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?