### 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 several common factors plus some additive error ('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 unobservable 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.

Original language | English |
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Pages (from-to) | 140-150 |

Number of pages | 11 |

Journal | Quantitative Finance |

Volume | 4 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 Apr |

Externally published | Yes |

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### ASJC Scopus subject areas

- Economics, Econometrics and Finance(all)

### Cite this

**A discrete-time model of high-frequency stock returns.** / Hayashi, Takaki.

Research output: Contribution to journal › Article

*Quantitative Finance*, vol. 4, no. 2, pp. 140-150. https://doi.org/10.1088/1469-7688/4/2/003

}

TY - JOUR

T1 - A discrete-time model of high-frequency stock returns

AU - Hayashi, Takaki

PY - 2004/4

Y1 - 2004/4

N2 - 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 several common factors plus some additive error ('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 unobservable 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.

AB - 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 several common factors plus some additive error ('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 unobservable 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.

UR - http://www.scopus.com/inward/record.url?scp=2442623479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442623479&partnerID=8YFLogxK

U2 - 10.1088/1469-7688/4/2/003

DO - 10.1088/1469-7688/4/2/003

M3 - Article

AN - SCOPUS:2442623479

VL - 4

SP - 140

EP - 150

JO - Quantitative Finance

JF - Quantitative Finance

SN - 1469-7688

IS - 2

ER -