Granger Centre Seminar: Lorenzo Trapani (University of Nottingham)

Change point detection in random coefficient autoregression models (with Lajos Horvath)

Abstract: 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 sequence. In order to ensure the ability to detect breaks at sample endpoints, we thoroughly study weighted CUSUM statistics. In this context, we analyse the asymptotics for virtually all possible weighing schemes, including the standardised CUSUM process (for which we derive a Darling-Erdos theorem) and even heavier weights (studying the so-called Rényi statistics). Our results are valid irrespective of whether the sequence is stationary or not, and indeed prior knowledge of stationarity or lack thereof is not required from a practical point of view. From a technical point of view, our results require the development of strong approximations which, in the nonstationary case, are entirely new. Similarly, we allow for heteroskedasticity of unknown form in both the error term and in the stochastic part of the autoregressive coefficient, proposing a family of test statistics which are robust to heteroskedasticity; again, our tests can be readily applied, with no prior knowledge as to the presence or type of heteroskedasticity. Technically, we remove heteroskedasticity without requiring any tuning parameters (such as e.g. the choice of a bandwidth or a kernel). Simulations show that our procedures work well in finite samples, under all cases considered (stationarity versus nonstationarity, homoskedasticity versus various forms of heteroskedasticity). We complement our theory with several applications to financial, economic and epidemiological time series.