zbMATH — the first resource for mathematics

Size and power of tests of stationarity in highly autocorrelated time series. (English) Zbl 1337.62224
Summary: Tests of stationarity are routinely applied to highly autocorrelated time series. Following D. Kwiatkowski et al. [J. Econom. 54, No. 1–3, 159–178 (1992; Zbl 0871.62100)], standard stationarity tests employ a rescaling by an estimator of the long-run variance of the (potentially) stationary series. This paper analytically investigates the size and power properties of such tests when the series are strongly autocorrelated in a local-to-unity asymptotic framework. It is shown that the behavior of the tests strongly depends on the long-run variance estimator employed, but is in general highly undesirable. Either the tests fail to control size even for strongly mean reverting series, or they are inconsistent against an integrated process and discriminate only poorly between stationary and integrated processes compared to optimal statistics.

62M07 Non-Markovian processes: hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI
[1] Andrews, D., Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858, (1991) · Zbl 0732.62052
[2] Andrews, D.; Monahan, J., An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica, 60, 953-966, (1992) · Zbl 0778.62103
[3] Caner, M.; Kilian, L., Size distortions of tests of the null hypothesis of stationarityevidence and implications for the PPP debate, Journal of international money and finance, 20, 639-657, (2001)
[4] Chan, N.; Wei, C., Asymptotic inference for nearly nonstationary AR(1) processes, The annals of statistics, 15, 1050-1063, (1987) · Zbl 0638.62082
[5] Choi, I., Residual based tests for the null of stationarity with applications to US macroeconomic time series, Econometric theory, 10, 720-746, (1994)
[6] Dufour, J.-M.; King, M., Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors, Journal of econometrics, 47, 115-143, (1991) · Zbl 0729.62079
[7] Elliott, G., Efficient tests for a unit root when the initial observation is drawn from its unconditional distribution, International economic review, 40, 767-783, (1999)
[8] Elliott, G.; Stock, J., Confidence intervals for autoregressive coefficients near one, Journal of econometrics, 103, 155-181, (2001) · Zbl 0969.62058
[9] Elliott, G.; Rothenberg, T.; Stock, J., Efficient tests for an autoregressive unit root, Econometrica, 64, 813-836, (1996) · Zbl 0888.62088
[10] Engel, C., Long-run PPP may not hold after all, Journal of international economics, 51, 243-273, (2000)
[11] Harris, D.; Inder, B., A test for the null of cointegration, (), 133-152
[12] Hobijn, B., Franses, P. Ooms, M., 1998. Generalizations of the KPSS-test for stationarity. Discussion Paper 9802, Econometric Institute, Erasmus University Rotterdam. · Zbl 1061.62136
[13] Kiefer, N.; Vogelsang, T., Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size, Econometric theory, 18, 1350-1366, (2002) · Zbl 1033.62081
[14] Kwiatkowski, D.; Phillips, P.; Schmidt, P.; Shin, Y., Testing the null hypothesis of stationarity against the alternative of a unit root, Journal of econometrics, 54, 159-178, (1992) · Zbl 0871.62100
[15] Lee, J., On the power of stationarity tests using optimal bandwidth estimates, Economics letters, 51, 131-137, (1996) · Zbl 0875.90184
[16] Leybourne, S.; McCabe, B., A consistent test for a unit root, Journal of business and economic statistics, 12, 157-166, (1994)
[17] Leybourne, S.; McCabe, B., Modified stationarity tests with data dependent model selection rules, Journal of business and economic statistics, 17, 264-270, (1999)
[18] MacNeill, I., Properties of sequences of partial sums of polynomial regression residuals with applications to test for change of regression at unknown times, Annals of statistics, 6, 422-433, (1978) · Zbl 0375.62064
[19] Müller, U., Elliott, G., 2001. Tests for unit roots and the initial observation. UCSD Working Paper 2001-19.
[20] Müller, U.; Elliott, G., Tests for unit roots and the initial condition, Econometrica, 71, 1269-1286, (2003) · Zbl 1152.62371
[21] Nabeya, S.; Tanaka, K., Asymptotic theory of a test for constancy of regression coefficients against the random walk alternative, Annals of statistics, 16, 218-235, (1988) · Zbl 0662.62098
[22] Nabeya, S.; Tanaka, K., A general approach to the limiting distribution for estimators in time series regression with nonstable autoregressive errors, Econometrica, 58, 145-163, (1990) · Zbl 0724.62088
[23] Nyblom, J., Testing for the constancy of parameters over time, Journal of the American statistical association, 84, 223-230, (1989) · Zbl 0677.62018
[24] Perron, P.; Vodounou, C., Asymptotic approximations in the near-integrated model with a non-zero initial condition, Econometrics journal, 4, 143-169, (2001) · Zbl 1029.62016
[25] Phillips, P., Towards a unified asymptotic theory for autoregression, Biometrika, 74, 535-547, (1987) · Zbl 0654.62073
[26] Phillips, P.; Perron, P., Testing for a unit root in time series regression, Biometrika, 75, 335-346, (1988) · Zbl 0644.62094
[27] Rogoff, K., The purchasing power parity puzzle, Journal of economic literature, 34, 647-668, (1996)
[28] Shin, Y., A residual-based test of the null of cointegration against the alternative of no cointegration, Econometric theory, 10, 91-115, (1994)
[29] Stock, J., Confidence intervals for the largest autoregressive root in US macroeconomic time series, Journal of monetary economics, 28, 435-459, (1991)
[30] Stock, J., Unit roots, structural breaks and trends, (), 2740-2841
[31] Stock, J., Watson, M., 1998. Business cycle fluctuations in US macroeconomic time series. NBER Working Paper 6528.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.