基于蒙特卡罗模拟的误差序列自相关检验研究

Research on Autocorrelation Test of Error Sequence Based on Monte Carlo Simulation

进行计量经济分析时一般都要检验模型是否存在自相关性,但目前常用的几种自相关检验方法都不同程度地存在一些问题,对此进行进一步的研究有重要意义。对于一阶自相关性检验,DW检验是最常用的方法,但其存在两个不确定区域。针对给定的解释变量,运用模拟方法,可以得到DW检验的临界值,从而克服了其存在不确定区域的缺陷。回归检验法则无可用的临界值,也可以用模拟方法计算其临界值,而且除检验功效很接近1的情形外,回归检验法的功效显著大于DW检验,可以替代DW检验。当样本量不是很大时,LM检验统计量的临界值与卡方分布的临界值差距较大,不能使用标准卡方临界值。在LM检验中,通常通过对最高阶滞后项系数进行t检验以确定自相关的阶数,但LM检验中最高阶滞后项系数的t统计量与标准t分布有较大差距,也不能用t分布临界值。

When performing econometric analysis,it is necessary to test whether there is autocorrelation in the model.However,several commonly used autocorrelation test methods have some problems in different degrees,and further research is of great significance.For the first-order autocorrelation test,the DW test is the most common method,but it has two uncertain regions.For a given explanatory variable,using the simulation method,the critical value of the DW test can be obtained,thereby overcoming the defect of the existence of the uncertain region.There is no threshold available for the regression test,and the critical value can also be calculated using the simulation method.Moreover,except for the case where the test power is very close to 1,the efficiency of the regression test is significantly greater than the DW test,which can replace the DW test.When the sample size is not very large,the critical value of the LM test statistic is far from the critical value of the chi-square distribution,and the standard chi-square threshold cannot be used.In the LM test,the t-test of the highest order lag term coefficient is usually used to determine the order of autocorrelation,but the t statistic of the highest order lag term coefficient in the LM test is far from the standard t distribution,and its threshold of t-distribution can’t be used.