Consistent estimation of breakpoints in time series, with application to wavelet analysis of Citigroup returns

Abstract

Simple and intuitive non-parametric methods are provided for estimating variance change points for time series data. Only slight alterations to existing open-source computer code applying CUSUM methods for estimating breakpoints are required to apply our proposed techniques. Our approach, apparently new in this context, is first to define two artificial time series of double the length of the original by reflective continuations of the original. We then search for breakpoints forwards and backwards through each of these symmetric extensions to the original time series. A novel feature of this paper is that we are able to identify common breakpoints for multiple time series, even when they collect data at different frequencies. In particular, our methods facilitate the reconciliation of breakpoint outputs from the two standard wavelet filters. Simulation results in this paper indicate that our methods produce accurate results for time series exhibiting both long and short term correlation; and we illustrate by an application to Citigroup stock returns for the last thirty years.