Time series : what model to choose

I'm still a beginner in statistics, and would like to ask for your help. I'm studying the effects of several variables divided into two groups (climatic, agricultural) on biological variables. I have daily data of insect captures from several traps at different locations, during several years. I would like to build a statistical model to interpret the effects of climatic and agricultural variables, as well as their interaction, on the biological variables, like annual captures for instance (taking account of the location of the traps).

I don't necessarily want my model to have a very good predictive capacity (but if it has, that would be nice though), my main goal is to : - see what are the important covariates that have an effect on my dependent variable - quantify these effects - see how the covariates interact with each other - see how the effects of the covariates can be different according to location (I can get latitude and longitude values)

As I’m studying time series, I thought about fitting an autoregressive model, like ARIMAX, so I could include covariates in it. But I’m encountering several difficulties and I would like to ask you a couple of questions :

• First, I’m studying several time series at once : one for each trap. Moreover, although the periods during which traps have been working often overlap, the traps have not always been working on the same periods. Is it possible to build an “ARIMAX-like” model that includes all these time series at once (with spatial location as a covariate) ? My goal being to interpret the general effects of the covariates on all the studied area, and the particularities in each location. I don’t know if I’m really clear…

• Secondly, is it possible to include interaction terms with this kind of model ? I mean, I would like to know if there are interactions between the climatic and agricultural covariates, not between t and t+1. I couldn’t manage to find anything about this.

So, now I’m rather thinking about fitting or fitting a GLM/GAM (maybe rather GAM because I have several non-linear relationships between my dependent variables and my explanatory variables), taking temporal autocorrelation into account. Actually, putting time as a fixed effect could interest me. Does it seem a good idea to you ? As I’m willing to explain rather than to predict, wouldn’t a GLM or a GAM be better than an autoregressive model ?

I’m sorry if I’m not clear of if I ask irrelevant/stupid questions. As I said I still have a lot to learn. I know my questions are a bit vague, but if you have some readings to advise I’m interested too  Thanks in advance for your answers !

• One of my favorite books: otexts.org/fpp – Chris Apr 1 '16 at 16:43