mrf_regression_one_step_forecast {mrf}

One Step Forecast with Regression

Description

This function creates a one step forecast using an autoregression method. The ccps parameter controls the number of coefficients chosen for each wavelet and smooth part level individually.

Usage

mrf_regression_one_step_forecast(UnivariateData, CoefficientCombination,
Aggregation, 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.

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

forecast

Numerical value with one step forecast

Author(s)

Quirin Stier

References

Aussem, A., Campbell, J., and Murtagh, F. Waveletbased Feature Extraction and Decomposition Strategies for Financial Forecasting. International Journal of Computational Intelligence in Finance, 6,5-12, 1998.

Renaud, O., Starck, J.-L., and Murtagh, F. Prediction based on a Multiscale De- composition. International Journal of Wavelets, Multiresolution and Information Processing, 1(2):217-232. doi:10.1142/S0219691303000153, 2003.

Murtagh, F., Starck, J.-L., and Renaud, O. On Neuro-Wavelet Modeling. Decision Support Systems, 37(4):475-484. doi:10.1016/S0167-9236(03)00092-7, 2004.

Renaud, O., Starck, J.-L., and Murtagh, F. Wavelet-based combined Signal Filter- ing and Prediction. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 35(6):1241-1251. doi:10.1109/TSMCB.2005.850182, 2005.

Examples

data(AirPassengers)
len_data = length(as.vector(array(AirPassengers)))
UnivariateData = as.vector(AirPassengers)[1:(len_data-1)]
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
forecast = mrf_regression_one_step_forecast(UnivariateData,
                                            CoefficientCombination,
                                            Aggregation)
true_value = array(AirPassengers)[len_data]
error = true_value - forecast