Fractional Integration and the Phillips-Perron Test

分數整合與Phillips-Perron檢定

李慶男(Ching-Nun Lee) ； 謝富順(Fu-Shuen Shie)

《經濟論文》 32卷2期 (2004/06) Pp. 273-312

https://doi.org/10.29628/AEP.200406.0001

摘要

本文在非定態分數整合的過程下，亦即I (1+d) 的d Є (-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d Є (-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d Є (0,0.5)下，只有從沒有截距項和沒有時間趨勢項迴歸下的t統計量是具一致性的。模擬的結果亦支持我們的發現，即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。

關鍵字

單根 ； 分數整合過程 ； 檢定力

並列摘要

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 Є (-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 Є (-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 Є (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.

並列關鍵字

Unit root ； Fractional integrated process ； Power

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