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A Sieve Bootstrap For The Test Of A Unit Root

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  • YOOSOON CHANG
  • JOON Y. PARK

Abstract

. In this paper, we consider a sieve bootstrap for the test of a unit root in models driven by general linear processes. The given model is first approximated by a finite autoregressive integrated process of order increasing with the sample size, and then the method of bootstrap is applied for the approximated autoregression to obtain the critical values for the usual unit root tests. The resulting tests, which may simply be viewed as the bootstrapped versions of Augmented Dickey–Fuller (ADF) unit root tests by Said and Dickey (1984), are shown to be consistent under very general conditions. The asymptotic validity of the bootstrap ADF unit root tests is thus established. Our conditions are significantly weaker than those used by Said and Dickey. Simulations show that bootstrap provides substantial improvements on finite sample sizes of the tests.

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  • Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:4:p:379-400
    DOI: 10.1111/1467-9892.00312
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    1. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    2. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    3. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Stephen Leybourne & Paul Newbold, 1999. "On the Size Properties of Phillips–Perron Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 51-61, January.
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