Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.