Stationarity test based on density approach

It is well known that a neighbourhood problem exists between stationarity and random walk with correlated error for any finite sample size n. That is, any stationary process is approximated by random walk with correlated error for any finite n. Hence, one cannot distinguish between them easily. In this article, we propose a stationarity test based on nonparametric density that resolves the neighbourhood problem successfully. Our stationarity test also emerges as a successful long-range dependence (LRD) stationarity test. Note that there is a similar neighbourhood problem between LRD stationarity and LRD non-stationarity [Samorodnitsky, G. (2006), 'Long Range Dependence', Foundations and Trends in Stochastic Systems, 1, 163-257].