VARMA Time Series Model Analysis Using Discrete Wavelet Transformation Coefficients for Coiflets Wavelet

Abstract
Multivariate time series models (Vector Autoregressive Moving Average (VARMA) models) are complex models and some traditional methods, such as optimization functions, are used to estimate the model parameters, but they are far from their true values. Therefore, approximate VAR models are usually used to get results closer to the true values of the autoregressive parameters. This article proposes to improve the performance of approximate VAR models through wavelet analysis, specifically Coiflets wavelet. The proposed method is based on the discrete wavelet transform (Coiflets wavelet) which divides the time series data into two parts the first part represents the approximation coefficients (low-pass filter), while the second part represents the detail coefficients (high-pass filter). Maximum likelihood estimation is used to estimate the parameters of the two approximate VAR models through which approximation and detail parameters are predicted. Maximum likelihood estimation is used to estimate the parameters of the two approximate VAR models through which approximation and detail coefficients are predicted. The inverse discrete wavelet transforms of the estimated coefficients of the Coiflets wavelet at orders (1, 2, ...,5) are used to obtain filtered data, which will be used to estimate the parameters of the approximate VAR models. The efficiency and accuracy of the estimated parameters using the classical and proposed methods were compared through simulation and real data based on the mean square error (MSE), Akaike Information Criterion (AIC),and Bayesian Information Criterion (BIC) . The approximate VAR models of the proposed method were more efficient than the classical method.