Bootstrap prediction intervals for threshold autoregressive models

Jing, Li (2009): Bootstrap prediction intervals for threshold autoregressive models.

Abstract

This paper examines the performance of prediction intervals based on bootstrap for threshold autoregressive models. We consider four bootstrap methods to account for the variability of estimates, correct the small-sample bias of autoregressive coefficients and allow for heterogeneous errors. Simulation shows that (1) accounting for the sampling variability of estimated threshold values is necessary despite super-consistency, (2) bias-correction leads to better prediction intervals under certain circumstances, and (3) two-sample bootstrap can improve long term forecast when errors are regime-dependent.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bootstrap; Interval Forecasting; Threshold Autoregressive Models; Time Series; Simulation
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General

References

Chan, K. S. (1990). Testing for threshold autoregression. The Annals of Statistics, 18,1886-1894.

Chan, K. S. (1993). Consistency and limiting distribution of the least squares estimator ofa threshold autoregressive model. The Annals of Statistics, 21, 520-533.

Chatfield, C. (1993). Calculating interval forecasts. Journal of Business & Economic Statistics, 11, 121-135.

Efron, B. and Tibshirani, R. J. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statistical Science, 1, 54-75.

Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. London: Chapman and Hall.

Granger, C. and Newbold, P. (1986). Forecasting Economic Time Series. San Diego: Academic Press.

Grigoletto, M. (1998). Bootstrap prediction intervals for autoregressions: some alternatives. International Journal of Forecasting, 14, 447-456.

Hansen, B. E. (2000). Sample splitting and threshold estimation. Econometrica, 68, 575-603.

Jarque, C. M. and Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55, 163-172.

Kilian, L. (1998). Small sample confidence intervals for impulse response functions. The Review of Economics and Statistics, 80, 218-230.

Kim, J. (1999). Asymptotic and bootstrap prediction regions for vector autoregression. International Journal of Forecasting, 15, 393-403.

Kim, J. (2001). bootstrap-after-bootstrap prediction intervals for autoregressive models. Journal of Business & Economic Statistics, 19, 117-128.

Kim, J. (2002). Bootstrap prediction intervals for autoregressive models of unknown or infinite lag order. Journal of Forecasting, 21, 265-280.

Kim, J. (2004). Bias-corrected bootstrap prediction regions for vector autoregression. Journal of Forecasting, 23, 141-154.

Maekawa, K. (1987). Finite sample properties of several predictors from an autoregressive model. Econometric Theory, 3, 359-370.

Masarotto, G. (1990). bootstrap prediction intervals for autoregressions. International Journal of Forecasting, 6, 229-239.

Shaman, P. and Stine, R. A. (1988). The bias of autoregressive coe±cient estimators. Journal of the American Statistical Association, 83, 842-848.

Thombs, L. A. and Schucany, W. R. (1990). bootstrap prediction intervals for autoregression. Journal of the American Statistical Association, 85, 486-492.

Tong, H. (1983). Threshold Models in Non-linear Time Series Analysis. New York: SpringerVerlag.