Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series

This paper provides asymptotic confidence intervals for the largest autoregressive root of a time series when this root is close to one. The intervals are readily constructed either graphically or using tables in the Appendix. When applied to the Nelson-Plosser (1982) data set, the main conclusion is that the confidence intervals typically are wide. The conventional emphasis on testing for whether the largest root equals one fails to convey the substantial sampling variability associated with this measure of persistence.

[1]  Peter C. B. Phillips,et al.  To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends , 1991 .

[2]  Ngai Hang Chan,et al.  The Parameter Inference for Nearly Nonstationary Time Series , 1988 .

[3]  Alok Bhargava,et al.  Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk , 1983 .

[4]  Peter C. B. Phillips,et al.  Towards a Unified Asymptotic Theory for Autoregression , 1987 .

[5]  John H. Cochrane,et al.  How Big Is the Random Walk in GNP? , 1988, Journal of Political Economy.

[6]  Glenn D. Rudebusch.  Trends and Random Walks in Macroeconomic Time Series: A Re-examination , 1992 .

[7]  Harald Uhlig,et al.  Understanding unit rooters: a helicopter tour , 1991 .

[8]  G. C. Tiao,et al.  Parameter inference for a nearly nonstationary first-order autoregressive model , 1984 .

[9]  Pierre Perron.  The Calculation of the Limiting Distribution of the Least-Squares Estimator in a Near-Integrated Model , 1989, Econometric Theory.

[10]  J. Stock,et al.  INFERENCE IN LINEAR TIME SERIES MODELS WITH SOME UNIT ROOTS , 1990 .

[11]  C. Z. Wei,et al.  Asymptotic Inference for Nearly Nonstationary AR(1) Processes , 1987 .

[12]  Martin Eichenbaum,et al.  Unit Roots in Real Gnp: Do We Know, and Do We Care? , 1989 .

[13]  Alok Bhargava,et al.  On the Theory of Testing for Unit Roots in Observed Time Series , 1986 .

[14]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[15]  D. Andrews.  Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models , 1993 .

[16]  H. V. Dijk,et al.  A Bayesian Analysis Of The Unit Root Hypothesis , 1989 .

[17]  C. Sims.  Bayesian skepticism on unit root econometrics , 1988 .

[18]  John Y. Campbell,et al.  Are Output Fluctuations Transitory? , 1986 .

[19]  Maurice G. Kendall,et al.  The advanced theory of statistics , 1945 .

[20]  A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors , 1990 .

[21]  C. Nelson,et al.  Trends and random walks in macroeconmic time series: Some evidence and implications , 1982 .

[22]  G. Schwert,et al.  Tests for Unit Roots: a Monte Carlo Investigation , 1988 .