Prediction Intervals for Time Series: A Modified Sieve Bootstrap Approach

Traditional Box–Jenkins prediction intervals perform poorly when the innovations are not Gaussian. Nonparametric bootstrap procedures overcome this handicap, but most existing methods assume that the AR and MA orders of the process are known. The sieve bootstrap approach requires no such assumption but produces liberal coverage due to the use of residuals that underestimate the actual variance of the innovations and the failure of the methods to capture variations due to sampling error of the mean. A modified approach, that corrects these deficiencies, is implemented. Monte Carlo simulations results show that the modified version achieves nominal or near nominal coverage.

[1]  D. Freedman,et al.  Bootstrapping a Regression Equation: Some Empirical Results , 1984 .

[2]  J. Hannan,et al.  Introduction to probability and mathematical statistics , 1986 .

[3]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[4]  P. Bühlmann.  Sieve bootstrap for time series , 1997 .

[5]  R. J. Bhansali.  A Simulation Study of Autoregressive and Window Estimators of the Inverse Correlation Function , 1983 .

[6]  Lutz Kilian,et al.  Confidence intervals for impulse responses under departures from normality , 1998 .

[7]  Juan Romo,et al.  Bootstrap predictive inference for ARIMA processes , 2004 .

[8]  Lori A. Thombs,et al.  Bootstrap Prediction Intervals for Autoregression , 1990 .

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

[10]  Juan Romo,et al.  On sieve bootstrap prediction intervals , 2003 .

[11]  Juan Romo,et al.  Effects of parameter estimation on prediction densities: a bootstrap approach , 1999 .

[12]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[13]  Robert A. Stine,et al.  Estimating Properties of Autoregressive Forecasts , 1987 .

[14]  Guido Masarotto,et al.  Bootstrap prediction intervals for autoregressions , 1990 .

[15]  Andrés M. Alonso.  JMASM Algorithms and Code JMASM10: A Fortran Routine For Sieve Bootstrap Prediction Intervals , 2004 .

[16]  Wenceslao González-Manteiga,et al.  Saving computer time in constructing consistent bootstrap prediction intervals for autoregressive processes , 1997 .

[17]  Juan Romo,et al.  Forecasting time series with sieve bootstrap , 2002 .

[18]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[19]  S. Geman,et al.  Nonparametric Maximum Likelihood Estimation by the Method of Sieves , 1982 .

[20]  Michael P. Clements,et al.  Bootstrapping prediction intervals for autoregressive models , 2001 .

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

[22]  Regina Y. Liu.  Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[23]  David F. Findley,et al.  On bootstrap estimates of forecast mean square error for autoregressive processes , 1986 .

[24]  J. Franke,et al.  BOOTSTRAPPING STATIONARY AUTOREGRESSIVE MOVING-AVERAGE MODELS , 1992 .

[25]  Matteo Grigoletto,et al.  Bootstrap prediction intervals for autoregressions: some alternatives , 1998 .

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

[27]  Juan Romo,et al.  Introducing model uncertainty in time series bootstrap , 2001 .

[28]  H. Künsch.  The Jackknife and the Bootstrap for General Stationary Observations , 1989 .