Temporal aggregation of multivariate GARCH processes

This paper derives results for the temporal aggregation of multivariate GARCH processes in the general vector specification. It is shown that the class of weak multivariate GARCH processes is closed under temporal aggregation. Fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables. The framework used in this paper can easily be extended to investigate joint temporal and contemporaneous aggregation. Discussing causality in volatility, I find that there is not much room for spurious instantaneous causality in multivariate GARCH processes, but that spurious Granger causality will be more common however numerically insignificant. Forecasting volatility, it is generally advisable to aggregate forecasts of the disaggregate series rather than forecasting the aggregated series directly, and unlike for VARMA processes the advantage does not diminish for large forecast horizons. Finally, results are derived for the distribution of multivariate realized volatility if the high frequency process follows multivariate GARCH. A numerical example illustrates some of the resultsmultivariate GARCH, temporal aggregation, causality in volatility, forecasting volatility, realized volatility

Dynamic stochastic copula models: Estimation, inference and applications

We propose a new dynamic copula model where the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling (EIS). We discuss goodness-of-fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that theproposed model outperforms standard competing models.econometrics;

Testing for Causality in Variance using Multivariate GARCH Models

Tests of causality in variance in multiple time series have been proposed recently, based on residuals of estimated univariate models. Although such tests are applied frequently little is known about their power properties. In this paper we show that a convenient alternative to residual based testing is to specify a multivariate volatility model, such as multivariate GARCH (or BEKK), and construct a Wald test on noncausality in variance. We compare both approaches to testing causality in variance in terms of asymptotic and finite sample properties. The Wald test is shown to have superior power properties under a sequence of local alternatives. Furthermore, we show by simulation that the Wald test is quite robust to misspecification of the order of the BEKK model, but that empirical power decreases substantially when asymmetries in volatility are ignored. --causality,multivariate volatility,local power

Estimating autocorrelations in the presence of deterministic trends

This paper considers the impact of ordinary least squares (OLS) detrending and the first difference (FD) detrending on autocorrelation estimation in the presence of long memory and deterministic trends. We show that the FD detrending results in inconsistent autocorrelation estimates when the error term is stationary. Thus, the FD detrending should not be employed for autocorrelation estimation of the detrended series when constructing e.g. portmanteau-type tests. In an empirical application of volume in Dow Jones stocks, we show that for some stocks, OLS and FD detrending result in substantial differences in ACF estimates.autocorrelations, OLS, first difference detrending, long memory.

Efficient Estimation of a Multivariate Multiplicative Volatility Model

We propose a multivariate generalization of the multiplicative volatility model ofEngle and Rangel (2008), which has a nonparametric long run component and aunit multivariate GARCH short run dynamic component. We suggest variouskernel-based estimation procedures for the parametric and nonparametriccomponents, and derive the asymptotic properties thereof. For the parametric partof the model, we obtain the semiparametric efficiency bound. Our method isapplied to a bivariate stock index series. We find that the univariate model of Engleand Rangel (2008) appears to be violated in the data whereas our multivariatemodel is more consistent with the data.GARCH, Kernel Estimation, Local Stationarity,Semiparametric

Information Spillover, Volatility and the Currency Markets for the Binary Choice Model

We use an impulse response methodology to analyse the effects of U.S. macroeconomic news announcements on the volatilities of three major exchange rates (Euro, Pound Sterling and Yen). Our data consist of 5 minute returns on exchange rates as well as the times of news announcements. In the definition of impulse responses, we allow for different types of news, and consider two categories in the application: those considered positive or negative for the U.S. economy. Using a multivariate GARCH model with exogenous news effects, we find that the initial impact of positive news on the volatility of the Pound is higher than that of the Euro, whereas the persistence of shocks is highest for the Yen. For negative news, we find that an important part of the impact on the Yen and Pound is induced by volatility spillover from the Euro.Information, Volatility, Impulse Response Function, Foreign Exchange

Simple approximations for option pricing under mean reversion and stochastic volatility

This paper provides simple approximations for evaluating option prices and implied volatilities under stochastic volatility. Simple recursive formulae are derived that can easily be implemented in spreadsheets. The traditional random walk assumption, dominating in the analysis of financial markets, is compared with mean reversion which is often more relevant in commodity markets. Deterministic components in the mean and volatility are taken into consideration to allow for seasonality, another frequent aspect of commodity markets. The stochastic volatility is suitably modelled by GARCH. An application to electricity options shows that the choice between a random walk and a mean reversion model can have strong effects for predictions of implied volatilities even if the two models are statistically close to each other

Semiparametric multivariate volatility models

Estimation of multivariate volatility models is usually carried out by quasi maximum likelihood (QMLE), for which consistency and asymptotic normality have been proven under quite general conditions. However, there may be a substantial efficiency loss of QMLE if the true innovation distribution is not multinormal. We suggest a nonparametric estimation of the multivariate innovation distribution, based on consistent parameter estimates obtained by QMLE. We show that under standard regularity conditions the semiparametric efficiency bound can be attained. Without reparametrizing the conditional covariance matrix (which depends on the particular model used), adaptive estimation is not possible. However, in some cases the e?ciency loss of semiparametric estimation with respect to full information maximum likelihood decreases as the dimension increases. In practice, one would like to restrict the class of possible density functions to avoid the curse of dimensionality. One way of doing so is to impose the constraint that the density belongs to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the e?ciency gain of the proposed estimator compared with QMLE. --Multivariate volatility,GARCH,semiparametric efficiency,adaptivity

Econometric analysis of volatile art markets

A new heteroskedastic hedonic regression model is suggested which takes into account time-varying volatility and is applied to a blue chips art market. A nonparametric local likelihood estimator is proposed, and this is more precise than the often used dummy variables method. The empirical analysis reveals that errors are considerably non-Gaussian, and that a student distribution with time-varying scale and degrees of freedom does well in explaining deviations of prices from their expectation. The art price index is a smooth function of time and has a variability that is comparable to the volatility of stock indices.Volatility, art markets, hedonic regression, semiparametric estimation