I am trying to understand the effect of sampling rate on the optimal order of an ARMA$(p,q)$ time series model. This is the scenario I have in mind:
- Assume that I have stationary time series data sampled at $T = 1$ sec and that an ARMA$(2,2)$ model adequately models the process.
- If I were to obtain the same data, but now sampled at, say, $T= 10$ sec or $T = 0.1$ sec, then could an ARMA$(2,2)$ model still represent the process as good as the above case, even if we allow different model coefficient values?
Intuitively, I think that if I sample some slowly varying signal much faster than the dynamics of the signal, then successive samples would be highly correlated, which might indicate a need for higher order models. But, I am looking to find a more robust, mathematical explanation tying ARMA models of the same signal sampled at different rates.
