基于傅里叶变换的时变参数回归模型:估计、设定检验和实证应用
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摘要
回归模型参数的时变性会严重影响模型的拟合程度和预测效果。基于卡尔曼滤波的时变参数模型需要估计很多的参数,因而造成效率损失。基于傅里叶变换建立一个简单的变系数回归模型,给出估计方法并证明参数收敛于真实值,并给出了模型设定检验的方法。通过蒙特卡洛模拟表明:新建立的时变参数回归模型能很好地处理连续的、随机的和跳跃的时变参数模型。最后,将新建立的方法应用于研究股市联动关系,发现:不考虑系数的时变性可能给出误导性结论,考虑时变性能捕捉更为丰富的联动特征。
The time-varying characteristics of parameters in regression model can deteriorate the fitness and forecasting.The time-varying model based on Kalman?filtering has many parameters to estimate,which can lead to inefficiency.This paper introduces a time-varying model based on Fourier transformation and shows that the estimators of parameters converge to the true value.Via simulations,we show that the new time-varying model can deal with the continuous,random and abrupt time-varying parameters.Then,the new method is used to examine the co-movement relationship between stock market of China and that of US.The empirical results imply that the time-varying model can capture more abundant interaction,while the classical model can obtain misleading conclusions.
The time-varying characteristics of parameters in regression model can deteriorate the fitness and forecasting.The time-varying model based on Kalman?filtering has many parameters to estimate,which can lead to inefficiency.This paper introduces a time-varying model based on Fourier transformation and shows that the estimators of parameters converge to the true value.Via simulations,we show that the new time-varying model can deal with the continuous,random and abrupt time-varying parameters.Then,the new method is used to examine the co-movement relationship between stock market of China and that of US.The empirical results imply that the time-varying model can capture more abundant interaction,while the classical model can obtain misleading conclusions.
引文
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[15]Zhang B,Li X M.Has There Been any Change in the Comovement Between the Chinese and US Stock Markets?[J].International Review of Economics&Finance,2014,29(1).
[16]Chou R Y,Cai Y.Range-based Multivariate Volatility Model with Double Smooth Transition in Conditional Correlation[J].Global Finance Journal,2009,20(2).
(1)误差项服从独立同分布时,传统F检验具有良好的有限样本表现。
[2]Beckers R,Enders W,Lee J.A Stationary Test in the Presence of an Unknown Number of Smooth Breaks[J].Journal of time series Analysis,2006,27(1).
[3]D'Agostino A,Gambetti L,Giannone D.Macroeconomic Forecasting and Structural change[J].Journal of Applied Econometrics,2013,28(1).
[4]Hamilton J D.Time Series Analysis[M].Princeton:Princeton university press,1994.
[5]Enders W,Lee J.The Flexible Fourier form and Dickey-Fuller Type Unit Root Tests[J].Economics Letters,2012,117(1).
[6]Lee C,Wu J L,Yang L.A Simple Panel Unit-Root Test with Smooth Breaks in the Presence of a Multifactor Error Structure[J].Oxford Bulletin of Economics&Statistics,2015,78(3).
[7]杨利雄,张春丽.基于傅里叶变换的含确定性趋势结构突变的协整回归模型和不等方差检验[J].统计研究,2014(11).
[8]杨利雄,张春丽,李庆男.含非线性的平稳变量之间的虚假回归研究[J].统计与信息论坛,2016(1).
[9]Sun Y.Let’s Fix It:Fixed-b Asymptotics Versus Small-b Asymptotics in Heteroskedasticity and Autocorrelation Robust Inference[J].Journal of Econometrics,2014,178(2).
[10]Kiefer N M,Vogelsang T J.Bunzel H.Simple Robust Testing of Regression Hypotheses[J].Econometrica,2000,68(3).
[11]Yang L,Lee C,Shie F.How Close a Relationship Does a Capital Market Have with Other Such Markets?A Re-Examination Based on the Equal Variance Test[J].Pacific-Basin Finance Journal,2014,26(3).
[12]Diamandis P F.International Stock Market Iinkages:Evidence from Latin America[J].Global Finance Journal,2009,20(1).
[13]杨利雄,李庆男.中国股市与国际股市联动关系的“密切”程度[J].山西财经大学学报,2013(3).
[14]蔡义杰,周雨田,李丹.次贷危机下美国和全球股市之联动[J].国际金融研究,2009(9).
[15]Zhang B,Li X M.Has There Been any Change in the Comovement Between the Chinese and US Stock Markets?[J].International Review of Economics&Finance,2014,29(1).
[16]Chou R Y,Cai Y.Range-based Multivariate Volatility Model with Double Smooth Transition in Conditional Correlation[J].Global Finance Journal,2009,20(2).
(1)误差项服从独立同分布时,传统F检验具有良好的有限样本表现。