Robust inference for seemingly unrelated regression models

Abstract

Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models is considered. MM-estimators are introduced to obtain estimators that have both a high breakdown point and a high normal efficiency. A fast and robust bootstrap procedure is developed to obtain robust inference for these estimators. Confidence intervals for the model parameters as well as hypothesis tests for linear restrictions of the regression coefficients in seemingly unrelated regression models are constructed. Moreover, in order to evaluate the need for a seemingly unrelated regression model, a robust procedure is proposed to test for the presence of correlation among the disturbances. The performance of the fast and robust bootstrap inference is evaluated empirically in simulation studies and illustrated on real data.

Volatility spillovers between real exchange rate returns and real stock price returns in Malaysia

“…The significance of the coefficient of β 11 in model (9) indicates long-run volatility or short-run volatility spillovers from real exchange rate return to real stock price return. The ordinary least squares estimator can be used to estimate each equation separately when there is no contemporaneous correlation among equations (Peremans & Van Aelst, 2018;Zellner, 1962). The SUR framework is used to estimate models 9 and 10 simultaneously (Bollerslev, 1990;Morales-Zumaqueroa & Sosvilla-Rivero, 2018).…”

“…The linear dependence of the errors in the same time period is called contemporaneous correlation. The ordinary least squares estimator can be used to estimate each equation separately when there is no contemporaneous correlation among equations (Peremans & Van Aelst, 2018;Zellner, 1962). The SUR framework is the simplification of the general linear model when some coefficients are restricted to be zero or the generalization of the general linear model when the regressors are different in each equation.…”

A Robust General Multivariate Chain Ladder Method

“…We now introduce MM-estimators for the SUR model in (5) as studied by Peremans and Van Aelst (2018). The system of equations in (5) can be rewritten as another linear regression model by reordering the equations.…”

“…For more details on the properties of S and MM-estimators, we refer to Peremans and Van Aelst (2018). We now explore the use of these robust estimators in the GMCL model to obtain robust reserve estimates and identify outliers in the run-off triangles.…”

“…Therefore, Hubert et al (2017) proposed the FastSUR algorithm, which implements the ideas of the FastS algorithm (Salibian-Barrera and Yohai 2006) for the SUR S-estimator. Recently, Peremans and Van Aelst (2018) developed robust inference for the SUR model based on MM-estimators. This paper is structured as follows.…”