分數整合與Phillips-Perron檢定

Fractional Integration and the Phillips Perron Test

本文在非定態分數整合的過程下，亦即I（1+d）的dÎ（-0.5, 0.5）下，推導出Phillips-Perron單根檢定統計量的漸進分配。藉由使用Newey-West的長期變異數估計式，我們證明出Phillips-Perron的t統計量和標準係數估計式，在非定態但均數復歸的分數整合過程，如I（1+d）的dÎ（-0.5, 0）下是具一致性的。然而，在非定態且非均數復歸的分數整合過程，如I（1+d）的dÎ（0, 0.5）下，只有從沒有截距項和沒有時間趨勢項回歸下的t統計量是具一致性的。模擬的結果亦支持我們的發現，及檢定統計量的檢定力，在大樣本下將隨著Newey-West的長期變異數估計式所選取的落後期數增加而遞減。

This paper derives the asymptotic distribution of the Phillips-Perron unit root tests statistics and some of their variants under a general non-stationary fractionally-integrated I(1 + d) process, for d ∈ (−0.5, 0.5). By using the Newey-West estimator of long-run variance, we show that both the Phillips-Perron’s t statistics and standardized coefficients estimator are consistent against a non-stationary but mean-reverting alternative, such as the I(1 + d) process for d ∈ (−0.5, 0). However, only the t statistic from a no-drift and no-time trend regression is consistent against a non-stationary and non-mean-reverting alternative, such as the I(1 + d) process for d ∈ (0, 0.5). Simulation results also confirm that the power of these test statistics in large samples will decrease as the lag number increases in the construction of a Newey-West estimator of the long-run variance.