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We propose a GARCH model augmented by a time-varying intercept. The intercept is parameterized by a logistic transition function with rescaled time as the transition variable, which provides a flexible and simple way of capturing deterministic non-linear changes in the conditional and unconditional variances. 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. It is common for financial time series to exhibit these types of shifts. The time-varying intercept makes the model 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 of the analysis, we provide a small simulation study. An empirical application on stock returns of large US corporations demonstrates the usefulness of the model. We find that the persistence implied by the workhorse GARCH(1,1) parameter estimates is reduced by incorporating a time-varying intercept. In particular, estimates that suggest an integrated volatility model can be reduced to lie within the stationary region.
