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

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.