Overlapping sub-sampling and invariance to initial conditions
This paper studies the use of the overlapping blocking scheme in unit root autoregression. When the underlying process is that of a random walk, the blocksâ€™ initial conditions are not fixed, but are equal to the sum of all the previous observationsâ€™ error terms. When non- overlapping subsamples are used, as first shown by Chambers and Kyriacou (2010), these initial conditions do not disappear asymptotically. In this paper we show that a simple way of overcoming this issue is to use overlapping blocks. By doing so, the effect of these initial conditions vanishes asymptotically. An application of these findings to jackknife estimators indicates that an estimator based on moving-blocks is able to provide obvious reductions to the mean square error
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- Peter C.B. Phillips, 1985.
"Time Series Regression with a Unit Root,"
Cowles Foundation Discussion Papers
740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Marcus J Chambers & Maria Kyriacou, 2010. "Jackknife Bias Reduction in the Presence of a Unit Root," Economics Discussion Papers 685, University of Essex, Department of Economics.
- Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
- Peter C. B. Phillips, 2012. "Folklore Theorems, Implicit Maps, and Indirect Inference," Econometrica, Econometric Society, vol. 80(1), pages 425-454, 01.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- Ye Chen & Jun Yu, 2011.
"Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models,"
12-2011, Singapore Management University, School of Economics.
- Ye Chen & Jun Yu, 2012. "Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models," Working Papers 15-2012, Singapore Management University, School of Economics.
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