I keep struggling with testing 9 samples if they are stationary. Each of these samples is a real valued time series with 714.000 values. If I use the KPSS test with the each compleete sample set, the hypothesis is rejected. But, if I split each sample in 20 parts of equal size, then test all these sample parts with KPSS in all most all cases KPSS accepts the sample parts to be stationary.
But, I cannot find any good explanation for this behaviour. Can you give me any explanation for it and maybe a reference?