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 …

This note presents insights on the Jordan structure of a matrix which are derived from an
extension of the I (1) and I (2) conditions in Johansen (1996). It is first observed that these …

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 …

This paper discusses the notion of cointegrating space for linear processes integrated of any
order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions …

We prove an extended Granger–Johansen representation theorem (GJRT) for finite‐or
infinite‐order integrated autoregressive time series on Banach space. We assume only that …

This paper consider inverting a holomorphic Fredholm operator pencil. Specifically, we
provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm …

We describe a systematic procedure to calculate the resolvent operator for a linear pencil on
Banach space and thereby simplify, unify and extend known methods for resolution and …