Chambers, Marcus J. and Kyriacou, Maria (2012): Jackknife bias reduction in autoregressive models with a unit root.

PDF
MPRA_paper_38255.pdf Download (274kB)  Preview 
Abstract
This paper is concerned with the application of jackknife methods as a means of bias reduction in the estimation of autoregressive models with a unit root. It is shown that the usual jackknife estimator based on nonoverlapping subsamples does not remove fully the firstorder bias as intended, but that an ‘optimal’ jackknife estimator can be de fined that is capable of removing this bias. The results are based on a demonstration that the subsample estimators converge to different limiting distributions, and the joint moment generating function of the numerator and denominator of these distributions (which are func tionals of a Wiener process over a subinterval of [0,1]) is derived and utilised to extract the optimal weights. Simulations demonstrate the ability of the jackknife estimator to produce substantial bias reductions in the parameter of interest. It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction despite the fact that the distributions of the fullsample and subsample estimators have greater bias in this case. Of interest, too, is the fact that the jackknife estimators can also reduce the overall root mean squared error compared to the ordinary least squares estimator, this requiring a larger (though still small) number of subsamples compared to the value that produces maximum bias reduction (which is typically equal to two).
Item Type:  MPRA Paper 

Original Title:  Jackknife bias reduction in autoregressive models with a unit root 
Language:  English 
Keywords:  Jackknife; bias reduction; unit root; moment generating function 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  38255 
Depositing User:  Maria Kyriacou 
Date Deposited:  30 Apr 2012 15:17 
Last Modified:  01 Oct 2019 16:44 
References:  Abadir, K.M. (1993), “The Limiting Distribution of the Autocorrelation Coefficient Under a Unit Root,” Annals of Statistics, 21, 1058–1070. Andrews, D.W.K. (1993), “Exactly Median Unbiased Estimation of First Order Autoregres sive/Unit Root Models,” Econometrica, 61, 139–165. Gonzalo, J., and Pitarakis, J.Y. (1998), “On the Exact Moments of Nonstandard Asymptotic Distributions in an Unstable AR(1) with Dependent Errors,” International Economic Review, 39, 71–88. Kendall, M.G. (1954), “Note on Bias in the Estimation of Autocorrelation,” Biometrika, 41, 403–404. Marriott, F.H.C., and Pope, J.A. (1954), “Bias in the Estimation of Autocorrelations,” Biometrika, 41, 390–402. Orcutt, G.H., and Winokur, H.S. (1969), “First Order Autoregression: Inference, Estimation, and Prediction,” Econometrica, 37, 1–14. Perron, P. (1991), “A Continuous Time Approximation to the Unstable FirstOrder Autore gressive Process: The Case without an Intercept,” Econometrica, 59, 211236. Phillips, P. C. B. (1987), “Time Series Regression with a Unit Root,” Econometrica, 55, 277–301. Phillips, P. C. B., and Yu, J. (2005), “Jackknifing Bond Option Prices,” Review of Financial Studies, 18, 707–742. Quenouille, M.H. (1956), “Notes on Bias in Estimation,” Biometrika, 43, 353–360. Shaman, P., and Stine, R. (1988), “The Bias of Autoregressive Coefficient Estimators,” Journal of the American Statistical Association, 83, 842–848. 26 Shenton, L.R., and Johnson, W.I. (1965), “Moments of a Serial Correlation Coefficient,” Journal of the Royal Statistical Society Series B, 27, 308–320. Shin, D.W., and So, B.S. (2001), “Recursive Mean Adjustment for Unit Root Tests,” Journal of Time Series Analysis, 22, 595–612. Stine, R. (1987), “Estimating Properties of Autoregressive Forecasts,” Journal of the Amer ican Statistical Association, 82, 1072–1078. Tanaka, K. (1996), Time Series Analysis: Nonstationary and Noninvertible Distribution Theory, New York: Wiley. Tukey, J.W. (1958), “Bias and Confidence in notquite Large Samples,” Annals of Mathe matical Statistics, 29, 614. White, J.S. (1958), “The Limiting Distribution of the Serial Correlation Coefficient in the Explosive Case,” Annals of Mathematical Statistics, 29, 1188–1197. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/38255 