Time series data

[mawais31]

Dear all,
I have 3 years daily accidents data and want see how much weather and lagged variables have effect on daily accidents.

the technique which I will use is Poisson regression, negative binomial regression.

My question is there any other technique beside PR, And NBR? and what procedure I follow to see whether data is linear related to response. If not then can I use Poisson regression?

Note: I have 583 records left as there were -1 values in precipitation.

Thanks