On regression-based tests for persistence in logarithmic volatility models

Building on the work of Pantula (1986), this paper discusses how the hypothesis of conditional variance nonstationarity in the logarithmic family of generalized autoregressive conditional heteroskedasticity (GARCH) and stochastic volatility processes may be tested using regression-based tests. The latter are easy to implement, have well-defined large-sample distributions, and are less sensitive to structural changes than tests based on the quasimaximum likelihood estimator.     

基于向量GARCH模型的国际证券市场波动溢出研究

以向量GARCH模型为基础,研究了国际证券市场中上海A股市场、香港市场和美国市场的均值溢出效应和波动溢出效应,并且给出了中国证券市场发展的政策建议。研究结果表明,三个市场均不存在单向的均值溢出效应,上海A股市场和美国证券市场存在双向的波动溢出效应。上海A股市场和美国证券市场存在波动溢出效应,反映了中国资本市场和美国资本市场融合程度的加强。     

Directional dependence via Gaussian copula beta regression model with asymmetric GARCH marginals

This article proposes a new directional dependence by using the Gaussian copula beta regression model. In particular, we consider an asymmetric Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) model for the marginal distribution of standardized residuals to make data exhibiting conditionally heteroscedasticity to white noise process. With the simulated data generated by an asymmetric bivariate copula, we verify our proposed directional dependence method. For the multivariate direction dependence by using the Gaussian copula beta regression model, we employ a three-dimensional archemedian copula to generate trivariate data and then show the directional dependence for one random variable given two other random variables. With West Texas Intermediate Daily Price (WTI) and the Standard & Poor’s 500 (S&P 500), our proposed directional dependence by the Gaussian copula beta regression model reveals that the directional dependence from WTI to S&P 500 is greater than that from S&P 500 to WTI. To validate our empirical result, the Granger causality test is conducted, confirming the same result produced by our method.     

Modeling exchange rate dynamics: Non-linear dependence and thick tails

This paper illustrates a new approach to the statistical modeling of non-linear dependence and leptokurtosis in exchange rate data. The student's t autoregressive model withdynamic heteroskedasticity (STAR) of spanos (1992) is shown to provide a parsimonious and statistically adequate representation of the probabilistic information in exchange rate data. For the STAR model, volatility predictions are formed via a sequentially updated weighting scheme which uses all the past history of the series. The estimated STAR models are shown to statistically dominate alternative ARCH-type formulations and suggest that volatility predictions are not necessarily as large or as variable as other models indicate.     

Modeling exchange rate dynamics: Non-linear dependence and thick tails

This paper illustrates a new approach to the statistical modeling of non-linear dependence and leptokurtosis in exchange rate data. The student's t autoregressive model withdynamic heteroskedasticity (STAR) of spanos (1992) is shown to provide a parsimonious and statistically adequate representation of the probabilistic information in exchange rate data. For the STAR model, volatility predictions are formed via a sequentially updated weighting scheme which uses all the past history of the series. The estimated STAR models are shown to statistically dominate alternative ARCH-type formulations and suggest that volatility predictions are not necessarily as large or as variable as other models indicate.     

Modelling the persistence of conditional variances

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical e imates of the logarithm of the exchange rate between the U.S. dollar and the Swiss franc are presented to illustrate the models.     

Likelihood-Based comparison of stable paretian and competing models: Evidence from daily exchange rates

Considering alternative models for exchange rates has always been a central issue in applied research. Despite this fact, formal likelihood-based comparisons of competing models are extremely rare. In this paper, we apply the Bayesian marginal likelihood concept to compare GARCH, stable, stable GARCH, stochastic volatility, and a new stable Paretian stochastic volatility model for seven major currencies. Inference is based on combining Monte Carlo methods with Laplace integration. The empirical results show that neither GARCH nor stable models are clear winners, and a GARCH model with stable innovations is the model best supported by the data.