It has long been known that the estimated persistence parameter in the GARCH(1,1) - model is biased upwards when the parameters of the model are not constant throughout the sample. The present paper explains the mechanics of this behavior for a particular class of estimates of the model...

Methods of dimension reduction are very helpful and almost a necessity if we want to analyze high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced Inverse Regression (SIR; Li (1991)), which...

We investigate the possibility of exploiting partial correlation graphs for identifying interpretable latent variables underlying a multivariate time series. It is shown how the collapsibility and separation properties of partial correlation graphs can be used to understand the relation between...