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I'm trying to fit a GLM-model based on negative binomial to a time series (I have data for the number of forrest fires in Sweden per every 3 months over a 20 year period) and wonder if I need to check for stationarity? If so, how would I do that?

I am using a package called "tscount" and my fitted model looks as follows: Y = $\beta_0$ + $\beta_1$$Y(t-2)$ + $\beta_3$Temperature_celsius + $\beta_4$Rain_mm + $\beta_5$Dummy(Vinter) + $\beta_6$Dummy(Spring) + $\beta_7$Dummy(Summer).

After checking the residuals I think the model looks okay, I have no autocorrelation etc.

Thanks!

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