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I am trying to identify if there is seasonality in the data set. The condition is that I don't want to use graphs or any kind of visual interpretation to understand seasonality, but to use statistics to tell me if seasonality is present and how significant is it? can anybody help me on this?

rolando2
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user207208
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    This is precisely what autocorrelation is used for. If you say more about your situation, including what type of data you have (daily? monthly?), no doubt people will have useful suggestions for you. Can you also say why you want to exclude visual evidence? – rolando2 May 06 '18 at 10:16
  • @rolando2 I have monthly data for 10k plus products and I want to identify which all products experience seasonality or trend or both. Graph is not an option because of the sheer volume of the products. I am looking for an indicator which can be used to tell me the presence of seasonality, or trend or both in the data set. Thanks in Advance – user207208 May 18 '18 at 10:55
  • One of the beautiful things about the R software is that, with a moderate amount of programming work up front, it enables one to test for trend and test for seasonality via autocorrelation, and to do this for 10,000 different products, saving the info on products that have a result that meets a certain threshold. – rolando2 May 18 '18 at 15:27
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    Not being able to look at all of your data is hardly a good reason for not looking at any of your data. – Nick Cox May 18 '18 at 16:36
  • @rolando2. What I understand is that by using R I can get the autocorrelation plot of the data set which will tell me if seasonality is present or not. The point is I can't see the graph and decide as I have 1000 products and I have just a week to do it. – user207208 May 18 '18 at 21:11
  • One can set R to loop through a large number of autocorrelation models, each time saving the value of a specified coefficient such as that for lag12. No plots need be involved. – rolando2 May 18 '18 at 23:19
  • @rolando2 Thanks a lot. I have a doubt the lag coefficient will give me only the value of correlation how is it going to tell me about the seasonality? – user207208 May 19 '18 at 04:50
  • I used lag12 as an example because (with monthly data) it's the most common lag at which seasonality will show up. I don't know how you're defining seasonality, though. Or trend for that matter. I've tried to give you a basic framework for addressing your problem; the specific implementation would depend on definitions and preferences that you would need to specify. Cheers ~ – rolando2 May 19 '18 at 12:28
  • With 10k products there must be some kind of hierarchcal structure on the series. You should try some form of hierarchcal predection/modeling, see https://stats.stackexchange.com/questions/240863/choice-of-time-series-model-for-store-sales-prediction/339038#339038 https://robjhyndman.com/hyndsight/thief/ – kjetil b halvorsen May 19 '18 at 16:25

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Things come to mind .... the auto-correlation function can be "blurred/obfuscated" by the presence of anomalous observations (pulses) and level shifts , trend changes among other things. Trend detection and seasonality detection can be done if one recognizes that there are two distinct forms of seasonality .. one is seasonal memory (sarima) the second is seasonal dummies . Discerning between them for each time series under consideration is important in the analysis.

If three months of the year are the only ones effected by seasonality while 9 are not the seasonal arima (memory) may not stand out while three seasonal dummies would be appropriate. I would make sure that this distinction is available in any software that you try to employ. Many researchers using freely available solutions often find that a pure seasonal memory model is not significant while upon closer inspection there is significant seasonality for some months. An important task worth doing is worth doing correctly .

I am unaware of any free software that comprehensively deals with this subject.

IrishStat
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    Although there are many good cautionary notes here, where is your answer to the question? – whuber May 18 '18 at 16:08