基于高频数据的PGARCH模型的拟极大指数似然估计
Quasi Maximum Exponential Likelihood Estimator of PGARCH Model Based on High Frequency Data
DOI: 10.12677/SA.2023.124111, PDF,    科研立项经费支持
作者: 黄丽燕, 张兴发：广州大学经济与统计学院，广东 广州；王珞谦：华南师范大学附属中学国际部，广东 广州；张本霖：江苏省淮安市车桥中学，江苏 淮安
关键词: PGARCH；高频数据；QMELE；波动率代表；PGARCH； High-Frequency Data； QMELE； Volatility Proxy
摘要: 作为GARCH族模型的重要拓展模型之一，PGARCH模型的估计往往采用基于日度数据的拟极大似然估计方法。为了探究高频信息对PGARCH模型估计的影响，基于Visser (2011)的研究，本文使用波动率代表模型来整合高频数据，并使用拟极大指数似然估计方法(QMELE)对PGARCH模型进行估计，同时探究了拟极大指数似然估计的渐近性质和模型估计效率的评判标准。模拟研究和实证分析证实，基于高频数据的拟极大指数似然估计有效地提升了PGARCH模型的参数估计精度，这说明基于高频数据的拟极大似然指数估计具有一定的应用价值。
Abstract: As one of the important extended models of the GARCH family model, it is more common to use quasi maximum likelihood estimator to fit PGARCH model with daily data. Referring to Visser (2011), this article applies volatility representative models to integrate high-frequency data, and then uses the quasi maximum exponential likelihood estimator (QMELE) to fit the PGARCH model, so that we can explore the impact of high-frequency information on the estimation of the PGARCH model. Meanwhile, we establish the asymptotic properties of QMELE and the evaluation criteria for model estimation efficiency. Simulation research and empirical analysis have confirmed that QMELE with high-frequency data effectively improves the parameter estimation accuracy of the PGARCH model, which indicates that the QMELE based on high-frequency data has a certain application value.
文章引用：黄丽燕, 张兴发, 王珞谦, 张本霖. 基于高频数据的PGARCH模型的拟极大指数似然估计[J]. 统计学与应用, 2023, 12(4): 1085-1095. https://doi.org/10.12677/SA.2023.124111

参考文献

[1] Engle, R.F. (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987-1007.
[Google Scholar] [CrossRef] 
[2] Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.
[Google Scholar] [CrossRef] 
[3] Higgins, M.L. and Bera, A.K. (1992) A Class of Nonlinear ARCH Models. International Economic Review, 33, 137-158.
[Google Scholar] [CrossRef] 
[4] Ding, Z., Granger Clive, W.J. and Engle, R.F. (1993) A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance, 1, 83-106.
[Google Scholar] [CrossRef] 
[5] Diebolt, J. and Guégan, D. (1994) Probabilistic Properties of the Béta-ARCH Model. Post-Print, 4, 71-87.
[6] Hwang, S.Y. and Kim, T.Y. (2004) Power Transformation and Threshold Modeling for ARCH Innovations with Applications to Tests for ARCH Structure. Stochastic Processes and Their Applications, 110, 295-314.
[Google Scholar] [CrossRef] 
[7] Pan, J., Wang, H. and Tong, H. (2007) Estimation and Tests for Power-Transformed and Threshold GARCH Models. Journal of Econometrics, 142, 352-378.
[Google Scholar] [CrossRef] [PubMed]
[8] An, H.Z., Chen, M. and Huang, F.C. (1997) The Geometric Ergodicity and Existence of Moments for a Class of Non-Linear Time Series Models. Statistics & Probability Letters, 31, 213-224.
[Google Scholar] [CrossRef] 
[9] Visser, M.P. (2011) GARCH Parameter Estimation Using High-Frequency Data. Journal of Financial Econometrics, 9, 162-197.
[Google Scholar] [CrossRef] 
[10] 黄金山. 基于高频数据的GARCH模型的参数估计[D]: [博士学位论文]. 合肥: 中国科学技术大学, 2013.
[11] Huang, J., Wu, W., Chen, Z. and Zhou, J.-J. (2015) Robust M-Estimate of GJR Model with High Frequency Data. Acta Mathematicae Applicatae Sinica, 31, 591-606.
[Google Scholar] [CrossRef] 
[12] Fan, P.-Y., Wu, S.-X., Zhao, Z.-L. and Chen, M. (2017) M-Estimation for Periodic GARCH Model with High-Frequency Data. Acta Mathematicae Applicatae Sinica, English Series, 33, 717-730.
[Google Scholar] [CrossRef] 
[13] 吴思鑫, 冯牧, 张虎, 陈敏. 基于高频数据的非平稳GARCH(1,1)模型的拟极大指数似然估计[J]. 中国科学: 数学, 2018, 48(3): 443-456.
[14] 张兴发, 李元. 一类GARCH-M模型的拟极大指数似然估计[J]. 应用数学学报, 2016, 36(3): 321-333.
[15] 张童巍. 若干广义自回归条件异方差模型的统计推断[D]: [博士学位论文]. 长春: 吉林大学, 2022.

为你推荐