Title: A volatility model with a time-varying intercept
Authors: Niklas Ahlgren - Hanken School of Economics (Finland) [presenting]
Alexander Back - Hanken School of Economics (Finland)
Timo Terasvirta - Aarhus University (Denmark)
Abstract: A GARCH model augmented by a time-varying intercept is proposed. The intercept is parameterised by a logistic transition function with rescaled time as the transition variable. This formulation provides a simple and flexible way to capture deterministic non-linear changes in the conditional and unconditional variances. It is common for financial time series to exhibit these types of shifts. By making the intercept a smooth function of time, it is possible to capture changes that occur gradually, rather than abruptly as in regime switching models. The model is globally nonstationary but locally stationary. We use the theory of locally stationary processes to derive the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of the parameters of the model. We show that the QMLE is consistent and asymptotically normally distributed. To corroborate the results, we provide a small simulation study. An empirical application to Intel Corporation stock returns demonstrates the usefulness of the model. We find that the persistence implied by the standard GARCH model parameter estimates is reduced by incorporating a time-varying intercept. In particular, estimates that suggest an integrated volatility model are reduced to lie within the stationary region.