I would like to estimate the parameters of a vector autogressive process VARX(p,q) with n endogenous variables y and m exogenous variables x: $$ y_t = v + B_1 y_{t-1} + ... + B_p y_{t-p} + \theta_0 x_t + ... + \theta_q x_{t-q} + e_t $$ where $$e_t \sim N(0,\Sigma)$$

The Mathematica functions TimeSeriesModelFit[data,mspec] and EstimatedProcess[data,proc] only accept ARMA, ARIMA and GARCH processes without exogenous variables.

What would be the best approach to estimate the coefficients $B_i$ and $\theta_i$? We could transform the system as $Y=B \cdot Z + U$ where $B = [v\space B_1\space B_2 ... B_p\space \theta_0\space \theta_1 ... \theta_q]$ and solve it by OLS. Is there a way to use the existing functions TimeSeriesModelFit and EstimatedProcess for processes with exogenous variables?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.