A dimension reduction factor approach for multivariate time series with long-memory: a robust alternative method

Abstract

This paper studies factor modeling for a vector of time series with long-memory properties to investigate how outliers affect the identification of the number of factors and also proposes a robust method to reduce their impact. The number of factors is estimated using an eigenvalue analysis for a non-negative definite matrix introduced by Lam et al. (2011). Two estimators are proposed; the first is based on the classical sample covariance function, and the second uses a robust covariance function estimate. In both cases, it is shown that the eigenvalues estimates have similar convergence rates. Empirical simulations support both estimators for multivariate stationary long-memory time series and show that the robust method is preferable when the data is contaminated with additive outliers. Time series of daily log returns are used as an example of application. In addition to abrupt observations, exchange rates exhibit non-stationarity properties with long memory parameters greater than one. Then we use semi-parametric long memory estimators to estimate the fractional parameters of the series. The number of factors was estimated using the classical and robust approaches. Due to the influence of the abrupt observations, these tools suggested a different number of factors to model the data. The robust method suggested two factors, while the classical approach indicated only one factor.