A frequent problem in applied time series analysis is the identification of dominating periodic components. A particularly difficult task is to distinguish deterministic periodic signals from periodic long memory. In this paper, a family of test statistics based on Whittle’s Gaussian...

We consider INAR(1) processes modulated by an unobserved strongly dependent 0-1process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the...

We consider INAR(1) processes modulated by an unobserved strongly dependent 0-1process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the...

We consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of...

A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long-range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence...

Duration series often exhibit long-range dependence and local nonstationarities. Here, exponential FARIMA (EFARIMA) and exponential SEMIFAR (ESEMIFAR) models are introduced. These models capture simultaneously nonstationarities in the mean as well as short- and long-range dependence, while...