I want to fit a fairly "standard" Poisson model, but with an autoregressive term.

$N_i sim mathrm{Pois}( lambda_i E_i)$

with $log lambda_i = X_i beta + delta$

$delta sim AR(1)$

$X_i$ is a vector of covariates.

$beta$ are my coefficients.

$delta$ is an autoregressive term.

$E_i$ is the size of population at time t.

The idea is that the count at time step $t$ is partially dependent on the count at time step $t-1$.

Ideally, I'd like to find some R package to fit this.

Any suggestions?

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#### Best Answer

I think you are looking for the model in Brandt et al. (2000) there called PEWMA, after the forecast function. R code to fit it is available here.

The paper also has some general discussion of possible conditionally Poisson AR models. Fro more of that, chapter 7 of Cameron and Trivedi (1998) is useful.

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