GILLES DE TRUCHIS

Narrow-band Weighted Nonlinear Least Squares Estimation of Unbalanced Cointegration Systems

Elena Ivona Dumitrescu, Gilles de Truchis

Abstract

We discuss cointegration relationships when covariance stationary observables exhibit unbalanced integration orders. Least squares type estimates of the long run coefficient are expected to converge either to 0 or to infinity if one does not account for the true unknown unbalance parameter. We propose a class of narrow-band weighted non-linear least squares estimators of these two parameters and analyze its asymptotic properties. The limit distribution is shown to be Gaussian, albeit singular, and it covers the entire stationary region in the particular case of the generalized non-linear least squares estimator, thereby allowing for straightforward statistical inference. A Monte Carlo study documents the good finite sample properties of our class of estimators. They are further used to provide new perspectives on the risk-return relationship on financial stock markets. In particular, we find that the variance risk premium estimated in an appropriately rebalanced cointegration system is a better return predictor than existing risk premia measures.

Mot(s) clé(s)

Unbalanced cointegration, Long memory, Stationarity, Generalized Least Squares, Nonlinear Least Squares

Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems

Florent Dubois, Elena Ivona Dumitrescu, Gilles de Truchis

Abstract

In this paper we propose a local Whittle estimator of stationary bivariate unbalanced fractional cointegration systems. Unbalanced cointegration refers to the situation where the observables have different integration orders, but their filtered versions have equal integration orders and are cointegrated in the usual sense. Based on the frequency domain representation of the unbalanced version of Phillips’ triangular system, we develop a semiparametric approach to jointly estimate the unbalance parameter, the long run coefficient, and the integration orders of the regressand and cointegrating errors. The paper establishes the consistency and asymptotic normality of this estimator. We find a peculiar rate of convergence for the unbalance estimator (possibly faster than root-n) and a singular joint limiting distribution of the unbalance and long-run coefficients. Its good finite-sample properties are emphasized through Monte Carlo experiments. We illustrate the relevance of the developed estimator for financial data in an empirical application to the information flowing between the crude oil spot and CME-NYMEX markets.

Mot(s) clé(s)

Unbalanced cointegration, Long memory, Stationarity, Local Whittle likelihood

Testing for Extreme Volatility Transmission with Realized Volatility Measures

Christophe Boucher, Elena Ivona Dumitrescu, Sessi Tokpavi, Gilles de Truchis

Abstract

This paper proposes a simple and parsimonious semi-parametric testing procedure for variance transmission. Our test focuses on conditional extreme values of the unobserved process of integrated variance since they are of utmost concern for policy makers due to their sudden and destabilizing effects. The test statistic is based on realized measures of variance and has a convenient asymptotic chi-square distribution under the null hypothesis of no Granger causality, which is free of estimation risk. Extensive Monte Carlo simulations show that the test has good small sample size and power properties. An extension to the case of spillovers in quadratic variation is also developed. An empirical application on extreme variance transmission from US to EU equity markets is further proposed. We find that the test performs very well in identifying periods of significant causality in extreme variance, that are subsequently found to be correlated with changes in US monetary policy.

Mot(s) clé(s)

Extreme volatility transmission, Granger causality, Integrated variance, Realized variance, Semi-parametric test, Financial contagion.