mrf_regression_lsm_optimization {mrf}

Least Square Method for Regression

Description

This function computes the weights for the autoregression depending on the given wavelet decomposition. It uses ordinary least square method for optimizing a linear equation system.

Usage

mrf_regression_lsm_optimization(points_in_future, lsmatrix)

Arguments

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.

Value

List of

weights

Array of weights carrying the solution for a matrix problem, which was solves with ordinary least squares.

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