Long-Memory Processes: Probabilistic Properties and Statistical Methods

Definition of Long Memory.- Origins and Generation of Long Memory.- Mathematical Concepts.- Limit Theorems.- Statistical Inference for Stationary Processes.- Statistical Inference for Nonlinear Processes.- Statistical Inference for Nonstationary Processes.- Forecasting.- Spatial and Space-Time Processes.- Resampling.- Function Spaces.- Regularly Varying Functions.- Vague Convergence.- Some Useful Integrals.- Notation and Abbreviations.

Jan Beran is a Professor of Statistics at the University of Konstanz (Department of Mathematics and Statistics). After completing his PhD in Mathematics at the ETH Zurich, he worked at several U.S. universities and the University of Zurich. He has a broad range of interests, from long-memory processes and asymptotic theory to applications in finance, biology and musicology.

Yuanhua Feng is a Professor of Econometrics at the University of Paderborn’s Department of Economics. He previously worked at the Heriot-Watt University, UK, after completing his PhD and postdoctoral studies at the University of Konstanz. His research interests include financial econometrics, time series and semiparametric modeling.

Sucharita Ghosh (M.Stat. Indian Statistical Institute; PhD Univ. Toronto) is a statistician at the Swiss Federal Research Institute WSL. She has taught at the University of Toronto, UNC Chapel Hill, Cornell University, the University of Konstanz, University of York and the ETH Zurich. Her research interests include space-time processes, nonparametric curve estimation and empirical transforms.

Rafal Kulik is an Associate Professor at the University of Ottawa’s Department of Mathematics and Statistics. He has previously taught at the University of Wroclaw, University of Ulm and University of Sydney. His research interests include limit theorems for weakly and strongly dependent random variables, time series analysis and heavy-tailed phenomena, with applications in finance.