We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describt tbe process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.

. Statistical analysis of data from the nancial markets shows that generalized hyperbolic (GH) distributions allow a more realistic description of asset returns than the classical normal distribution. GH distributions contain as subclasses hyperbolic as well as normal inverse Gaussian (NIG) distributions which have recently been proposed as basic ingredients to model price processes. GH distributions generate in a canonical way Levy processes, i.e. processes with stationary and independent increments. We introduce a model for price processes which is driven by generalized hyperbolic Levy motions. This GH model is a generalization of the hyperbolic model developed by Eberlein and Keller (1995). It is incomplete. We derive an option pricing formula for GH driven models using the Esscher transform as martingale measure and compare the prices with classical Black-Scholes prices. The objective of this study is to examine the consistency of our model assumptions with the empirically obser...

This paper investigates the impact of the frequency of general and currency-specific news headlines on de-seasonalized intraday DEM-USD exchange rate changes. We find a significant relationship between volatility and the frequency of news. In particular, more news is associated with an increase in volatility. The result that spot exchange rates are more volatile during periods for which there is a lot of economic news accords with market participants' explanations for observed volatility clustering.

The strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a class of ARCH(∞) processes are established. The conditions imply that the process need not have finite variance, and allow for a wide range of rates of decay of the influence of observations in the remote past on the conditional variance, thereby covering a variety of parametric specifications of interest.

. In this paper we develop a practical strategy for evaluating efficiency gains when estimating models with dynamic conditional expectations and dynamic conditional variances using the likelihood principle. We prove that the factors which contribute to differences in efficiency between a maximum likelihood (ML) estimator and a quasi-maximum likelihood (QML) estimator are the Fisher information for location, the Fisher information for scale, and the coefficient of kurtosis of the probability density function of the error term. The quantification of these three factors can lead to the construction of an ML variance-covariance matrix which recovers efficiency losses arising in QML settings. Furthermore, the researcher can take advantage of the estimation of the Fisher information for location and scale to test for density functional form. We propose both parametric and nonparametric tests for density functional form. We apply our proposed tests in the context of testing the null of a Stud...

. In this paper we investigate the loss of efficiency of semiparametric (SP) and quasi-maximum likelihood (QMLE) estimators relative to maximum likelihood (MLE) estimators in models with Generalized Autoregressive Conditional Heteroscedasticity (GARCH). We demonstrate that the factors which contribute to differences in efficiency are the Fisher information for scale and the coefficient of kurtosis of the conditional density when this density is symmetric, and in addition the coefficient of skewness when it is asymmetric. We provide a necessary and sufficient condition for equal efficiency of the three estimators if the density is symmetric. If asymmetry is present, we show that there is no density for which equal efficiency holds, even though the SP estimator may be as efficient as the MLE. Based on the Fisher information for scale we propose both parametric and nonparametric tests for density functional form. We apply our proposed tests in the context of testing the null of a Student-...

this paper, we focus on the efficient estimation

We give necessary and sucient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models to almost surely nite random variables, assuming no a priori conditions whatsoever; in particular, no moment or log-moment assumptions are made. Our proofs proceed by relating the processes to discrete time perpetuities. The methodology we develop suggests an extension of the GARCH concept to certain purejump continuous time processes, which we set out and analyse using recent results on the convergence of stochastic integrals.

We use a discrete time analysis, giving necessary and sucient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes.

We prove asymptotic normality of a suitably standardized integrated square difference between a kernel type error density estimator based on residuals and the expected value of the error density estimator based on innovations in GARCH models. This result is similar to that of Bickel-Rosenblatt under i.i.d. set up. Consequently the goodness-of-fit test for the innovation density of the GARCH processes based on this statistic is asymptotically distribution free, unlike the tests based on the residual empirical process. A simulation study comparing the finite sample behavior of this test with Kolmogorov-Smirnov test and the test based on integrated square difference between the kernel density estimate and null density shows some superiority of the proposed test. 1