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Random aggregation with applications in high‐frequency finance


  • Ruey S. Tsay
  • Jin‐Huei Yeh


In this paper we consider properties of random aggregation in time series analysis. For application, we focus on the problem of estimating the high-frequency beta of an asset return when the returns are subject to the effects of market microstructure. Specifically, we study the correlation between intraday log returns of two assets. Our investigation starts with the effect of non‐synchronous trading on intraday log returns when the underlying return series follows a stationary time series model. This is a random aggregation problem in time series analysis. We also study the effect of non‐synchronous trading on the covariance of two asset returns. To overcome the impact of non‐synchronous trading, we use Markov chain Monte Carlo methods to recover the underlying log return series based on the observed intraday data. We then define a high‐frequency beta based on the recovered log return series and propose an efficient method to estimate the measure. We apply the proposed analysis to many mid‐ or small‐cap stocks using the Trade and Quote Data of the New York Stock Exchange, and discuss implications of the results obtained. Copyright (C) 2010 John Wiley & Sons, Ltd.

Suggested Citation

  • Ruey S. Tsay & Jin‐Huei Yeh, 2011. "Random aggregation with applications in high‐frequency finance," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(1), pages 72-103, January.
  • Handle: RePEc:jof:jforec:v:30:y:2011:i:1:p:72-103

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    References listed on IDEAS

    1. Nieto, Fabio H. & Guerrero, Victor M., 1995. "Kalman filter for singular and conditional state-space models when the system state and the observational error are correlated," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 303-310, March.
    2. Víctor Guerrero & Fabio Nieto, 1999. "Temporal and contemporaneous disaggregation of multiple economic time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 459-489, December.
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    4. repec:adr:anecst:y:1987:i:6-7 is not listed on IDEAS
    5. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    6. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    7. F. Javier Fernandez Macho & Andrew C. Harvey & James H. Stock, 1987. "Forecasting and Interpolation Using Vector Autoregressions with Common Trends," Annals of Economics and Statistics, GENES, issue 6-7, pages 279-287.
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