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Reducing the size distortion of the KPSS test. (English) Zbl 1416.62466
Summary: We propose a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by D. Sul et al. [“Prewhitening bias in HAC estimation”, Oxf. Bull. Econ. Stat. 67, 517–546 (2005)] to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of the numerator of the test statistic up to the \(1/T\) order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long-run parameter in the model satisfies the boundary condition.

62M07 Non-Markovian processes: hypothesis testing
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[1] Andrews, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60 pp 953– (1992) · Zbl 0778.62103
[2] Aznar, A point optimal test for the null of near integration (2008)
[3] Berk, Consistent autoregressive spectral estimates, Annals of Statistics 2 pp 289– (1974) · Zbl 0317.62064
[4] Brillinger, Time Series Data Analysis and Theory (1981)
[5] Caner, Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate, Journal of International Money and Finance 20 pp 639– (2001)
[6] Carrion-i-Silvestre, A guide to the computation of stationarity tests, Empirical Economics 31 pp 33– (2006)
[7] Cheung, Further investigation of the uncertain unit root in GNP, Journal of Business and Economic Statistics 15 pp 68– (1997)
[8] Harris, Modified KPSS tests for near integration, Econometric Theory 23 pp 355– (2007) · Zbl 1274.62593
[9] Kuo, Re-examining long-run purchasing power parity, Journal of International Money and Finance 18 pp 251– (1999)
[10] Kurozumi, Construction of stationarity tests with less size distortions, Hitotsubashi Journal of Economics 50 pp 87– (2009)
[11] Kwiatkowski, Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of Econometrics 54 pp 159– (1992) · Zbl 0871.62100
[12] Lanne, Reducing size distortions of parametric stationarity tests, Journal of Time Series Analysis 24 pp 423– (2003) · Zbl 1036.62083
[13] Leybourne, A consistent test for a unit root, Journal of Business and Economic Statistics 12 pp 157– (1994)
[14] Leybourne, Modified stationarity tests with data-dependent model-selection rules, Journal of Business and Economic Statistics 17 pp 264– (1999)
[15] Müller, Size and power of tests of stationarity in highly autocorrelated time series, Journal of Econometrics 128 pp 264– (2005) · Zbl 1337.62224
[16] Müller, The impossibility of consistent discrimination between I(0) and I(1) processes, Econometric Theory 24 pp 616– (2008) · Zbl 1284.62141
[17] Perron, Useful modifications to some unit root tests with dependent errors and their local asymptotic properties, Review of Economic Studies 63 pp 435– (1996) · Zbl 0872.62085
[18] Rothman, More uncertainty about the unit root in U.S. real GNP, Journal of Macroeconomics 19 pp 771– (1997)
[19] Saikkonen, Testing for a moving average unit root in autoregressive integrated moving average models, Journal of the American Statistical Association 88 pp 596– (1993a) · Zbl 0775.62240
[20] Saikkonen, Point optimal tests for testing the order of differencing in ARIMA models, Econometric Theory 9 pp 343– (1993b)
[21] Sul, Prewhitening bias in HAC estimation, Oxford Bulletin of Economics and Statistics 67 pp 517– (2005)
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