Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (4): 68-78.doi: 10.16088/j.issn.1001-6600.2020091601

Previous Articles     Next Articles

Daily GARCH Model Estimation Using High Frequency Data

LI Lili1, ZHANG Xingfa1,2*, LI Yuan1,2, DENG Chunliang1   

  1. 1. School of Economics and Statistics, Guangzhou University, Guangzhou Guangdong 510006, China;
    2. Lingnan Research Institute of Statistical Science, Guangzhou University, Guangzhou Guangdong 510006, China
  • Revised:2020-10-10 Online:2021-07-25 Published:2021-07-23

PDF (PC)

306

Abstract: This paper studies the daily GARCH model estimation by introducing the intraday high frequency data. Existing results assume that the constant term in GARCH equation is given, which restricts the extensive applications of the method. In this paper, based on the framework of GARCH(1, 1) model, two estimators for all model parameters, together with the according asymptotic properties, are discussed. A criterion is given to choose the optimal volatility proxy. Simulation studies show that the estimators have smaller asymptotic standard deviation and the empirical study gives a specific application.

Key words: GARCH model, intraday high frequency data, quasi maximum likelihood estimation

CLC Number: 

  • O212.1
[1]ENGLE R F. Autoregressiveconditional heteroscedasticity with estimates of the variance of United Kingdom inflation[J]. Econometrica, 1982, 50(4): 987-1008.
[2]BOLLERSLEV T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 21(3): 307-328.
[3]ENGLE R F,BOLLERSLEV T. Modelling the persistence of conditional variances[J]. Econometric Reviews,1986, 5(1): 1-50.
[4]NELSON D B. Conditional heteroskedasticity in asset returns: a new approach[J]. Modelling Stock Market Volatility, 1991, 59(2): 347-370.
[5]GLOSTEN L, JAGANNATHAN R, RUNKLE D. On the relation between the expected value and the volatility of the nominal excess return on stocks[J]. Journal of Finance, 1993, 48: 1779-1801.
[6]BOLLERSLEV T, GHYSELS E. Periodic autoregressive conditional heteroskedasticity[J]. Journal of Business a Economic Statistics, 1996, 14(2): 139-151.
[7]BAILLIE R T, BOLLERSLEV T, MIKKELSEN H O. Fractionally integrated generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1996, 74(1): 3-30.
[8]BERKES I, ATH L H, KOKOSZKA P. GARCH processes: structure and estimation[J]. Bernoulli, 2003, 9(2): 201-227.
[9]FRANCQ C, ZAKOIAN J. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes[J]. Bernoulli, 2004, 10(4): 605-637.
[10]HALL P, YAO Q. Inference in ARCH and GARCH models with heavy-tailed errors[J]. Econometrica, 2003, 71(1): 285-317.
[11]BERKES I, HORVATH L. The efficiency of the estimators of the parameters in GARCH processes[J]. Annals of Statistics, 2004, 32(2): 633-655.
[12]邹建军, 张宗益, 秦拯. GARCH模型在计算我国股市风险价值中的应用研究[J]. 系统工程理论与实践, 2003, 23(5): 20-25,135.
[13]王娟. 国际市场现货价格与期货价格指数波动的GARCH族分析[J]. 统计与决策, 2015(16): 160-162.
[14]孙柏, 李小静. 基于GARCH 类模型的人民币汇率非线性依赖关系研究[J]. 财经理论与实践, 2016, 37(1): 41-47.
[15]王朋吾. 基于GARCH(1,1)模型的粮食市场价格波动溢出效应比较[J]. 统计与决策, 2017(16): 138-141.
[16]黄宗远, 沈小燕. ARCH模型在我国金融市场的应用情况研究[J]. 广西师范大学学报(哲学社会科学版), 2007, 43(1): 21-25.
[17]VISSER M P. GARCH parameter estimation using high-frequency data[J]. Journal of Financial Econometrics, 2011, 9(1): 162-197.
[18]HUANG J S, WU W Q, CHEN Z, et al. Robust M-estimate of GJR model with high frequency data[J]. Acta Mathematicae Applicatae Sinica, 2015, 31(3): 591-606.
[19]樊鹏英, 兰勇, 陈敏. 高频数据下基于PGARCH模型的VaR估计方法及应用[J]. 系统工程理论与实践, 2017, 37(8): 2052-2059.
[20]吴思鑫, 冯牧, 张虎, 等. 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.
[21]WANG M, CHEN Z, WANG C D. Composite quantile regression for GARCH models using high-frequency data[J]. Econometrics and Statistics, 2018, 7: 115-133.
[22]STRAUMANN D, MIKOSCH T. Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: a stochastic recurrence equations approach[J]. Annals of Statistics, 2006, 34(5): 2449-2495.
[1] LIN Song, YIN Changming. Asymptotic Properties of Estimation of Penalized Generalized Estimating Equations for Two Stage Logit Models [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 126-130.
[2] HE Lin, YANG Shanchao. Asymptotic Variance Edge Frequency Polygons Estimator for α-Mixing Random Fields [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(1): 88-94.
[3] LEI Qingzhu,QIN Yongsong,LUO Min. Empirical Bayes Estimation and Test for Scale ExponentialFamilies under Strong Mixing Samples [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(3): 63-74.
[4] ZHANG Junjian, LAI Tingyu, YANG Xiaowei. Bayesian Empirical Likelihood Estimation on VaR and ES [J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(4): 38-45.
[5] ZHANG Xin-cheng, ZHANG Jun-jian, ZHAN Huan. A Goodness-of-fit Test Based on Empirical Euclidean Likelihood and Vertical Density Representation [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(4): 60-65.
[6] DU Xue-song, BIN Shi-yu, LIN Yong, TANG Zhang-sheng, ZHANG Yong-de, ZENG Lan, YANG Hui-zan, CHEN Zhong. Cold Tolerance Determination Model of Tilapia Based on ULCIZ and SIT [J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(4): 134-139.
[7] ZHANG Jun-jian, ZHAN Huan, YAN Zhen. A Goodness of Fit Test Based on Empirical Euclidean Likelihood [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(3): 30-35.
[8] ZHANG Jun-jian, YANG Xiu-qin. Minimum Weighted KS Estimate [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(4): 54-58.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] DAI Yunfei, ZHU Longji. Research on Switch Quasi-Z Source Bidirectional DC/DC Converter Applied to Super Capacitor Energy Storage[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(3): 11 -19 .
[2] LÜ Huilian, HU Weiping. Research on Speech Emotion Recognition Based on End-to-End Deep Neural Network[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(3): 20 -26 .
[3] HU Jinming, WEI Duqu. Hybrid Projective Synchronization of Fractional-order PMSM with Different Orders[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 1 -8 .
[4] WU Kangkang, ZHOU Peng, LU Ye, JIANG Dan, YAN Jianghong, QIAN Zhengcheng, GONG Chuang. FIR Equalizer Based on Mini-batch Gradient Descent Method[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 9 -20 .
[5] LIU Dong, ZHOU Li, ZHENG Xiaoliang. A Very Short-term Electric Load Forecasting Based on SA-DBN[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 21 -33 .
[6] ZHANG Weibin, WU Jun, YI Jianbing. Research on Feature Fusion Controlled Items Detection Algorithm Based on RFB Network[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 34 -46 .
[7] WANG Jinyan, HU Chun, GAO Jian. An OBDD Construction Method for Knowledge Compilation[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 47 -54 .
[8] LU Miao, HE Dengxu, QU Liangdong. Grey Wolf Optimization Algorithm Based on Elite Learning for Nonlinear Parameters[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 55 -67 .
[9] LI Songtao, LI Qunhong, ZHANG Wen. Co-dimension-two Grazing Bifurcation and Chaos Control of Three-degree-of-freedom Vibro-impact Systems[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 79 -92 .
[10] ZHAO Hongtao, LIU Zhiwei. Decompositions of λ-fold Complete Bipartite 3-uniform Hypergraphs λK(3)n,n into Hypergraph Triangular Bipyramid[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 93 -98 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd