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Why is it necessary to evaluate stationarity and seasonality of model residuals? Or is it? The model in question is an OLS model that represents a relationship between Y and a bunch of economic variables.

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    $\begingroup$ Stationarity is irrelevant if your data are not temporal or spatial. Seasonality is irrelevant if you do not have data indexed by date within year. These replies are trivial but the question presumes a context which it does not spell out. Conversely, the question is much more general than just economic applications. $\endgroup$ – Nick Cox Feb 21 '15 at 14:45
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OLS is only supposed to work (and deliver minimum variance unbiased estimates) under a set of assumptions. If you run OLS but do not check the assumptions, you will not know whether you can trust the results. Therefore you want to check the assumptions.

Model residuals being non-stationary (for example, due to having a seasonal component in them) is a violation of the assumptions. Some forms of non-stationarity may be less harmful than other; if residuals are only heteroskedastic, OLS will still deliver consistent estimates (ones that converge to the true values when the sample size grows) although they will no longer be minimum variance (a.k.a. efficient); if residuals follow an integrated process (a.k.a. unit-root process), OLS is no longer consistent (am I right on this one?), and that is something you really do not want. Generally, if you see some pattern (like seasonality) in the residuals, it indicates that you have misspecified the model. The cure would be to think about model specification again (e.g. model the seasonality explicitly).

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  • $\begingroup$ Ok - I am not a statistician so I don't understand technical jargon. In plain english, OLS assumption is residuals should be normally distributed. So we should be checking for this by drawing the historam. Where is this pattern and seasonality and non-stationarity coming into play. Non-stationarity to me is if the variance is not constant over time. I don't quite understand how all of this is linked together. I have not heard/read any OLS assumption that talks about residual non-stationarity $\endgroup$ – Freewill Feb 21 '15 at 17:17
  • $\begingroup$ Normality is not among the regular OLS assumptions. (It can be used as an auxiliary assumption, though.) In the answer I tried to be clear that if you see some pattern in the residuals (e.g. non-stationarity and seasonality), generally it indicates that you have misspecified the model. $\endgroup$ – Richard Hardy Feb 21 '15 at 18:08
  • $\begingroup$ Thanks, the book I read on OLS mentioned normality of residals as being one of the assumptions unless i understood it wrong. That is the reason we do QQ plot of normality of residuals. Is it not $\endgroup$ – Freewill Feb 21 '15 at 20:47
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    $\begingroup$ Normality does not hurt but is not essential (in my understanding of what is essential and what is not). Normality gives you exact small sample properties of estimators while without normality you have the same properties only asymptotically (i.e. for large samples). Also, normality makes OLS coincide with maximum likelihood estimation. However, normality is not needed for unbiasedness, consistency and efficiency of OLS estimators. I guess the book you read mentioned OLS as the 5th assumption of 5 assumptions, not the 1st one. But as I said, normality does not hurt. $\endgroup$ – Richard Hardy Feb 21 '15 at 21:20

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