Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses

A Monte Carlo analysis of the coverage accuracy and average length of alternative bootstrap confidence intervals for impulse-response estimators shows that the accuracy of equal-tailed and symmetric percentile-t intervals can be poor and erratic in small samples (both in models with large roots and in models without roots near the unit circle). In contrast, some percentile bootstrap intervals may be both shorter and more accurate. The accuracy of percentile-t intervals improves with sample size, but the sample size required for reliable inference can be very large. Moreover, for such large sample sizes, virtually all bootstrap intervals tend to have excellent coverage accuracy.

[1]  L. Kilian.  Small-sample Confidence Intervals for Impulse Response Functions , 1998, Review of Economics and Statistics.

[2]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[3]  D. Runkle,et al.  Vector Autoregressions and Reality , 1987 .

[4]  P. Hall.  Theoretical Comparison of Bootstrap Confidence Intervals , 1988 .

[5]  Jonathan H. Wright.  Confidence Intervals for Univariate Impulse Responses With a Near Unit Root , 2000 .

[6]  Helmut Lütkepohl,et al.  Introduction to multiple time series analysis , 1991 .

[7]  Bruce E. Hansen,et al.  The Grid Bootstrap and the Autoregressive Model , 1999, Review of Economics and Statistics.

[8]  Jeremy Berkowitz,et al.  Recent developments in bootstrapping time series , 1996 .

[9]  Ar Tremayne,et al.  On the Adequacy of Symmetric Confidence Intervals for the Largest Autoregressive Root , 2000 .

[10]  B. Efron.  Nonparametric standard errors and confidence intervals , 1981 .

[11]  Olivier J. Blanchard,et al.  The Dynamic Effects of Aggregate Demand and Supply Disturbances , 1988 .

[12]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[13]  Helmut Lütkepohl,et al.  Problems Related to Bootstrapping Impulse Responses of Autoregressive Processes , 1997 .

[14]  P. Hall.  The Bootstrap and Edgeworth Expansion , 1992 .

[15]  J. Stock,et al.  Confidence Intervals for the Largest Autoregressive Root in U , 1991 .

[16]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[17]  Stefano Fachin,et al.  Asymptotic normal and bootstrap inference in structural VAR analysis , 1996 .

[18]  Francis X. Diebold,et al.  Measuring Predictability: Theory and Macroeconomic Applications , 1997 .

[19]  J. Galí,et al.  Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations , 1996 .

[20]  Helmut Lütkepohl,et al.  Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models , 1990 .

[21]  James H. Stock.  Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series , 1991 .

[22]  R. Tibshirani.  Variance stabilization and the bootstrap , 1988 .

[23]  Yongcheol Shin,et al.  Cointegration and speed of convergence to equilibrium , 1996 .