wavelet_training_equations {mrf}

Generic Training Scheme for wavelet framework

Description

This function computes the input for the training phase required for one step forecasts. This computational step is required for all one step forecast procedures contained in this package.

Usage

wavelet_training_equations(UnivariateData, WaveletCoefficients,
SmoothCoefficients, Scales, CoefficientCombination, Aggregation)

Arguments

UnivariateData

[1:n] Numerical vector with n values.

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.

Scales

Number of wavelet levels.

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

points_in_future

n many values of the time series, for which there is an equation from a prediction scheme.

lsmatrix

Matrix carrying predictive equations associated with a specific value of the time series.

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