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I am analysing a time series (stock returns) and I am trying to check whether variance in the second half of my sample is different from the first half. I assigned a period to the observations. Here is an example (not the real data, but this is what it looks like):

Period     return        Date
      1    .02784243     1/8/2010
      1    .01478848     1/15/2010
      1    -.04267111    1/22/2010
      2    -.011348      1/29/2010
      2    -.09616897    2/5/2010 

I use STATA for the Levene's test, but my question is in the first place whether I can use time series in this way/with this method.

robvar return, by(Periode)

Summary of return
Periode         Mean            Std. Dev.        Freq.
        
1               .0000922          .0367802        261
2               .00006544        .02613092        261
        
Total           .00007882        .03187241        522

W0  = 10.8059198   df(1, 520)     Pr > F    =    0.00108013

W50 =  9.6731110   df(1, 520)     Pr > F    =    0.0019724

W10 =  9.8870904   df(1, 520)     Pr > F    =    0.00175953 

I am wondering whether using the Levene's test and breaking up the data like this is a valid method for time series? Anyone around here who can help me answer this question? If it isn't, is there another method (that is not too hard for a beginner?) Thanks in advance!!

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I am wondering whether using the Levene's test and breaking up the data like this is a valid method for time series?

There are a number of non-parametric tests for changes in variance which might be of interest to you. These have been used (by academics) for financial time series which suggests the 'change in variance' question and splitting the data are both legitimate.

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Yes, the Levene test is a legitimate and proper test in this situation.

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Never used the Levene's test, but I also like the regime-switching GARCH approach, as presented in this interesting paper by Sichert (starting from page 7). At least with this approach you won't have to specify the size of your samples.

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