I am working with uniformly-spaced time series data where I am interested in knowing whether there are changes in temporal auto-covariance. The mean can be assumed constant. Visually, there are no abrupt/obvious changes in variance or temporal correlation.
Intuitively, it seems to make sense to divide up the data into contiguous blocks, compute for each block the sample auto-covariance at some number of lags, and compare the sample auto-covariances for each block. I suppose that one could apply procedures to see if the per-block auto-covariance estimates come from the same distribution (which, I guess, would imply stationarity).
Can anyone point me to a some papers where this sort of thing has been done?
Also, are there other methods out there which could apply?
- I have seen unit root tests. While an AR process may be appropriate, I'm not sure if the non-stationarity can be described by a unit root--perhaps instead slowly time-varying AR coefficients?
I have also seen some wavelet approaches, which seem to focus on detecting abrupt changes, which is not the case here.