经验贝叶斯单位根检验
摘要
为避免经典贝叶斯检验中先验分布函数对检验的影响,文章应用经验贝叶斯方法对一阶自回归模型作单位根检验,通过收集历史数据,应用非参数经验贝叶斯方法,推导出贝叶斯决策函数。Monte-Carlo模拟显示,经验贝叶斯方法与经典统计方法相比,经验贝叶斯方法有较高的势;与传统贝叶斯方法相比,经验贝叶斯方法作单位根检验比传统的贝叶斯方法有更高的势。文章最后提供了一个金融实例,收集了NASDAQ综合指数从2015年9月21至2016年7月6日的数据,对其收益率作单位根检验,验证收益率序列是一个平稳过程。
引文
[1]David A.Dickey,Wayne A.Fuller.Distribution of the Estimators for Autoregressive Time Series with a Unit R oot[J].Journal of the American Statistical Association,1979,74(366):427-431.
[2]Dickey D A,Fuller W A.Likelihood R atio Statistics for Autoregressive Time Series with a Unit R oot[J].Econometrica,1981,49(4):1057-1072.
[3]Sims C A.Bayesian skepticism on unit root econometrics[J].Journal of Economic Dynamics&Control,1988,12(2-3):463-474.
[4]Dejong D N,Whiteman C H.R econsidering‘trends and random walks in macroeconomic time series’[J].Journal of Monetary Economics,1991,28(2):221-254.
[5]Schotman P,Dijk H V.A Bayesian analysis of the unit root in real exchange rates[J].Journal of Econometrics,2004,49(1-2):195-238.
[6]Sims C A,Uhlig H.Understanding Unit R ooters:A Helicopter Tour[J].Discussion Paper,1988,59(6):1591-1599.
[7]R obbins H.An Empirical Bayes Approach to Statistics[J].Matematika,1956,35(1):133-140.
[8]R obbins H.The Empirical Bayes Approach to Statistical Decision Problems[J].Annals of Mathematical Statistics,1964,35(1):1-20.
[9]Johns M V.Convergence R ates For Empiical Bayes Two-Action Problems I.Discrete Case.[J].Annals of Mathematical Statistics,1971,42(5):1521-1539.
[10]Johns M V.Convergence R ates For Empirical Bayes Two-Action Problems II.Continuous Case.[J].Annals of Mathematical Statistics,1972,43(3):934-947.
[11]Lubrano M.Testing for unit roots in a Bayesian framework[J].Journal of Econometrics,1995,69(1):81-109.
[12]Wei L.Convergence rates of empirical Bayesian estimation in a class of linear models[J].Statistica Sinica,1998,8(2):589-605.
[13]Wei L,Chen J.Empirical Bayes estimation and its superiority for two-way classification model[J].Statistics&Probability Letters,2003,63(2):165-175.
[2]Dickey D A,Fuller W A.Likelihood R atio Statistics for Autoregressive Time Series with a Unit R oot[J].Econometrica,1981,49(4):1057-1072.
[3]Sims C A.Bayesian skepticism on unit root econometrics[J].Journal of Economic Dynamics&Control,1988,12(2-3):463-474.
[4]Dejong D N,Whiteman C H.R econsidering‘trends and random walks in macroeconomic time series’[J].Journal of Monetary Economics,1991,28(2):221-254.
[5]Schotman P,Dijk H V.A Bayesian analysis of the unit root in real exchange rates[J].Journal of Econometrics,2004,49(1-2):195-238.
[6]Sims C A,Uhlig H.Understanding Unit R ooters:A Helicopter Tour[J].Discussion Paper,1988,59(6):1591-1599.
[7]R obbins H.An Empirical Bayes Approach to Statistics[J].Matematika,1956,35(1):133-140.
[8]R obbins H.The Empirical Bayes Approach to Statistical Decision Problems[J].Annals of Mathematical Statistics,1964,35(1):1-20.
[9]Johns M V.Convergence R ates For Empiical Bayes Two-Action Problems I.Discrete Case.[J].Annals of Mathematical Statistics,1971,42(5):1521-1539.
[10]Johns M V.Convergence R ates For Empirical Bayes Two-Action Problems II.Continuous Case.[J].Annals of Mathematical Statistics,1972,43(3):934-947.
[11]Lubrano M.Testing for unit roots in a Bayesian framework[J].Journal of Econometrics,1995,69(1):81-109.
[12]Wei L.Convergence rates of empirical Bayesian estimation in a class of linear models[J].Statistica Sinica,1998,8(2):589-605.
[13]Wei L,Chen J.Empirical Bayes estimation and its superiority for two-way classification model[J].Statistics&Probability Letters,2003,63(2):165-175.