# KPSS test and heteroscedasticity

I am trying to transform a time series to make it stationary. After two differencings it looks like this:

KPSS test value is 0.01075801 with p-value=0.1, so the stationarity is not rejected. But just from looking at the chart, the time series seems very heteroscedastic, with clear clusters of high and low volatility. Doesn't it make the series non-stationary? If so, is KPSS not sensitive to this kind of non-stationarity? What would be the appropriate test then?

• This is a case where I’d go with the eyeball test and conclude that the variance is dynamic. Does KPSS examine for mean stationarity only, though? Then it shouldn’t be catching changing variance any more than a t-test should be able to tell apart $N(0,1)$ and $N(0,5)$.
– Dave
Mar 27, 2020 at 5:15
• Just to support what dave said, all of the unit root related tests are testing for stationarity of the mean. I imagine that there must be tests out there for changing variance but they may not be called or viewed as tests of stationarity. I would google for "tests for non-constant variance in time series" and see if anything useful comes up. Mar 27, 2020 at 6:28
• Second order differencing is a bit much in most situations. Visually, it seems to me you have overdifferenced your series. Mar 27, 2020 at 7:10
• @RichardHardy After the first differencing the series looked very similar to the above, but KPSS was significant (p-val 0.01). I believe that's another argument that KPSS is not useful in this case? Mar 27, 2020 at 14:20
• The above shows no stochastic trend (random walk). If that was roughly the case before differencing, I would go with the first difference. Mar 27, 2020 at 15:09