Changepoint detection in random coefficient autoregressive models

TL;DR

This paper introduces a family of CUSUM-based methods for detecting changepoints in the deterministic part of random coefficient autoregressive models, applicable regardless of stationarity and heteroskedasticity, with strong theoretical backing and practical validation.

Contribution

It develops robust, weighted CUSUM statistics for changepoint detection in RCA models, including new asymptotic results and handling of heteroskedasticity without prior knowledge.

Findings

Methods perform well in finite samples

Theoretical results hold for stationary and nonstationary sequences

Applications demonstrate effectiveness in financial, economic, and epidemiological data

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 (RCA) sequence. In order to ensure the ability to detect breaks at sample endpoints, we thoroughly study weighted CUSUM statistics, analysing 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 R\'enyi statistics). Our results are valid irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Technically, our results require 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, without requiring any prior knowledge as to the presence or type thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial, economic and epidemiological time series.