Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models
提出了一族基于CUSUM的统计量，用于检测随机系数自回归模型中自回归参数确定性部分的变点，适用于非平稳、条件异方差等情况，并引入加权CUSUM统计量以检测端点断点。
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 <i>weighted</i> CUSUM statistics, deriving the asymptotics for virtually all possible weighing schemes, including the standardized CUSUM process (for which we derive a Darling-Erdős theorem) and even heavier weights (so-called Rényi statistics). Simulations show that our procedures work very well in finite samples. We complement our theory with an application to several financial time series.