A Non-Stationary Paradigm for the Dynamics of Multivariate Financial Returns

40 Pages Posted: 24 Feb 2006

See all articles by Stefano Herzel

Stefano Herzel

University of Rome Tor Vergata - Faculty of Economics

Catalin Starica

University of Neuchatel - Faculty of Economics and Business; Economics; Economics

Reha Tutuncu

AQR Capital Management, LLC

Date Written: July 2003

Abstract

A simple non-stationary paradigm for the dynamics of multivariate returns is discussed. Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous and non-stationary. The vectors of returns are assumed to be animated by a slowly changing {making it unconditional} covariance structure. The methodological frame is that of non-parametric regression with fixed, equidistant design points. The regression function is the time evolving unconditional covariance. Special attention is payed to the accurate description of the extremal dependence of the vector of returns. The non-stationary paradigm is first applied to describe the changing dynamics of a multivariate data set of returns on three financial risk factors: a foreign exchange rate, an index and an interest rate. Then, its one-day-ahead multivariate distributional forecast performance is evaluated. We show through an out-of sample simulation experiment that our methodology is superior to the plain-vanilla specification of the industry standard RiskMetrics in forecasting the distribution of returns on portfolios of the three risk factors over horizons of one day, ten days and twenty days.

Keywords: stock returns, volatility, sample autocorrelation, long range dependence, non-parametric regression, kernel estimator, distributional forecast, heavy tails

JEL Classification: C14, C16, C32

Suggested Citation

Herzel, Stefano and Starica, Catalin and Tutuncu, Reha, A Non-Stationary Paradigm for the Dynamics of Multivariate Financial Returns (July 2003). Available at SSRN: https://ssrn.com/abstract=882824 or http://dx.doi.org/10.2139/ssrn.882824

Stefano Herzel

University of Rome Tor Vergata - Faculty of Economics ( email )

Via Columbia n.2
Rome, rome 00100
Italy

Catalin Starica (Contact Author)

University of Neuchatel - Faculty of Economics and Business ( email )

A.-L. Breguet 2
CH-2000 Neuchatel
Switzerland

Economics ( email )

Box 605
SE 405 30 Goeteborg
Sweden

HOME PAGE: http://www.math.chalmers.se\~starica

Economics ( email )

Box 640
Vasagatan 1 E-building floor 5 & 6
Göteborg, 40530
Sweden

HOME PAGE: http://www.math.chalmers.se\~starica

Reha Tutuncu

AQR Capital Management, LLC ( email )

Greenwich, CT
United States