Monitoring Procedures to Detect Unit Roots and Stationarity

TL;DR

This paper introduces sequential monitoring procedures using kernel-weighted variance-ratio statistics to detect stationarity or unit roots in time series, with proven asymptotic properties and high early detection power.

Contribution

It provides the first results for sequential monitoring of time series for stationarity, including asymptotic distributions and change-point detection methods.

Findings

High power detection in Monte Carlo simulations

Effective early decision-making capability

Asymptotic distributions established for various models

Abstract

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical tests for that problem are well studied in the literature. In this paper we provide first results for the problem to monitor sequentially a time series. Our stopping times are based on a sequential version of a kernel-weighted variance-ratio statistic. The asymptotic distributions are established for I(1) processes, a rich class of stationary processes, possibly affected by local nonpara- metric alternatives, and the local-to-unity model. Further, we consider the two interesting change-point models where the time series changes its behaviour after a certain fraction of the observations and derive the associated limiting laws. Our Monte-Carlo studies show that the proposed detection procedures have high power when interpreted as a hypothesis test, and that the decision can often be made very early.