A multivariate time series model with time varying conditional variances and covariances, but constant conditional correlations is proposed. In a multivariate regression framework, the model is readily interpreted as an extension of the Seemingly Unrelated Regression (SUR) model allowing for heteroskedasticity. Parameterizing each of the conditional variances as a univariate Generalized Autoregressive Conditional Heteroskedastic (GARCH) process, the descriptive validity of the model is illustrated for a set of five nominal European U.S. dollar exchange rates following the inception of the European Monetary System (EMS). When compared to the pre- EMS free float period, the comovements between the currenciess are found to be significantly higher over the later period. Copyright 1990 by MIT Press.

The behavior of quote arrivals and bid-ask spreads is examined for continuously recorded deutsche mark-dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid-ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread.

ABSTRACT The behavior of quote arrivals and bid‐ask spreads is examined for continuously recorded deutsche mark‐dollar exchange rate data over time, across locations, and by market participants. A pattern in the intraday spread and intensity of market activity over time is uncovered and related to theories of trading patterns. Models for the conditional mean and variance of returns and bid‐ask spreads indicate volatility clustering at high frequencies. The proposition that trading intensity has an independent effect on returns volatility is rejected, but holds for spread volatility. Conditional returns volatility is increasing in the size of the spread.

[Motivated by the implications from a stylized self-contained general equilibrium model incorporating the effects of time-varying economic uncertainty, we show that the difference between implied and realized variation, or the variance risk premium, is able to explain a nontrivial fraction of the time-series variation in post-1990 aggregate stock market returns, with high (low) premia predicting high (low) future returns. Our empirical results depend crucially on the use of "model-free," as opposed to Black-Scholes, options implied volatilities, along with accurate realized variation measures constructed from high-frequency intraday as opposed to daily data. The magnitude of the predictability is particularly strong at the intermediate quarterly return horizon, where it dominates that afforded by other popular predictor variables, such as the P/E ratio, the default spread, and the consumption-wealthratio.]

This paper provides a detailed characterization of the volatility in the deutsche mark–dollar foreign exchange market using an annual sample of five-minute returns. The approach captures the intraday activity patterns, the macroeconomic announcements, and the volatility persistence (ARCH) known from daily returns. The different features are separately quantified and shown to account for a substantial fraction of return variability, both at the intraday and daily level. The implications of the results for the interpretation of the fundamental “driving forces” behind the volatility process is also discussed.

Recent empirical evidence suggests that the interdaily volatility clustering for most speculative returns are best characterized by a slowly mean-reverting fractionally integrated process. Meanwhile, much shorter lived volatility dynamics are typically observed with high frequency intradaily returns. The present article demonstrates that, by interpreting the volatility as a mixture of numerous heterogeneous short-run information arrivals, the observed volatility process may exhibit long-run dependence. As such, the long-memory characteristics constitute an intrinsic feature of the return generating process, rather than the manifestation of occasional structural shifts. These ideas are confirmed by the authors' analysis of a one-year time series of five-minute Deutschemark-U.S. dollar exchange rates.

Multivariate tests due to Soren Johansen, as implemented by Richard T. Baillie and Tim Bollerslev (1989) and Francis X. Diebold, Javier Gardeazabal, and Kamil Yilmaz (1994), reveal mixed evidence on whether a group of exchange rates are cointegrated. Further analysis of the deviations from the cointegrating relationship suggests that it possesses long memory and may possibly be well described as a fractionally integrated process. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons.

Abstract Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the volatility, features short memory. This paper develops the first internally consistent equilibrium-based explanation for all these empirical facts. Using newly available high-frequency intraday data for the S&P 500 and the VIX volatility index, the authors show that the qualitative implications from the new theoretical continuous-time model match remarkably well with the distinct shapes and patterns in the sample autocorrelations and dynamic cross-correlations actually observed in the data.

Four foreign exchange spot rate series, recorded on an hourly basis for a six-month period in 1986 are examined. A seasonal GARCH model is developed to describe the time-dependent volatility apparent in the percentage nominal return of each currency. Hourly patterns in volatility are found to be remarkably similar across currencies and appear to be related to the opening and closing of the worlds major markets. Robust LM tests designed to deal with the extreme leptokurtosis in the data fails to uncover any evidence of misspecification or the presence of volatility spillover effects between the currencies or across markets.