Lp-functionals for change point detection in random coefficient autoregressive models

We study a family of Lp-functionals of the weighted CUSUM test statistic to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient AutoRegressive sequence of order 1 (RCA(1)). Our statistics are robust against the presence of heteroskedasticity of unknown form, and can be applied irrespective of whether the sequence is stationary or not, with no prior knowledge of stationarity or lack thereof required.