Fractionally integrated curve time series with cointegration

TL;DR

This paper develops new methods for analyzing fractionally cointegrated curve time series, including tests and estimators for long-memory parameters, supported by simulations and real data applications.

Contribution

It introduces a variance-ratio test for subspace dimension determination and applies local Whittle estimators for long-memory parameter estimation in fractionally cointegrated series.

Findings

Variance-ratio test effectively identifies nonstationary and stationary subspaces.

Local Whittle estimators are consistent for long-memory parameters.

Empirical applications demonstrate practical utility of the methods.

Abstract

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 stationary subspaces. For each subspace, we apply a local Whittle estimator to estimate the long-memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications.