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A duscrete-time model of high-frequency stock returns

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  • Takaki Hayashi

Abstract

A model of intraday financial time series is developed. The model is a dynamic factor model consisting of two equations. First, a rate of return of a 'stock' in a single day is assumed to be generated by serveral common factors plus some additive erros ('intraday equation'). Secondly, the joint distribution of those common factors is assumed to depend on the hidden state of the day, which fluctuates according to a Markov chain ('day-by-day equation'). Together the equations compose a hidden Markov model. We investigate properties of the model. Among them is a central limit theorem for cumulative returns, which agrees with the well-known empirical phenomenon in the stock markets that the distributions of longer-horizon returns are closer to the normal. We propose a two-step procedure consisting of the method of principal components and the EM algorithm to estimate the model parameters as well as the unboservable states. In addition, we propose a procedure for predicting intraday returns. Finally, the model is fitted to empirical data, the Standard&Poors 500 Index 5 min return data, to see if the model is capable of describing intraday movements of the index.

Suggested Citation

  • Takaki Hayashi, 2004. "A duscrete-time model of high-frequency stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 140-150.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:2:p:140-150
    DOI: 10.1080/14697680400000018
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    Cited by:

    1. Bolano, Danilo & Berchtold, André, 2016. "General framework and model building in the class of Hidden Mixture Transition Distribution models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 131-145.

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