Time series of variance If the mean or total of a variable studied over time displays seasonality, should I expect that the variance of that variable should display seasonality similar to the mean? Why or why not?
The data are company assets. There is no max value. Nor are the data strictly positive, but the vast majority of the data is positive. I'm not sure if it is relevant, but it is very left skewed (simply because more small companies exist than large companies). 
 A: I have worked on detecting time varying variances of the residuals ( never the original data as all the assumptions are about the errors from a reasonable model) . Sometimes the error variance/standard deviation is proportional to the expected value and in these cases power transformations are suitable When (and why) should you take the log of a distribution (of numbers)?. In many other cases (meaning a lot ! ) the error variance changes at specific ( to be discovered) deterministic points in time . This case is readily treated with Weighted Least Squares. Now in either case I recently have developed schemes to predict the error variance for certain subsets of the data ( e.g. error variance proven to be heterogeneous across days of the week or months of the year) and forecast confidence limits need to reflect that. So in this last example not only is the expected value possibly different from day-to-day but the error variance may also be predictably different on a day-to=day basis. All of these improvements/refinements in advanced time series can now be accessed via either extensive programming/heuristic developments on your part in R or through commercially available software. In terms of transparency I have helped develop these things in AUTOBOX but I feel confident that similar approaches exist/or will exist as a result of this post in SAS and SPSS and elsewhere. I hope this helps you as I have been pursuing these kinds of questions/improvements for a long time now. I would be interested in scrutinizing closely some of your data and thus possibly improving the procedures that I think are currently very successful but like all heuristics need to be constantly challenged.
