# Multivariate biological time series : VAR and seasonality

I have a multivariate time series dataset including interacting biological and environmental variables (plus possibly some exogenous variables). Beside seasonality, there is no clear long-term trend in the data. My purpose is to see which variables are related to each other. Forecasting is not really looked for.

Being new to time-series analysis, I read several references. As far as I understand, Vector Autoregressive (VAR) model would be appropriate, but I don’t feel comfortable with seasonality and most examples I found concerned economics field (as often with time series analysis…) without seasonality.

What should I do with my seasonal data? I considered deseasonalizing them – for example in R, I would use decompose and then use the $trend +$rand values to obtain a signal which appears pretty stationary (as judged per acf). Results of the VAR model are confusing me (a 1-lag model is selected while I would have intuitively expected more, and only coefficients for autoregression – and not for regression with other lagged variables - are significant). Am I doing anything wrong, or should I conclude that my variables are not (linearly) related / my model is not the good one (subsidiary question: is there a non-linear equivalent to VAR?).

[Alternatively, I read I could probably use dummy seasonal variables, though I can’t figure out exactly how to implement it].

Step-by-step suggestions would be very appreciated, since details for experienced users might actually be informative to me (and R code snippets or links towards concrete examples are very welcome, of course).

• Much depends on how you think about seasonality. My patchy reading of the literature indicates that economists often regard seasonality as an uninteresting nuisance while environmental scientists often feel much more positive about it. The method of dummy variables as used in economics hinges, frequently, on data being quarterly or monthly and effects of holidays (in every sense of the word) being sometimes spikey; witn environmental data you can sometimes do well with some Fourier (sinusoidal) terms and need not resort to dummies. – Nick Cox Jan 14 '14 at 16:33
• Thanks, @Nick Cox. Fourier terms do not appear to be a solution in my particular case, where variables show more complicated seasonal pattern than sinusoidal signals (unless I use several harmonics, but this is not so much the purpose here). And despite seasonality is clearly not an uninteresting nuisance term in my case, I was more looking for something helping me to explain the extra variability in the data beyond seasonality (i.e., the longer-term trend) as a function of other variables. – ztl Jan 15 '14 at 10:17
• What about a multivariate ARMA model? It's similar to VAR, but if I understand correctly, permits more dynamical interaction between variables. Someone else may be able to confirm/ reject my suspicion. – rbatt Feb 16 '14 at 3:04