How to test the variance in timeseries? I have a doubt regarding the variance, I try to explain It with an example.
I have two vectors, like:
a <- c(1:10)
1  2  3  4  5  6  7  8  9 10

b <- c(10:1)
10  9  8  7  6  5  4  3  2  1

the variance is obviouly the same:
> var(a)
9.166667
> var(b)
9.166667

Ok, I need to test if the variances are similar, and for this test I use var.test().
The problem is that the variances are equals, OK! but the follow a different direction, the first move from 1 to 10 and the second from 10 to 1. SO the variances are the same and the test pass successfully(obviously), but I need also check the direction, so:


*

*Are the variances similar? Ok...

*Are the variances (I know 'variances' here is wrong but try to understand what I mean reading the example above) moving in the same direction? 


With the same direction I mean, the variance is equal(similar) BUT are they UP/DOWN togheter?
I need to do those checks because I'm analyzing two financial lists of prices, and I need to know if the variance between their returns is constant and on the same direction.
How Can I do?
Thanks!
 A: I would suggest covariance because it will tell you direction with variance. e.g.,
cov(a,b)= -9.16667
you can also do correlation test in R. e.g., cor.test(a,b)
A: Variance Change Detection is part of diagnostic checking to ensure that the Gaussian Assumptions are met regarding the error series. Make sure that there are no violations of the mean of the errors being zero everywhere or at least not-significantly different from zero as this oftentimes is the cause of perceived variance changes. To validate this make sure there are no pulses , no seasonal pulses , no level shifts and no time trends in the residuals via Intervention Detection schemes. If this is true and there is no evidence of any auto-correlation in the noise series and all lag structures have been exacted from any user-specified causal series then simply try different points in time and see if the variance of the two groups , before and after the time point , are statistically significantly different from each other. This is the Chow Test applied to time series. Now if that test fails to prove a difference then one might then consider evaluating the Box-Cox test to determine if there is need for a power transform which untreated would falsely suggest variance change points. If you wished to post your series we could demonstrate these things using commercially available software ( that I have helped write ). Hope my remarks help you.
