Sequential monitoring for explosive volatility regimes

TL;DR

This paper introduces two sequential monitoring procedures for detecting explosive volatility regimes in GARCH(1,1) models, enabling timely detection of regime changes including volatility bubbles, without prior knowledge of the initial regime.

Contribution

It develops novel CUSUM-based detectors with weighted boundaries for early detection of regime shifts in GARCH models, applicable regardless of stationarity of historical data.

Findings

The proposed methods effectively detect volatility regime changes in simulations.

The procedures can identify explosive regimes in stock return data.

Theoretical detection delay distributions are derived and validated.

Abstract

In this paper, we develop two families of sequential monitoring procedure to (timely) detect changes in a GARCH(1,1) model. Whilst our methodologies can be applied for the general analysis of changepoints in GARCH(1,1) sequences, they are in particular designed to detect changes from stationarity to explosivity or vice versa, thus allowing to check for volatility bubbles. Our statistics can be applied irrespective of whether the historical sample is stationary or not, and indeed without prior knowledge of the regime of the observations before and after the break. In particular, we construct our detectors as the CUSUM process of the quasi-Fisher scores of the log likelihood function. In order to ensure timely detection, we then construct our boundary function (exceeding which would indicate a break) by including a weighting sequence which is designed to shorten the detection delay in the presence of a changepoint. We consider two types of weights: a lighter set of weights, which ensures timely detection in the presence of changes occurring early, but not too early after the end of the historical sample; and a heavier set of weights, called Renyi weights which is designed to ensure timely detection in the presence of changepoints occurring very early in the monitoring horizon. In both cases, we derive the limiting distribution of the detection delays, indicating the expected delay for each set of weights. Our theoretical results are validated via a comprehensive set of simulations, and an empirical application to daily returns of individual stocks.