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Econometric analysis of high frequency data

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Summary

Owing to enormous advances in data acquisition and processing technology the study of high (or ultra) frequency data has become an important area of econometrics. At least three avenues of econometric methods have been followed to analyze high frequency financial data: Models in tick time ignoring the time dimension of sampling, duration models specifying the time span between transactions and, finally, fixed time interval techniques. Starting from the strong assumption that quotes are irregularly generated from an underlying exogeneous arrival process, fixed interval models promise feasibility of familiar time series techniques. Moreover, fixed interval analysis is a natural means to investigate multivariate dynamics. In particular, models of price discovery are implemented in this venue of high frequency econometrics. Recently, a sound statistical theory of ‘realized volatility’ has been developed. In this framework high frequency log price changes are seen as a means to observe volatility at some lower frequency.

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References

  • Admati, A. R., Pfleiderer, P. (1988). A theory of intraday patterns: Volume and price variability. Review of Financial Studies 1 3–40.

    Article  Google Scholar 

  • Aït-Sahalia, Y., Mykland, P. A., Zhang, L. (2005). Ultra high frequency volatility estimation with dependent microstructure noise. National Bureau of Economic Research, Paper in Asset Pricing, Working Paper No. 11380.

  • Andersen, T. G., Bollerslev, T., Diebold, F. X. (2005). Parametric and nonparametric volatility measurement. In Handbook of Financial Econometrics (L. P. Hansen, Y. Aït-Sahalia, eds.), forthcoming. North Holland, Amsterdam.

    Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics 61 43–76.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association 96 42–55.

    Article  MATH  MathSciNet  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica 71 579–625.

    Article  MATH  MathSciNet  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., Wu (2004). Realized beta: Persistence and predictability. Northwestern University, Duke University and University of Pennsylvania, Manuscript.

  • Back, K. (1991). Asset pricing for general processes. Journal of Mathematical Economics 20 371–395.

    Article  MATH  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O. E., Shephard, N. (2002a). Econometric analysis of realized volatility and its use in estimation stochastic volatility models. Journal of the Royal Statistical Society, Series B 64 253–280.

    Article  MATH  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O. E., Shephard, N. (2002b). Estimating quadratic variation using realized variance. Journal of Applied Econometrics 17 457–477.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., Shephard, N. (2004). Econometric analysis of realized covariation: High frequency based covariance, regression and correlation in financial economics. Econometrica 72 885–925.

    Article  MATH  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O. E., Shephard, N. (2005). How accurate is the asymptotic approximation to the distribution of realized volatility?. In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg (D. W. F. Andrews, J. H. Stock, eds.), Cambridge University Press, Cambridge.

    Google Scholar 

  • Black, F. (1976). Studies of stock market volatility changes. Proceedings of the American Statistical Association, Business and Economic Statistics Section 177–181.

  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31 307–327.

    Article  MATH  MathSciNet  Google Scholar 

  • Bollerslev, T. (1987). A conditional heteroscedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69 542–547.

    Article  Google Scholar 

  • Dacorogna, M. M., Müller, U. A., Nagler, R. J., Olsen, R. B., Pictet, O. V. (1993). A geographical model for the daily and weekly seasonal volatility in the foreign exchange market. Journal of International Money and Finance 12 413–438.

    Article  Google Scholar 

  • de Jong, F., Nijman, T. (1997). High-frequency analysis of lead-lag relationships between financial markets. Journal of Empirical Finance 4 187–212.

    Article  Google Scholar 

  • de Jong, F., Mahieu R., Schotman P. (1998). Price discovery in the foreign exchange market: An empirical analysis of the Yen/Dmark rate. Journal of International Money and Finance 17 5–27.

    Article  Google Scholar 

  • Easley, D., O'Hara, M. (1992). Time and the process of security price adjustment. Journal of Finance 19 69–90.

    Google Scholar 

  • Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50 987–1008.

    Article  MATH  MathSciNet  Google Scholar 

  • Engle, R. F., Gonzalez-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business an Economic Statistics 9 435–459.

    Google Scholar 

  • Engle, R. F., Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation and testing. Econometrica 55 251–276.

    Article  MATH  MathSciNet  Google Scholar 

  • Engle, R. F., Russell, J. R. (1998). Autoregressive conditional duration: A new model for irregularly spaced data. Econometrica 66 1127–1162.

    Article  MATH  MathSciNet  Google Scholar 

  • Engle, R. F., Russell, J. R. (2005). Analysis of high frequency financial data. In Handbook of Financial Econometrics (L. P. Hansen, Y. Aït-Sahalia, eds.), forthcoming. North Holland, Amsterdam.

    Google Scholar 

  • Frijns, B., Schotman, P. (2003) Price discovery in tick time. Limburg Institute of Financial Economics LIFE, Working Paper 03-024.

  • Ghysels, E., Gouriéroux, C., Jasiak, J. (1997). Market time and asset price movements: Theory and estimation. In Statistics in Finance (D. Hand, S. Jacka, eds.), 307–332. Edward Arnold London.

    Google Scholar 

  • Goodhart, C. A. E., O'Hara, M. (1997). High frequency data in financial markets: Issues and applications. Journal of Empirical Finance 4 73–114.

    Article  Google Scholar 

  • Goodhart, C. A. E., Hall, S. G., Henry, S. G. B., Pesaran B. (1993). News effects in a high frequency model of the Sterling-Dollar exchange rate. Journal of Applied Econometrics 8 1–13.

    Google Scholar 

  • Grammig, J., Melvin, M., Schlag, C. (2005). Internationally cross-listed stock prices during overlapping trading hours: Price discovery and exchange rate effects. Journal of Empirical Finance 12 139–164.

    Article  Google Scholar 

  • Granger, C. W. J. (1980). Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control 2 329–352.

    Article  MathSciNet  Google Scholar 

  • Hansen, P. R., Lunde, A. (2004). An unbiased measure of realized variance. Brown University, Working Paper.

  • Harris, F. H. DeB., Shoesmith, G. L., McInish, T. H., Wood, R. A. (1995). Cointegration, error correction, and price discovery on informationally linked security markets. Journal of Financial and Quantitative Analysis 30 563–579.

    Article  Google Scholar 

  • Hasbrouck, J. (1995). One security, many markets, determining the contributions to price discovery. Journal of Finance 50 1175–1199.

    Article  Google Scholar 

  • Herwartz, H. (2001). Investigating the JPY/DEM rate: Arbitrage opportunities and a case for asymmetry. International Journal of Forecasting 17 231–245.

    Article  Google Scholar 

  • Huang R. D. (2002). The quality of ECN and market maker quotes. Journal of Finance 57 1285–1319.

    Article  Google Scholar 

  • Johansen, S. (1995). Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Jones R. H. (1980). Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics 22 389–395.

    Article  MATH  MathSciNet  Google Scholar 

  • Jordà, Ò., Marcellino, M. (2003) Modeling high-frequency foreign exchange data dynamics. Macroeconomic Dynamics 7 618–635.

    Article  MATH  Google Scholar 

  • Karpoff, J. M. (1987). The relation between price changes and trading volume: A survey. Journal of Financial and Quantitative Analysis 22 109–26.

    Article  Google Scholar 

  • Kohn, R., Ansley, C. F. (1986). Estimation, prediction, and interpolation for ARIMA models with missing data. Journal of the American Statistical Association 81 751–761.

    Article  MATH  MathSciNet  Google Scholar 

  • Lo, M. C., Zivot, E. (2001). Threshold cointegration and nonlinear adjustment to the low of one price. Macroeconomic Dynamics 5 533–576.

    MATH  Google Scholar 

  • Lütkepohl, H. (1991). Introduction to Multiple Time Series Analysis. Springer, Berlin.

    Google Scholar 

  • Nelson, D. B. (1990). ARCH models as diffusion approximations. Journal of Econometrics 45 7–39.

    Article  MATH  MathSciNet  Google Scholar 

  • Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4 141–183.

    Article  MathSciNet  Google Scholar 

  • Oomen, R. C. (2003). Three Essays on the Econometric Analysis of High Frequency Financial Data. European University Institute, Ph. D. thesis.

  • Protter, P. (1990). Stochastic Integration and Differential Equations: A New Approach. Springer, New York.

    Google Scholar 

  • Schreiber, P. S., Schwartz, R. A. (1986). Price discovery in securities markets. Journal of Portfolio Management 12 43–48.

    Google Scholar 

  • Schwert, G. W. (1989) Why does stock market volatility change over time? Journal of Finance 44 1115–1153.

    Article  Google Scholar 

  • Schwert, G. W. (1990). Stock volatility and the crash of '87. Journal of Financial Studies 3 77–102.

    Article  Google Scholar 

  • Taylor, S. J. (1986). Modeling financial time series. John Wiley, Chichester.

    Google Scholar 

  • Teräsvirta T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89 208–218.

    Article  Google Scholar 

  • White, H. (1984). Asymptotic Theory for Econometricians. Academic Press, Orlando.

    Google Scholar 

  • Zhang, L., Mykland, P. A., Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association (forthcoming).

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Herwartz, H. Econometric analysis of high frequency data. Allgemeines Statistisches Arch 90, 89–104 (2006). https://doi.org/10.1007/s10182-006-0223-3

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