Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics

This paper analyses multivariate high frequency financial data using realised covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis and covariance. It will be based on a fixed interval of time (e.g. a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions and covariances change through time. In particular we provide confidence intervals for each of these quantities.

[1]  R. Fisher 014: On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. , 1921 .

[2]  F. David,et al.  Tables of the Ordinates and Probability Integral of the Distribution of the Correlation Coefficient in Small Samples , 1938 .

[3]  J. Lintner THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[4]  J. Schmee An Introduction to Multivariate Statistical Analysis , 1986 .

[5]  F. Diebold,et al.  The dynamics of exchange rate volatility: a multivariate latent factor ARCH model , 1986 .

[6]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[7]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[8]  P. Protter Stochastic integration and differential equations : a new approach , 1990 .

[9]  Kerry Back,et al.  Asset pricing for general processes , 1991 .

[10]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[11]  D. Florens-zmirou On estimating the diffusion coefficient from discrete observations , 1993, Journal of Applied Probability.

[12]  Dean P. Foster,et al.  Continuous Record Asymptotics for Rolling Sample Variance Estimators , 1994 .

[13]  N. Shephard Statistical aspects of ARCH and stochastic volatility , 1996 .

[14]  H. Luetkepohl The Handbook of Matrices , 1996 .

[15]  M. Pitt,et al.  Time Varying Covariances: A Factor Stochastic Volatility Approach (with discussion , 1998 .

[16]  T. Bollerslev,et al.  ANSWERING THE SKEPTICS: YES, STANDARD VOLATILITY MODELS DO PROVIDE ACCURATE FORECASTS* , 1998 .

[17]  T. Andersen THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[18]  F. Comte,et al.  Long memory in continuous‐time stochastic volatility models , 1998 .

[19]  K. Demeterfi,et al.  A Guide to Volatility and Variance Swaps , 1999 .

[20]  F. Diebold,et al.  The Distribution of Exchange Rate Volatility , 1999 .

[21]  G. Mason,et al.  Beyond Merton’s Utopia: Effects of Non-normality and Dependence on the Precision of Variance Estimates Using High-frequency Financial Data , 2000 .

[22]  N. Shephard,et al.  Econometric analysis of realised volatility and its use in estimating stochastic volatility models , 2000 .

[23]  N. Meddahi,et al.  Série Scientifique Scientific Series Temporal Aggregation of Volatility Models , 2022 .

[24]  R. Gencay,et al.  An Introduc-tion to High-Frequency Finance , 2001 .

[25]  Francis X. Diebold,et al.  Modeling and Forecasting Realized Volatility , 2001 .

[26]  N. Shephard,et al.  Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics , 2001 .

[27]  F. Diebold,et al.  The distribution of realized stock return volatility , 2001 .

[28]  N. Shephard,et al.  Realised power variation and stochastic volatility models , 2003 .

[29]  S. Howison,et al.  On the pricing and hedging of volatility derivatives , 2004 .

[30]  N. Meddahi,et al.  A theoretical comparison between integrated and realized volatility , 2002 .

[31]  N. Shephard,et al.  Estimating quadratic variation using realized variance , 2002 .