5
$\begingroup$

When to use an AR model and when to use an MA model to model time-series data. What aspects of data are modelled by the AR process which can't be done by MA and vice-versa?

$\endgroup$
2
$\begingroup$

TL;DR

  • You would choose an AR model if you believe that previous observations have a direct effect on the time series.
  • You would choose an MA model if you believe that the weighted sum of differences (errors) have a direct effect on the time series.

To see what I mean with this, suppose you have a time series of the form $\{S_t\}_{t=1}^T$. Let's say that $S_t$ is the price of a stock at time $t$. Since $S_t$ is a random variable, we assume that it is normally distributed (stock prices cannot take negative values, as it is assumed on a normal distribution, but for the sake of the example, let's assume that this is true) with constant variance $\sigma^2$. If we were to model an AR(P) process, then $S_t$ would be distributed as

$$ S_t \sim \mathcal{N}\left(\psi + \sum_{p=1}^P \phi_pS_{t-p}, \ \sigma^2\right). $$

As you can see, under an AR(P) process, we assume that the price at time $t$ has a mean that is given by the weighted sum of past observations plus a constant. Of course, the higher $\phi_p$, the greater effect a previous time-step has on what we think will be the current value of $S_t$. You can think this one as the weighted cumulative sum of previous returns, up to $Q$ periods.

On the other hand, if we were to model an MA(Q) process, then $S_t$ would be distributed as

$$ S_t \sim \mathcal{N}\left(\psi + \sum_{q=1}^Q \phi_pr_{t-q}, \ \sigma^2\right). $$

If we denote $r_t$ as the return of the stock at time $t$, i.,e, $r_t= S_t - S_{t-1}$, then we can see that the MA(Q) process assumes that the current price has a mean that is given by the weighted sum of past returns plus a constant.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Generally , if the pure AR model has p coefficients AND the pure MA model has q coefficients select/use the AR model if p = < q OTHERWISE use the MA model.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.