Costationarity of Locally Stationary Time Series

• Activity Number: 56
• Type: Topic Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guy Nason* and Alessandro Cardinali+
• Companies: University of Bristol and University of Bristol
• Keywords: costationarity ; local stationarity ; wind power ; asset allocation

Abstract

Given more than one locally stationary (LS) time series, we describe a method to discover time-varying linear combinations of the LS series that are stationary. Systems for which this can occur are called costationary and the associated combinations are called costationary vectors. The vectors shed light on the nature of a potentially interesting relationship between the series. The derived stationary series is often of independent interest. We discuss why a spectral approach is often preferred to the time-domain, why costationary vectors need to be complexity constrained and demonstrate an interesting error-correction formula which shows how costationary systems must evolve to maintain stationarity in response to system shocks. We illustrate our methodology with two examples: (i) asset allocation in portfolio construction, and (ii) mitigating intermittency in wind power generation.