrf_model_selection(UnivariateData, Aggregation, Horizon = 1, Window = 2,
Method = "r", crit = "AIC", itermax = 1, lower_limit = 1, upper_limit = 2,
NumClusters = 1, Threshold="hard", Lambda=0.05)

Arguments

UnivariateData

[1:n] Numerical vector with n values.

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".

crit

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

itermax

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

lower_limit

[1:Scales+1] Numeric vector: Lower limit for coefficients selected for each level.

upper_limit

[1:Scales+1] Numeric vector: Higher limit for coefficients selected for each level.

NumClusters

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

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

The evaluation function (optimization function) is built with a rolling forecasting origin (rolling_window function), which computes a h-step ahead forecast (for h = 1, ..., horizon) for 'Window' many steps. The input space is searched with an evolutionary optimization method. The search is restricted to one fixed aggregation scheme (parameter: 'Aggregation'). The deployed forecast method can be an autoregression or a neural network (multilayer perceptron with one hidden layer).

Value

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. Best combination of coefficients found by the model selection algorithm.

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. Best Aggregation scheme found by the model selection algorithm.

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(entsoe)
UnivariateData = entsoe$value
Aggregation = c(2,4)
res = mrf_model_selection(UnivariateData, Aggregation, Horizon = 1, Window = 2,
Method = "r", crit = "AIC", itermax = 1, lower_limit = 1, upper_limit = 2,
NumClusters = 1)
BestCoefficientCombination = res$CoefficientCombination