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I am reading an article in which the author claims the means and standard deviations for the annual weather data she's studying vary along the years; i.e., every year has different mean and standard deviation. (She didn't mention how much variation she detected.)

The author didn't delve into the topic, yet she affirmed these values needed to be deseasonalized so the time series would go from non-stationary to stationary.

The problem is that she does not give a statistical reason for that; e.g., 'the data set has means and standard deviations that are too disparate' or 'the seasonality is overshadowing other important factors'. She simply did it. It's very likely it's easy to understand why she did it but since I am new to all this, it makes no sense to me.

I've Googled the topic looking for a direct and simple answer but had no success in doing so.

I also wonder why would one deseasonalize data in the first place if seasonality is embedded in it? Isn't it a vital part of the data? An important "trend"?"

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  • $\begingroup$ Similar question has been asked a few hrs ago: stats.stackexchange.com/questions/192347/… $\endgroup$
    – IcannotFixThis
    Jan 25, 2016 at 13:05
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    $\begingroup$ Variability within a year is seasonality but a summary measure of such variability is not seasonality. But more generally people want to remove seasonality if they think it's not interesting or useful but distracting or irrelevant to the current purpose. That is in my experience often true in economics and business, less often true in epidemiology or environmental science, say. (As a matter of terminology, seasonality is often regarded as different from trend.) $\endgroup$
    – Nick Cox
    Jan 25, 2016 at 13:28
  • $\begingroup$ Not whitening the TS, removing the effect of trends and seasonality, might lead to spurious regressions (see my previous link) $\endgroup$
    – IcannotFixThis
    Jan 25, 2016 at 13:46
  • $\begingroup$ @NickCox and Hugo A., I have an alternative answer to the question linked by IcannotFixThis. I hope my answer there may give some intuition with respect to this question as well. NickCox, since you are a high reputation user and presumably well versed in the subject, I was wondering if that answer makes sense to you. $\endgroup$
    – Richard Hardy
    Jan 25, 2016 at 20:35
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    $\begingroup$ Can you link the PMID for the article in question? Hard to give a specific answer to a specific question without specific context. $\endgroup$
    – AdamO
    Sep 12, 2017 at 12:37

2 Answers 2

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You deaseasonalize when the focus is on the secular trends. For instance, you're interested where the sales are going as opposed to what will be the sales in the next month. Sales are usually highly seasonal, e.g. home sales are up in summer and down in winter.

So, if your focus is on figuring out whether the general trend of sales is up, you deseasonalize, and possibly forget about the seasonal component. However, if you need to forecast the sales in next quarter, then you need take into account both the secular trend and seasonality. You could do this by analyzing the components separately, or aggregated. In the latter case you don't bother deseasonalizing.

see also "WHY ADJUST?" section in "Seasonality: Causation, Interpretation, and Implications," Granger, URL: http://www.nber.org/chapters/c4321

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You can only make a regression line using deseasonalised data. The Regression line equation can then be used to make deseasonalised future predictions. From this you can find the seasonalised future values. So perhaps this was done to forcast future values?

Though, i'm not too certain on how this correlates to stationary and non-stationary data.

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    $\begingroup$ I disagree. Deseasonalizing can be done by fitting 3 fixed effects for Fall:Summer, Winter:Summer, Spring:Summer. This produces a line-equation (for the mean), predictions, and so on. $\endgroup$
    – AdamO
    Sep 12, 2017 at 12:46

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