This article defines the class of H-valued autoregressive (AR) processes with a unit root of
finite type, where H is a possibly infinite-dimensional separable Hilbert space, and derives a …

A generalization of the Granger and the Johansen Representation Theorems valid for any
(possibly fractional) order of integration is presented. This Representation Theorem is based …

This article concerns the tail probabilities of a light-tailed Markov-modulated Lévy process
stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at …

Nonstationary fractionally integrated functional time series Page 1 Bernoulli 29(2), 2023,
1505–1526 https://doi.org/10.3150/22-BEJ1508 Nonstationary fractionally integrated …

We propose a statistical procedure to determine the dimension of the nonstationary
subspace of cointegrated functional time series taking values in the Hilbert space of square …

We extend the notion of cointegration for time series taking values in a potentially infinite
dimensional Banach space. Examples of such time series include stochastic processes in …

In this article we provide a complete description of the set of all solutions to an
autoregressive law of motion in a finite-dimensional complex vector space. Every solution is …

Functional principal component analysis (FPCA) has played an important role in the
development of functional time series analysis. This note investigates how FPCA can be …

This paper studies statistical inference on unit roots and cointegration for time series in a
Hilbert space. We develop statistical inference on the number of common stochastic trends …

We introduce methods and theory for fractionally cointegrated curve time series. We develop
a variance ratio test to determine the dimensions associated with the nonstationary and …