# Time-dependent Poisson regression

I have a time series that count the number of "type 1" events in a city, for each day. The serie contains a lot of zeros because type 1 events are rare (about 80% of counts are zeros). I'm using a Poisson Model but I don't know how to handle temporal dependencies. For example, I know that there are some other events (let say "type 2") which will increase the probability of an event of type 1 in the current day and/or in the next days. The Poisson parameter is not constant over time.

Do you know a good R package to handle this and a good way to model this situation ?

Thanks

$$\log(\lambda_i) = \alpha t_i + \beta^T x_i .$$
This of course has problems because it assumes a linear relationship between $t_i$ and $\log(\lambda_i)$, and if you feel that certain days have more of an impact than others you might include indicator variables for those days and give them their own coefficients.
• I tried the Poisson Regression using the variable $t_i$ like you said, it helps a little. Then, predicting $x_t$, I added $x_{t-1}, ..., x_{t-7}$ to the model. It helped but the coefficient are not coherent since this is far from monotonous and I expect that $coeff(x_{t-1}) > ... > coeff(x_{t-7})$. Either I'm wrong with this expectation or I need a better model, I don't know. Dec 21, 2015 at 16:39