Analysis of Some Linear Dynamic Systems with Bivariate Wavelets

There are many statistical methods related to the forecasting of time series without any input variables such as autoregressive integrated moving average (ARIMA models). In this research, some linear dynamic systems, represented by ARIMA with exogenous input variables (ARIMAX models) were used to forecast crude oil prices (considered as output variable) for OPEC organization with the help of crude oil production (considered as input variable) depending on the data starting from the period of 1973 until 2018. Using traditional ARIMAX method and proposed method (Bivariate Wavelet Filtering) for the time series data in order to select one of them for forecasting through comparing some measures of accuracy, such as MSE, FPE, and AIC. Then, applying crude oil prices for OPEC using the traditional ARIMAX models and ARIMAX models with applying the bivariate wavelet filtering, especially bivariate Haar wavelet. The main conclusions of the research were that the success of bivariate wavelet filtering in forecasting of crude oil prices using proposed model was more appropriate than traditional models, and the forecasting of crude oil prices using proposed method in 2020 will be fairly less than 2019.