Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models

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

Automated summary

We propose a family of CUSUM-based statistics to detect changepoints in the deterministic part of the autoregressive parameter in a RCA sequence. Our tests can be applied regardless of stationarity and the independence of error term and autoregressive coefficient. Weighted CUSUM statistics are introduced to ensure the detection of breaks at sample endpoints, and simulations show the effectiveness of our procedures. The theory is applied to financial time series.