Estimating the Degrees of Freedom of the Realized Volatility Wishart Autoregressive Model

Abstract

In this paper an in-depth analysis of the estimation of the realized volatility Wishart Autoregressive model is presented. We focus in particular on the estimation of the degrees of freedom. A new estimator is proposed. Monte Carlo simulations show that this novel estimator is more efficient when compared to the standard estimator proposed in literature. We also studied the effect of extreme observation in the variance-covariance process. Analytically and relying on simulation, we show that extreme observations in the variance-covariance process induce a bias toward zero of the estimated degrees of freedom, no matter which estimator one uses. However, the new proposed estimator is more robust compared to the standard one. An empirical application to the S&P 500 - NASDAQ 100 futures realized variance-covariance series confirms that the estimated degrees of freedom result sensitively lower when extremely high values in the volatility process are present and they increase with the sampling frequency.

Keywords: Wishart process, realized volatility, outliers, cointegration

JEL Classification: C13, C16, C51, C63