A new GARCH model with a deterministic time-varying intercept

TL;DR

This paper introduces a GARCH model with a deterministic, time-varying intercept to better capture gradual changes in financial volatility, improving modeling of nonstationary time series.

Contribution

It proposes a novel GARCH extension with a linear combination of logistic functions for the intercept, derived from volatility decomposition, and demonstrates its theoretical and empirical advantages.

Findings

Reduced persistence in volatility estimates with the new model

The QMLE estimator is consistent and asymptotically normal

Empirical application shows improved modeling of stock return volatility

Abstract

It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a standard GARCH model by a deterministic time-varying intercept. It captures structural change that slowly affects the amplitude of a time series while keeping the short-run dynamics constant. We parameterize the intercept as a linear combination of logistic transition functions. We show that the model can be derived from a multiplicative decomposition of volatility and preserves the financial motivation of variance decomposition. We use the theory of locally stationary processes to show that the quasi maximum likelihood estimator (QMLE) of the parameters of the model is consistent and asymptotically normally distributed. We examine the quality of the asymptotic approximation in a small simulation study. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model. We find that the persistence implied by the GARCH parameter estimates is reduced by including a time-varying intercept in the volatility equation.