We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since...

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the...

The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class...

Vector‐valued‐60 extensions of univariate generalized binary auto‐regressive (gbAR) processes are proposed that enable the joint modeling of serial and cross‐sectional‐50 dependence of multi‐variate binary data. The resulting class of generalized binary vector auto‐regressive...