A Bootstrap Theory for Weakly Integrated Processes
This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n?1. We call such processes weakly integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n-1/2+_) for any espial > 0. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.
|Date of creation:||Jun 2003|
|Date of revision:|
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- Joon Y. Park & Peter C. B. Phillips, 1999.
"Nonlinear Regressions with Integrated Time Series,"
Working Paper Series
no6, Institute of Economic Research, Seoul National University.
- Park, Joon, 2002.
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2003-04, Rice University, Department of Economics.
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- Chang, Yoosoon & Park, Joon & Song, Kevin, 2002.
"Bootstrapping Cointegrating Regressions,"
2002-04, Rice University, Department of Economics.
- Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
- 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, 07.
- Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
- Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 161-68, April.
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