Modelling Over-Dispersion in Price Jumps Arrivals: A Comparison Between Mixture of Poisson and Linear Hawkes Model

關於價格跳躍的過度離散程度：比較混合Poisson與線性Hawkes模型的實證研究

蔡秉真(Ping-Chen TSAI)

《中國統計學報》 59卷2期 (2021/06) Pp. 98-128

摘要

Price jumps may display some degree of clustering and this feature is typically manifested through a phenomenon known as over-dispersion in count data. The time series of counts will see a variance larger than its mean, and hence a simple Poisson null hypothesis should be rejected. Two competing models - mixture of Poisson and linear Hawkes models - are shown to be able to reproduce the over-dispersion feature, but the former by definition has a clustering parameter CP = 0, whereas the latter has CP ＞ 0. Different versions of the two models are fitted to high-frequency price jumps data, and a comparison on estimated degree of over-dispersion is made possible by using a non-parametric CP approximation from linear Hawkes model. A simulation study and a residual analysis are conducted to check the robustness of results.

關鍵字

Price jumps ； Over-dispersion ； Mixture of poisson model ； Linear hawkes model

並列摘要

價格跳躍可能會有群聚發生的特性，而這一性質通常以在計數資料中常見的過度離散的形式所表現出來，即計數資料的時間序列之變異數將大於其平均數，因此使用一簡單的Poisson模型不足以描述此性質。本文探討了兩方法－混和Poisson模型與線性Hawkes模型－兩者均能產生過度離散性，但前者的群聚係數為0，而後者的群聚係數大於0。兩模型的不同版本都配適到由高頻資料得出的價格跳躍數據中，進而比較所得出的過度離散估計值。模擬實驗與殘差分析也提供了所得出結果的可靠性。

並列關鍵字

價格跳躍 ； 過度離散 ； 混合Poisson模型 ； 線性Hawkes模型

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