平稳的平滑转移自回归过程之间的虚假回归问题研究
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摘要
文章研究平稳的平滑转移自回归过程之间的虚假回归问题。通过推导最小二乘回归估计量及其对应的t统计量的极限分布,发现:标准的t检验流程中的t统计量并不趋于标准正态分布,其极限分布依赖于模型参数,从而导致了虚假回归的可能。采用蒙特卡洛模拟研究了有限样本下数据生成过程的各项参数对虚假回归的影响,研究表明:虚假回归现象也可能普遍存在于平稳变量之间,为此,在做统计推断时,考虑平稳变量的具体特征是必要的。
This paper examines the problem of spurious regression between the stationary smooth transition autoregressive processes.By deriving the limiting distributions of the estimates and t-statistics,we find that the t statistics of the standard t test cannot converge to the standard normal distribution,and its distribution depends on the parameters of the data generating processes,which leads to the possibility of spurious regression.We analyze the impact of the parameters of data generating processes and the sample size on spurious regression via Monte Carlo simulations.The evidences of Monte Carlo simulations support our theory.This paper implies that the phenomenon between stationary variables may a common existence.Therefore,it is necessary to consider the specific characteristics of stationary variables in statistical inference to avoid the spurious regression phenomenon.
This paper examines the problem of spurious regression between the stationary smooth transition autoregressive processes.By deriving the limiting distributions of the estimates and t-statistics,we find that the t statistics of the standard t test cannot converge to the standard normal distribution,and its distribution depends on the parameters of the data generating processes,which leads to the possibility of spurious regression.We analyze the impact of the parameters of data generating processes and the sample size on spurious regression via Monte Carlo simulations.The evidences of Monte Carlo simulations support our theory.This paper implies that the phenomenon between stationary variables may a common existence.Therefore,it is necessary to consider the specific characteristics of stationary variables in statistical inference to avoid the spurious regression phenomenon.
引文
[1]Terasvirta T,Anderson H M.Characterizing Nonlinearilies in Business Cycles Using Smooth Transition Autoregressive Models[J].Journal of Applied Econometrics,1992,7(S 1).
[2]Dijk D V,Terasvirta T,Franses P H.Smooth Transition Autoregressive Models—A Survey of Recent Developments[J].Econometric Reviews,2002,21(l).
[3]Kapetanios G,Shin Y,Snell A.Testing for a Unit Root in the Nonlinear STAR Framework[J].Journal of Econometrics,2003,112(2).
[4]Granger C W J,Newbold P.Spurious Regressions in Econometrics[J].Journal of Econometrics,1974,2(2).
[5]Granger I V,Clive W,Hyung N,et al.Spurious Regressions With Stationary Series[J].Applied Economics,2001,33(7).
[6]Phillips P C B.Understanding Spurious Regressions in Econometrics[J].Joumal of Econometrics,1985,33(3).
[7]Marmol F.Spurious Regressions Between I(d)Processes[J].Journal of Time,1995,16(3).
[8]Marmol F.Spurious Regression Theory With Nonstationary Fractionally Integrated Processes[J].Journal of Econometrics,1997,84(2).
[9]Tsay W J,Chung C F.The Spurious Regression of Fractionally Integrated Process[J].Joumal of Econometrics,2000,96(1).
[10]Kim T H,Lee Y S.Newbold P.Spurious Regressions With Stationary Processes Around Linear Trends[J].Economics Letters,2004,83(2).
[2]Dijk D V,Terasvirta T,Franses P H.Smooth Transition Autoregressive Models—A Survey of Recent Developments[J].Econometric Reviews,2002,21(l).
[3]Kapetanios G,Shin Y,Snell A.Testing for a Unit Root in the Nonlinear STAR Framework[J].Journal of Econometrics,2003,112(2).
[4]Granger C W J,Newbold P.Spurious Regressions in Econometrics[J].Journal of Econometrics,1974,2(2).
[5]Granger I V,Clive W,Hyung N,et al.Spurious Regressions With Stationary Series[J].Applied Economics,2001,33(7).
[6]Phillips P C B.Understanding Spurious Regressions in Econometrics[J].Joumal of Econometrics,1985,33(3).
[7]Marmol F.Spurious Regressions Between I(d)Processes[J].Journal of Time,1995,16(3).
[8]Marmol F.Spurious Regression Theory With Nonstationary Fractionally Integrated Processes[J].Journal of Econometrics,1997,84(2).
[9]Tsay W J,Chung C F.The Spurious Regression of Fractionally Integrated Process[J].Joumal of Econometrics,2000,96(1).
[10]Kim T H,Lee Y S.Newbold P.Spurious Regressions With Stationary Processes Around Linear Trends[J].Economics Letters,2004,83(2).