在本篇論文中，我們研究隨機擴散模型非等距時間股價的平方報酬之自我相關函數的估計問題。假設股票價格服從 Heston 連續隨機波動模型，交易發生為一個卜瓦松過程。將不等距時間的資料應用前步插值法轉換成等距資料，採用其平方報酬所對應的樣本自我相關函數為估計值。我們推導出用前步插值法的樣本自我相關函數的漸近性質。最後使用模擬來驗證我們的理論結果。

In this paper, we investigate the problem of estimating the autocorrelation of squared returns modeled by diffusion processes with data observed at non-equi-spaced discrete times. Throughout, we will suppose that the stock price processes evolve in continuous time as the Heston-type stochastic volatility processes and the transactions arrive randomly according to a Poisson process. In order to estimate the autocorrelation at a fixed delay, the original non-equispaced data will be synchronized. When imputing missing data, we adopt the previous-tick
interpolation scheme. Asymptotic property of the sample autocorrelation of squared returns
based on the previous-tick synchronized data will be investigated. Simulation studies are performed
and applications to real examples are illustrated.

1 Introduction 1
2 ACF of the Heston model’s squared return 2
2.1 Heston model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 ACF of the squared returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Estimation of the Squared Return ACF 7
3.1 Previous-tick interpolation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Poisson arrival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Asymptotic property of ˆr(h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Simulation study 14
5 Conclusion 16
6 Appendix 16
References 25

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