Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models

We propose a family of CUSUM-based statistics to detect the presence changepoints in deterministic part autoregressive parameter Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective whether sequence is stationary or not, and no prior knowledge stationarity lack thereof required. Similarly, our even when error term stochastic coefficient are non iid, covering cases conditional volatility shifts variance, again without requiring any as type thereof. In order ensure ability breaks at sample endpoints, we weighted CUSUM statistics, deriving asymptotics for virtually all possible weighing schemes, including standardized process (for which derive Darling-Erdős theorem) heavier weights (so-called Rényi statistics). Simulations show that procedures work very well finite samples. complement theory with an application several financial time series.