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My data set is quarterly time seires data (around 140 data points).

Method 1: simple OLS regression with 5-6 exogenous variables, which are drivers of the dependent variable. None of the explanatory variables are lagged, AR or MA.

Method 2: ARIMA model using maximum likelihood with the same exogenous variables. AR, MA, or differencing are based on residual plots. I chose differencing with the same quarter of the prior year and AR of the same quarter of the prior year.

AIC or BIC from OLS regression are around 200 but from ARIMA are around 900. I have tried various ARIMA models by testing different p,q,d but AIC is still higher than OLS's.

Is it reasonable to select models between OLS regression and ARIMA for time series data based on AIC or BIC? What criterion should be used?

Amy comments would be appreciated.

Amanda

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  • $\begingroup$ OLS is an estimation technique while ARIMA is a model. Comparing the two is like comparing apples to oranges. What you actually seem to be doing is comparing a linear model (what you call OLS regression) to an ARIMA model. That makes more sense. $\endgroup$ – Richard Hardy Nov 30 '18 at 11:38
  • $\begingroup$ Thanks for pointing out this, Richard! I have edited my original post to reflect this correction. $\endgroup$ – amanda Nov 30 '18 at 14:52
  • $\begingroup$ The title remains unchanged. Also, OLS regression is in your case a jargon for a linear model with a normally distributed error term. That is what you are actually using when calculating AIC for what you call OLS regression. $\endgroup$ – Richard Hardy Nov 30 '18 at 16:32
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If I understood correctly, your two regressions have different dependent variables, the level of variable in Method 1, and the first-difference of the variable in Method 2. If so, cannot use AIC, BIC to compare these 2 regressions. Must have same dependent variable to use AIC, BIC for comparison.

Note that OLS for time series only makes sense if all the variables used in the regression are stationary. Otherwise, you'll get what Granger and Newbold referred to as the Spurious Regression Problem. Chances are the OLS regression will not model all the serial correlation. You can test this easily by checking whether your residuals from Method 1 are correlated. If you've selected your ARIMA model correctly, chances are that you won't have any residual correlation left. You can easily check this as well.

Intuitively, note that with OLS you are attempting a higher bar, so to speak, because you are looking to forecast one variable with a set of different variables. Whereas in the ARIMA case, if you are using AR terms, for example, then you're using own past values to forecast future values.

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