偏差修正的预白化HAC法在平稳过程伪回归中的应用

在传统预白化HAC法存在有限样本偏差的基础上，提出将自回归参数偏差修正法和残差调整法来减少预白化HAC法的偏差，从而降低相互独立的平稳过程之间发生伪回归的概率。通过一系列的蒙特卡罗模拟表明：第一修正的预白化HAC法确实减少了伪回归概率，且自回归参数偏差修正法减少的幅度要比残差调整法要大得多；第二相对于同方差情形而言，存在GARCH类异方差的回归中预白化HAC法具有更低的伪回归概率；第三当数据过程是AR(2)过程时，在持久性相同的情况下预白化HAC法的伪回归概率要低于相应的AR(1)数据过程。但在高于2阶的自回归数据过程的回归中，残差调整的预白化HAC的伪回归概率具有优势。在样本容量较大(T≥500)时自回归参数修正的预白化HAC法的伪回归概率很接近检验水平，但残差调整的预白化HAC法具有微弱的向下检验水平扭曲.

Application of Bias-correction Prewhitening HAC Methods in the Spurious Regression

Owing to finite sample bias in the traditional prewhitening HAC, the paper provides a bias correction method of autoregressive parameters and a residual- adjusted method to residual series in the model between independent stationary processes with the purpose of reducing bias of prewhitening HAC method and reducing the spurious regression probability. Through a series of Monte Carlo simulations show: the first is the modified prewhitening HAC method does reduce the spurious regression probability, and the autoregression parameters bias correction method to reduce the magnitude of spurious regression is much larger than the residual-adjusted method. Second, the prewhitening HAC methods have a lower probability of spurious regression in the models with GARCH-type heteroscedasticity compared to models with homoscedasticity. Third, the spurious probability of prewhitening HAC is lower than the corresponding AR(1) data process under the same persistence when the DGP are AR(2) processes. But the residual-adjusted method has the advantage over the autoregression parameters bias correction method when data generate process is higher than 2 order autoregression. When sample size is larger than 500, the autoregression bias correction method has the spurious probability close to test size, but the residual-adjusted method has a weak downward test size distortion.