基于Spatial AIC准则的空间自回归模型变量选择研究
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摘要
变量选择直接决定着空间计量经济模型的有效程度与实证研究结果。为有效解决空间自回归模型(即SAR模型)的变量选择问题,本文利用Kullback-Laible信息量最大化,把AIC准则运用到SAR模型构建,推导出Spatial AIC统计量,提出Spatial AIC准则。然后利用统计理论证明Spatial AIC准则选择SAR模型变量的渐近最优性;利用蒙特卡洛模拟方法,比较Spatial AIC准则、经典AIC准则和Lasso方法用于SAR模型变量选择的有限大样本性质;利用空间相关的沪深300成分股股票收益率数据,采用Spatial AIC准则和Lasso方法,分别构建股票收益率财务因素的空间自相关模型,实证比较其相对有效性。三种结果均表明Spatial AIC准则能够更好地解决SAR模型变量选择问题。
Variable selection directly determines the effectiveness of spatial econometric models and empirical findings. Combining the classical linear Akaike Information Criterion(AIC) with Spatial Autoregressive Model(SAR), this paper proposed a method for SAR variable selection — Spatial AIC. We firstly used Kullback-Laible information to obtain the Spatial AIC, and then proved that Spatial AIC is asymptotically optimal in SAR variable selection process. We also analyzed the finite sample property differences of Spatial AIC, classical AIC and Lasso by Monte Carlo simulation. Finally, on the basis of verifying the spatial correlation of stock returns, we used Spatial AIC and Lasso to study the financial factors affecting stock returns. The results showed Spatial AIC is more effective in solving SAR variable selection.
Variable selection directly determines the effectiveness of spatial econometric models and empirical findings. Combining the classical linear Akaike Information Criterion(AIC) with Spatial Autoregressive Model(SAR), this paper proposed a method for SAR variable selection — Spatial AIC. We firstly used Kullback-Laible information to obtain the Spatial AIC, and then proved that Spatial AIC is asymptotically optimal in SAR variable selection process. We also analyzed the finite sample property differences of Spatial AIC, classical AIC and Lasso by Monte Carlo simulation. Finally, on the basis of verifying the spatial correlation of stock returns, we used Spatial AIC and Lasso to study the financial factors affecting stock returns. The results showed Spatial AIC is more effective in solving SAR variable selection.
引文
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[7]刘明,赵彦云.基于投入要素的中国制造业省域空间溢出效应:测度与实证[J].数理统计与管理,2018,37(1):122-134.
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[18] Fernandez V. Spatial linkages in international financial markets[J]. Quantitative Finance, 2011,11(2):237-245.
[19]文海涛,倪晓萍.我国上市公司财务指标与股价相关性实证分析[J].数量经济技术经济研究,2003,(11):118-122.
[20]张媛媛.我国创业板上市公司财务指标与股票收益率的关联性研究[D].华东政法大学,2016.
[21]张玉华,宋韫埘,张元庆.基于空间面板数据模型的股票收益率影响因素分析[J].中国软科学,2016,(5):172-183.
[22] Lee L, Liu X. Efficient GMM estimation of high order spatial autoregressive models with autoregressive disturbances[J]. Econometric Theory, 2010, 26(1):187-230.
[23] Kelejian H H, Prucha I R. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances[J]. Journal of Econometrics, 2010, 157(1):53-67.
[2] Kelejian H H, Prucha I R. A generalized moments estimator for the autoregressive parameter in a spatial model[J]. International Economic Review, 1999, 40(2):509-533.
[3] Kelejian H H, Prucha I R. A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances[J]. Journal of Real Estate Finance and Economics, 1998, 17(1):99-121.
[4] Lee L. Asymptotic distributions of quasi-maximum likelihood estimators for spatial econometric models[J]. Econometrica, 2004, 72(6):1899-1925.
[5]方丽婷.空间滞后模型的贝叶斯估计[J].统计研究,2014, 31(5):102-106.
[6]张红历,梁银鹤,杨维琼.市场潜能、预期收入与跨省人口流动—基于空间计量模型的分析[J].数理统计与管理,2016, 35(5):868-880.
[7]刘明,赵彦云.基于投入要素的中国制造业省域空间溢出效应:测度与实证[J].数理统计与管理,2018,37(1):122-134.
[8]王大荣,张忠占.线性回归模型中变量选择方法综述[J].数理统计与管理,2010, 29(4):615-627.
[9] Akaike H. Information theory and the maximum likelihood principle[A]. 2nd international symposium on information theory[C]. Budapest, 1973:267-281.
[10] Schwarz G. Estimating the dimension of a model[J]. Annals of Statistics, 1976, 6(2):461-464.
[11] Akaike H. On entropy maximization principle[J]. Applications of Statistics, 1977, 2(1):27-41.
[12] Nishii R. Asymptotic properties of criteria for selection of variables in multiple regression[J]. Annal of Statistics, 1984, 12(2):758-765.
[13] Shao J. An asymptotic theory for linear model selection[J]. Statistica Sinica, 1997, 7:211-264.
[14] Wang D R, Zhang Z Z. Variable selection in joint generalized linear model[J]. Chinese Journal of Applied Probability and Statistics, 2009, 25(3):245-256.
[15]陈心洁,林鹏,邹国华.线性混合效应模型的FIC选择准则[J].统计研究,2015, 32(3):100-103.
[16] Li K C. Asymptotic optimality for Cp, CL, Cross-validation and generalized cross-validation:discrete index set[J]. Annals of Statistics, 1987, 15(3):958-975.
[17] Tibshirani R. Regression shrinkage and selection via the Lasso[J]. Journal of the Royal Statistical Society, 1996, 1(58):267-288.
[18] Fernandez V. Spatial linkages in international financial markets[J]. Quantitative Finance, 2011,11(2):237-245.
[19]文海涛,倪晓萍.我国上市公司财务指标与股价相关性实证分析[J].数量经济技术经济研究,2003,(11):118-122.
[20]张媛媛.我国创业板上市公司财务指标与股票收益率的关联性研究[D].华东政法大学,2016.
[21]张玉华,宋韫埘,张元庆.基于空间面板数据模型的股票收益率影响因素分析[J].中国软科学,2016,(5):172-183.
[22] Lee L, Liu X. Efficient GMM estimation of high order spatial autoregressive models with autoregressive disturbances[J]. Econometric Theory, 2010, 26(1):187-230.
[23] Kelejian H H, Prucha I R. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances[J]. Journal of Econometrics, 2010, 157(1):53-67.