How to include a dummy interaction term in an ARIMA model? Can we use the dependent variable (in this case, say the log return of an asset price at time $t$) to multiply with the dummy variable as an interaction term?
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An ARIMA model with an interaction term would not be called ARIMA anymore, but certainly you can formulate a model of the kind. E.g. starting from ARMA(1,1) and excluding the intercept for simplicity $$ y_t=\varphi_1 y_{t-1}+u_t+\theta_1 u_{t-1} $$ you could obtain $$ y_t=\varphi_1 y_{t-1}\color{blue}{+\gamma_1 d_1y_{t-1}}+u_t+\theta_1 u_{t-1} $$ where $d_1$ is the dummy variable. The dummy interacts with a lag of the dependent variable. I am not sure if it would make any sense to interact it with the (nonlagged) dependent variable, though. (If you explain us what you are trying to achieve, perhaps we can elaborate further.)
answered Mar 25 at 12:33
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$\begingroup$ Thanks, @Richard Hardy. However, if the model is ARMA(3,2), how do I create the interaction term? Basically, I am trying to establish if a particular exogenous variable has any effect on an ARMA process. $\endgroup$ Mar 26 at 7:22
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$\begingroup$ @JyotiNair, what do you mean by how? Conceptually, $d_1y_{t-1}$ is a product of $d_1$ and $y_{t-1}$. If you are asking for code (which is off topic), check out
TSA::arimax,sysid::armaxormarima::marima. I have not used any of these myself, but Google search suggests they might do what you want. $\endgroup$ Mar 26 at 13:48