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dhirschi
Topic Author
Posts: 4
Joined: July 11th, 2012, 7:19 pm

### Mean Reversion Testing for Variances

Hi everyone, I would like to test variances for mean reversion and ran into a few problems (sadly, I am not much of an econometrician...):1. I have time series of daily prices and returns per product (mostly commodity futures) counting between ca. 100 and 250 observations. Can I derive a time series for the variance (per product) by calculating it as a 5 day moving average? For example var1 would be calculated using returns (n, n-1, n-2, n-3, n-4), var2 would use (n-1, n-2, n-3, n-4, n-5) and so on?2. Is it valid to use a standard Dickey-Fuller test on a moving-average time series?3. Is there a better (yet computational easy) test? I only have MS excel available, no eViews or Matlab.Any help is greatly appreciated!D.

willsmith
Posts: 281
Joined: January 14th, 2008, 11:59 pm

### Mean Reversion Testing for Variances

1. Variance in financial terms is usually expressed as volatility i.e. the square root. Stick with volatilities would be my advice, the units are sensible. Volatility is just (annualized) standard deviation if you assume normality.You are correct about moving average to calculate it, You can use any window length you want for your moving average. The shorter the window length the more choppy the volatility process will be. You can also choose between a simple window and an exponentially weighted moving average - look up GARCH if you want to get into the latter.2. Yes I believe so.3. It should be pretty easy in Excel. Failing a dickie-fuller test, just plot the variance and visually look for a positive or negative drift.Some things you are likely to see in commodities:1) Samuelson effect - increasing vol as you approach futures expiry2) Theory of storage effect - more vol as inventories are lower3) Inverse leverage effect (opposite of equities). More vol as prices go higher (try a scattergram of vol against price).4) More vol in recent years - probably due to #3.

quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

### Mean Reversion Testing for Variances

QuoteOriginally posted by: dhirschi1. I have time series of daily prices and returns per product (mostly commodity futures) counting between ca. 100 and 250 observations. Can I derive a time series for the variance (per product) by calculating it as a 5 day moving average?no

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