Reducing the orders of mixed model (ARMA) before and after the wavelet de-noising with application
In this paper, the estimated linear model of Box-Jenkins such as ARMA(p,q) has been compared from time series observations ,before and after wavelet shrinkage filtering (used to solve the problem of contamination (or noise) if it found in the observations) and then reducing the order of the estimated model from filtered observations (with preserving the accuracy and suitability of the estimated models) and re-compared with the estimated linear model of original observations , depending on some statistical criteria , including the Root Mean Square Error (RMSE) , the Mean Absolute Error (MAE) , and the Akaike`s Information Criterion (AIC) ,through taking practical application of time series (the housing permits) by using statistical programs (Statgraphics, NCSS and MATLAB). The results showed the efficiency of wavelet shrinkage filters in solving the noise problem and obtaining the efficient estimated models, and specifically the wavelet shrinkage filter (dmey) with Soft threshold which estimated it's level using the Fixed Form method of filtered observations, and the possibility of obtaining linear models of the filtered observations with lower orders and higher efficiency compared with the corresponding estimated model of original observations.
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