Testing for Variance Changes in Financial Time Series
Summary
The discussion considers whether Levene’s test can compare return variances across two halves of a financial time series. The example divides observations into periods and reports Levene test statistics indicating a difference in variance. Respondents say testing for variance changes and splitting a sample are legitimate approaches, and mention nonparametric change tests used in financial research.
One response specifically endorses Levene’s test for this setting, while another suggests regime-switching GARCH as an alternative that does not require choosing the sample split in advance. The exchange offers brief guidance rather than a full methodological treatment: it does not discuss how serial dependence or changing market conditions affect test assumptions, nor compare the tests’ performance. Researchers should therefore treat the example as a starting point and consider whether the chosen test’s assumptions fit their return data.
Key ideas
- Levene’s test can be used to compare return variances across two sample periods.
- Nonparametric tests are also used to detect changes in variance in financial time series.
- A regime-switching GARCH model is suggested as an alternative that avoids a fixed sample split.
- The discussion does not analyze how serial dependence affects the tests’ assumptions.
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Full text
# Change in variance time series
# Change in variance time series
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!!
## Answer by user42108 (score 1)
https://quant.stackexchange.com/a/58381
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.
## Answer by nbbo2 (score 1)
https://quant.stackexchange.com/a/59053
Yes, the Levene test is a legitimate and proper test in this situation.
## Answer by DomingoBrown (score 0)
https://quant.stackexchange.com/a/58382
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.