Articlegreen1994

Multivariate Stochastic Variance Models

Andrew C. Harvey · Esther Ruiz · Neil Shephard

1,367 citations0/0 files storedThe Review of Economic Studies

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Complex Systems and Time Series Analysis

Abstract

Changes in variance, or volatility, over time can be modelled using the approach based on autoregressive conditional heteroscedasticity (ARCH). However, the generalizations to multivariate series can be difficult to estimate and interpret. Another approach is to model variance as an unobserved stochastic process. Although it is not easy to obtain the exact likelihood function for such stochastic variance models, they tie in closely with developments in finance theory and have certain statistical attractions. This article sets up a multivariate model, discusses its statistical treatment and shows how it can be modified to capture common movements in volatility in a very natural way. The model is then fitted to daily observations on exchange rates.

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References

1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1988Statistical analysis of cointegration vectors 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1992ARCH modeling in finance 1990Modelling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized Arch Model 1988A Capital Asset Pricing Model with Time-Varying Covariances 1987A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return

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2003Forecasting Volatility in Financial Markets: A Review 2002Bayesian Analysis of Stochastic Volatility Models 1997An Overview of Value at Risk 2010Volatility forecast comparison using imperfect volatility proxies 2002Range‐Based Estimation of Stochastic Volatility Models 19965 Stochastic volatility

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