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Basically, my question is similar to Time series dynamic poisson regression, yet I didn't get any clue by its answer.

I'm modeling dengue incidents with GLM (poisson regression; because the response was count data). But the explanatory variables is time-dependent. Let Y(t) as the response in time $t$, $X(i,t)$ be the $i$th explanatory variable (or predictor) in time $t$. $X$ is continuous variable. Let's say we have 2 predictors ($i=2$).

So we can write the model be Y(t)~intercept+Y(t-1)+X(1,t)+X(1,t-2)+X(2,t), how could I estimate its parameters? I have read so many papers (publications) like PEWMA method, PAR, VAR(p), GMM, etc, but still don't understand which is the right method for my problem. Please help immediately, I really wait for your answer, masters!

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  • $\begingroup$ I think you need to clarify this some more. Why do the predictors include $X_{1,t-2}$ rather than $X_{1,t-1}$? $\endgroup$
    – mdewey
    Commented Jun 9, 2019 at 14:43
  • $\begingroup$ Hi @mdewey I really appreciate your comment. To be clear, $ Y_t $ is count data at time t, and I wanna regress it to its explanatory variables $ X_{1,t−t1} $, $ X_{2,t-t2} $ , $ X_{3,t-t3} $, and $ Y_{t-lag} $ as well. t1,t2, and t3 are chosen depending on the cross-correlation between Y and $ X_1 $ , $ X_2 $, and $ X_3 $ respectively. For example, from the cross-correlation between Y and $ X_1 $, we get the high correlation is when $ X_1 $ is lagged 2. so I put the $ X_{1,t-2} $ as the explanatory variable. $\endgroup$
    – Clarice Taylor
    Commented Jun 9, 2019 at 16:31
  • $\begingroup$ That's why, $ Y_t $ ~ $ intercept + Y_{t-1} + X_{1,t} + X_{2,t} + X_{3,t} + X_{1,t-2} + X_{3, t-4} $ because the ACF of $ Y $ shows it has lag 1, and t1 = 2, t2 = 0, and t3 = 4. $\endgroup$
    – Clarice Taylor
    Commented Jun 9, 2019 at 16:34
  • $\begingroup$ Please add that new info as edits to the original post! Few people really read comments ... $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jun 11, 2019 at 15:53

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