wavelet_prediction_equation {mrf}

One Step Forecast with Regression

Description

This function delivers the required wavelet and smooth coefficients from the decomposition based on a prediction scheme.

Usage

wavelet_prediction_equation(WaveletCoefficients, SmoothCoefficients,
CoefficientCombination, Aggregation)

Arguments

WaveletCoefficients

[Scales, n] Matrix with 'Scales' many wavelet scales row-wise with n columns corresponding to the time domain of a time series.

SmoothCoefficients

[Scales, n] Matrix with 'Scales' many smooth approximation scales row-wise with n columns corresponding to the time domain of a 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.

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.

Value

future_point

Numerical value carrying 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(array(AirPassengers))
CoefficientCombination = c(1,1,1)
Aggregation = c(2,4)
UnivariateData = as.vector(AirPassengers)
# Decomposition
dec_res <- wavelet_decomposition(UnivariateData, Aggregation)
# Training
trs_res <- wavelet_training_equations(UnivariateData,
                                      dec_res$WaveletCoefficients,
                                      dec_res$SmoothCoefficients,
                                      dec_res$Scales,
                                      CoefficientCombination, Aggregation)
arr_future_points = trs_res$points_in_future
matrix = trs_res$lsmatrix
# Optimization method
weights = mrf_regression_lsm_optimization(arr_future_points, matrix)
# Forecast
scheme = wavelet_prediction_equation(dec_res$WaveletCoefficients,
dec_res$SmoothCoefficients, CoefficientCombination, Aggregation)
forecast = weights