Medel, Carlos and Pincheira, Pablo (2015): The Outofsample Performance of an Exact MedianUnbiased Estimator for the NearUnity AR(1) Model.

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Abstract
We analyse the multihorizon forecasting performance of several strategies to estimate the stationary AR(1) model in a nearunity context. We focus on the Andrews' (1993) exact medianunbiased estimator (BC), the OLS estimator, and the driftless random walk (RW). In addition, we explore the forecasting performance of pairwise combinations between these individual strategies. We do this to investigate whether the Andrews' (1993) correction of the OLS downward bias helps in reducing mean squared forecast errors. Via simulations, we find that BC forecasts typically outperform OLS forecasts. When BC is compared to the RW we obtain mixed results, favouring the latter as the persistence of the true process increases. Interestingly, we also find that the combination of BC and RW performs well when the persistence of the process is high.
Item Type:  MPRA Paper 

Original Title:  The Outofsample Performance of an Exact MedianUnbiased Estimator for the NearUnity AR(1) Model 
Language:  English 
Keywords:  Nearunity autoregression; medianunbiased estimation; unbiasedness; unit root model; forecasting; forecast combinations 
Subjects:  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 > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling 
Item ID:  62552 
Depositing User:  Carlos A. Medel 
Date Deposited:  06 Mar 2015 08:05 
Last Modified:  27 Sep 2019 16:32 
References:  Andrews, D.W.K., 1993, "Exactly MedianUnbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica 61(1): 139165. Andrews, D.W.K. and H.Y. Chen, 1994, "Approximately MedianUnbiased Estimation of Autoregressive Models," Journal of Business and Economic Statistics 12(2): 187204. Bates, J.M. and C.W.J. Granger, 1969, "The Combination of Forecasts," Operational Research Quarterly 20(4):451468. Clements, M.P. and D.F. Hendry, 2001, "Forecasting with Di¤erence Stationary and Trend Stationary Models," Econometrics Journal 4: S1S19. Frisch, R. and F.V. Waugh, 1933, "Partial Time Regressions as Compared with Individual Trends," Econometrica 1(4): 387401. Gospodinov, N., 2002, "Median Unbiased Forecasts for Highly Persistent Autoregressive Processes," Journal of Econometrics 111(1): 85101. Hansen, B.E., 1999, "The Grid Bootstrap and the Autoregressive Model," Review of Economics and Statistics 81(4): 594607. Hansen, B.E., 2010, "Averaging Estimators for Autoregressions with a Near Unit Root," Journal of Econometrics 158(1): 142155. Kendall, M.G., 1954, "Note on Bias in the Estimation of Autocorrelation," Biometrika 41(34): 403404. Kim, J.H., 2003, "Forecasting Autoregressive Time Series with Biascorrected Parameter Estimators," International Journal of Forecasting 19(4): 493502. Kim, H. and N. Durmaz, 2012, "Bias Correction and Outofsample Forecast Accuracy," International Journal of Forecasting 28(3): 575586. Lovell, M., 2008, "A Simple Proof of the FWL Theorem," Journal of Economic Education 39(1): 8891. Maekawa, K., 1987, "Finite Sample Properties of Several Predictors from an Autoregressive Model," Econometric Theory 3: 359370. Marriott, F.H.C. and J.A. Pope, 1954, "Bias in the Estimation of Autocorrelations," Biometrika 41(34): 393403. Mikusheva, A., 2007, "Uniform Inference in Autoregressive Models," Econometrica 75(5): 14111452. Orcutt, G.H. and H.S. Winokur, 1969, "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica 37(1): 114. Patterson, K.D., 2000, "Bias Reduction in Autoregressive Models," Economics Letters 68(2): 135141. Pincheira, P. and C.A. Medel, 2012, "Forecasting Inflation with a Random Walk," Working Paper 669, Central Bank of Chile. Pincheira, P. and C.A. Medel, 2015, "Forecasting Inflation with a Random Walk," manuscript, [available upon request]. Rachev, S., B. RachevaIotova, and S. Stoyanov, 2010, "Capturing Fat Tails," Risk Magazine May: 7277. Roy, A. and W.A. Fuller, 2001, "Estimation for Autoregressive Time Series with a Root Near One," Journal of Business and Economic Statistics 19(4): 482493. Shaman, P. and R.A. Stine, 1988, "The Bias of Autoregressive Coe¢ cient Estimators," Journal of the American Statistical Association 83(403): 842848. So, B.S. and D.W. Shin, 1999, "Recursive Mean Adjustment in Timeseries Inferences," Statistics and Probability Letters 43(1): 6573. Stine, R.A. and P. Shaman, 1989, "A Fixed Point Characterization for Bias of Autoregressive Estimators," Annals of Statistics 17(3): 12751284. Stock, J.H. and M.W. Watson, 2004, "Combination Forecasts of Output Growth in a Sevencountry Data Set," Journal of Forecasting 23: 405430. Withers, C.S. and S. Nadarajah, 2011, "Estimates of Low Bias for the Multivariate Normal," Statistics and Probability Letters 81(11): 16351647. Yu, J., 2012, "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Journal of Econometrics 169(1): 114122. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/62552 