Comparing the accuracy of multivariate density forecasts in selected regions of the copula support

This paper develops a testing framework for comparing the predictive accuracy of competing multivariate density forecasts with different predictive copulas, focusing on specific parts of the copula support. The tests are framed in the context of the Kullback–Leibler Information Criterion, using (out-of-sample) conditional likelihood and censored likelihood in order to focus the evaluation on the region of interest. Monte Carlo simulations document that the resulting test statistics have satisfactory size and power properties for realistic sample sizes. In an empirical application to daily changes of yields on government bonds of the G7 countries we obtain insights into why the Student-t and Clayton mixture copula outperforms the other copulas considered; mixing in the Clayton copula with the t-copula is of particular importance to obtain high forecast accuracy in periods of jointly falling yields.     

Sampling distributions associated with the multivariate t distribution

The known sampling distributions and simulation methods associated with multivariate t distributions are reviewed. We believe that this review will serve as an important reference and encourage further research activities in the area.     

How to model multivariate extremes if one must?

In this paper we discuss some approaches to modeling extremely large values in multivariate time series. In particular, we discuss the notion of multivariate regular variation as a key to modeling multivariate heavy-tailed phenomena. The latter notion has found a variety of applications in queuing theory, stochastic networks, telecommunications, insurance, finance and other areas. We contrast this approach with modeling multivariate extremes by using the multivariate student distribution and copulas.     

Dynamic correlation multivariate stochastic volatility with latent factors

Modeling the correlation structure of returns is essential in many financial applications. Considerable evidence from empirical studies has shown that the correlation among asset returns is not stable over time. A recent development in the multivariate stochastic volatility literature is the application of inverse Wishart processes to characterize the evolution of return correlation matrices. Within the inverse Wishart multivariate stochastic volatility framework, we propose a flexible correlated latent factor model to achieve dimension reduction and capture the stylized fact of ‘correlation breakdown’ simultaneously. The parameter estimation is based on existing Markov chain Monte Carlo methods. We illustrate the proposed model with several empirical studies. In particular, we use high‐dimensional stock return data to compare our model with competing models based on multiple performance metrics and tests. The results show that the proposed model not only describes historic stylized facts reasonably but also provides the best overall performance.     

基于不同分布假设GARCH模型对上证指数波动性预测能力的比较研究

本文在四种不同的分布假设(Normal,Student-t,GED和SkewedStudent-t)下,对上证指数波动性进行了GARCH(1,1)模型预测能力实证比较研究,目的在于揭示分布假设对GARCH模型预测能力的影响。研究结果表明,使用厚尾分布假设(Student-t,GED)提高了模型的预测绩效。但引入偏斜student-t分布并未能进一步提高模型预测能力。     

Multivariate t and beta distributions associated with the multivariate F distribution

Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result is two new distributions: a multivariate t/skew t distribution (on ℜ^m) and a multivariate beta distribution (on (0,1)^m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ⁺)^m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal and conditional distributions; moments; correlations; local dependence; and some limiting cases. Received: March 2001     

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.     

The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors

We consider the normalized least squares estimator of the parameter in a nearly integrated first-order autoregressive model with dependent errors. In a first step we consider its asymptotic distribution as well as asymptotic expansion up to order O_p(T⁻¹). We derive a limiting moment generating function which enables us to calculate various distributional quantities by numerical integration. A simulation study is performed to assess the adequacy of the asymptotic distribution when the errors are correlated. We focus our attention on two leading cases: MA(1) errors and AR(1) errors. The asymptotic approximations are shown to be inadequate as the MA root gets close to −1 and as the AR root approaches either −1 or 1. Our theoretical analysis helps to explain and understand the simulation results of Schwert (1989) and DeJong, Nankervis, Savin, and Whiteman (1992) concerning the size and power of Phillips and Perron's (1988) unit root test. A companion paper, Nabeya and Perron (1994), presents alternative asymptotic frameworks in the cases where the usual asymptotic distribution fails to provide an adequate approximation to the finite-sample distribution.     

Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent. Supported by National Natural Science Foundation of China (Grant No. 10571159) and Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 2002335090).