To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standardized errors, incorporating multiplicatively both parametric and nonparametric estimators of the conditional covariance matrix together. For every parametric MV-GARCH model, we could construct a corresponding SM-GARCH model. In both Monte Carlo simulation and empirical applications in stock indexes and foreign exchange rates, our SM-GARCH models outperform the corresponding parametric MV-GARCH models in terms of loss function (including mean absolute value of conditional correlation, mean squared error of conditional covariance matrix and Value-at-Risk (VaR) loss of the portfolio) and the p-value of the dynamic quantile test based on VaR and hit.

In addition to clear-cut seasonality in mean and variance, weekly Dutch temperature data appear to have a strong asymmetry in the impact of unexpectedly high or low temperatures on conditional volatility. Furthermore, this asymmetry also shows fairly pronounced seasonal variation. To describe these features, we propose a univariate seasonal time series model with asymmetric This paper was prepared for a special issue of Environmental Modeling and Software. We thank the editor Michael McAleer for several helpful comments and Richard Tol for making the Dutch temperature data available to us. y Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands, email: franses@few.eur.nl (corresponding author). z Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands. x Tinbergen Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR Rotterdam, The Netherlands, email: djvandij...

This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a onestep local partial-likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial-likelihood estimator. Furthermore, a penalized local likelihood estimator is proposed to select important risk variables in the model. Numerical examples are used to illustrate the effectiveness of the proposed procedures. 1. Introduction. One

this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm.The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the t -statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate nonlinear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink--muskrat data in 1925--1994 and the pound--dollar exchange rates in 1974--1983

We would like to thank Yongmiao Hong and Tae-Hwy Lee for sharing their computer program, Qi Li and particularly two anonymous referees for numerous helpful comments and suggestions.

Using a flexible semiparametric varying coefficient model specification, this paper examines the role of fiscal policy on the U.S. asset markets (stocks, corporate and treasury bonds). We consider two possible roles of fiscal deficits (or surpluses): as a separate direct information variable and as a (indirect) conditioning information variable indicating binding constraints on monetary policy actions. The results show that the impact of monetary policy on the stock market varies, depending on fiscal expansion or contraction. The impact of fiscal policy on corporate and treasury bond yields follow similar patterns as in the equity market. The results are consistent with the notion of strong interdependence between monetary and fiscal policies. Key words: fiscal deficits; monetary policy; stock market; semiparametric estimation.

We propose marginal integration estimation and testing methods for the coefficients of varying-coefficient multivariate regression models. Asymptotic distribution theory is developed for the estimation method, which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (β-mixing). Application of the test procedure to West German real GNP (gross national product) data reveals that a partially linear varying coefficient model is best parsimonious in fitting the data dynamics, a fact that is also confirmed with residual diagnostics.

Additive coefficient model (Xue and Yang, 2006a, 2006b) is a flexible regression and autoregression tool that circumvents the “curse of dimensionality. ” We propose spline-backfitted kernel (SBK) and spline-backfitted local linear (SBLL) estimators for the component functions in the additive coefficient model that are both (i) computationally expedient so they are usable for analyzing high dimensional data, and (ii) theoretically reliable so inference can be made on the component functions with confidence. In addition, they are (iii) intuitively appealing and easy to use for practitioners. The SBLL procedure is applied to a varying coefficient extension of the Cobb-Douglas model for the U.S. GDP that allows nonneutral effects of the R&D on capital and labor as well as in total factor productivity (TFP). 1.

A fundamental issue of applying copula method in applications is how to choose an appropriate copula function. In this article we address this issue by proposing a new copula selection approach via penalized likelihood. The proposed method selects the appropriate copula functions and estimates copula coefficients simultaneously. The asymptotic properties, including the rate of convergence and asymptotic normality and abnormality, are established for the proposed penalized likelihood estimator. Particularly, when the true coefficient parameters may be on the boundary of the parameter space and the dependence parameters are in an unidentifiable subset of the parameter space, it shows that the limiting distribution for boundary parameters is abnormal and the penalized likelihood estimator for unidentified parameters converges to an arbitrary value. Moreover, the EM algorithm is proposed for optimizing penalized likelihood function. Finally, Monte Carlo simulation studies are carried out to illustrate the finite sample performance of the proposed method and the proposed method is used to investigate the correlation structure and comovement of financial stock markets.

The existing parametric multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model could hardly capture the nonlinearity and the non-normality, which are widely observed in financial data. We propose semiparametric conditional covariance (SCC) model to capture the information hidden in the standardized residuals and missed by the parametric MGARCH models. Our two-stage SCC estimator incorporates the parametric and nonparametric estimators of the conditional covariance in a multiplicative way. We prove the consistency and asymptotic normality of our semiparametric estimator. We conduct a small set of Monte Carlo experiments to demonstrate the advantage of our SCC estimators over their parametric counterparts in terms of mean squared error. For both insample fitting and out-of-sample forecasting conditional covariance matrix, our SCC models also outperform the parametric ones in empirical applications on bivariate stock indices and two stock portfolios with thirty underlying stocks.