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Simultaneous calibrated prediction intervals for time series
Last modified: 2018-05-18
Abstract
This paper deals with simultaneous prediction for time series models. In
particular, it presents a simple procedure which gives well-calibrated simultaneous
predictive intervals with coverage probability equal or close to the target nominal
value. Although the exact computation of the proposed intervals is usually not feasi-
ble, an approximation can be easily obtained by means of a suitable bootstrap sim-
ulation procedure. This new predictive solution is much simpler to compute than
those ones already proposed in the literature based on asymptotic calculations. An
application of the bootstrap calibrated procedure to first order autoregressive models
is presented.
particular, it presents a simple procedure which gives well-calibrated simultaneous
predictive intervals with coverage probability equal or close to the target nominal
value. Although the exact computation of the proposed intervals is usually not feasi-
ble, an approximation can be easily obtained by means of a suitable bootstrap sim-
ulation procedure. This new predictive solution is much simpler to compute than
those ones already proposed in the literature based on asymptotic calculations. An
application of the bootstrap calibrated procedure to first order autoregressive models
is presented.
References
1. Alpuim, M.T.: One-sided simultaneous prediction intervals for AR(1) and MA(1) processes with exponential innovations. Journal of Forecasting, 16, 19–35 (1997).
2. Barndorff-Nielsen, O.E., Cox, D.R.: Prediction and asymptotics. Bernoulli, 2, 319–340 (1996).
3. Beran, R.: Calibrating prediction regions. Journal of the American Statistical Association, 85, 715–723 (1990).
4. Clements, M.P., Kim, J.H.: Bootstrap prediction intervals for autoregressive time series. Computational Statistics & Data Analysis, 51, 3580–3594 (2007).
5. Corcuera, J.M., Giummolè, F.: Multivariate Prediction. Bernoulli, 12, 157–168 (2006).
6. Fonseca, G., Giummolè, F., Vidoni, P.: Bootstrap Calibrated Predictive Distributions For Time Series. In: Proceedings of S.Co. 2011: Complex Data Modeling and Computationally Intensive Statistical Methods For Estimation and Predictions, Padova, CLEUP, September 19-21, 2011.
7. Fonseca, G., Giummolè, F., Vidoni, P.: Calibrating predictive distributions. Journal of Statistical Computation and Simulation, 84, 373–383 (2014).
8. Giummolè, F., Vidoni, P.: Improved prediction limits for a general class of Gaussian models. Journal of Time Series Analysis, 31, 483–493 (2010).
9. Hall, P., Peng, L., Tajvidi, N.: On prediction intervals based on predictive likelihood or bootstrap methods. Biometrika, 86, 871–880 (1999).
10. Kabaila, P.: An efficient simulation method for the computation of a class of conditional expectations. Australian & New Zeland Journal of Statistics, 41, 331–336 (1999).
11. Kabaila, P., Syuhada, K.: Improved prediction limits for AR(p) and ARCH(p) processes. Journal of Time Series Analysis, 29, 213–223 (2007).
12. Ravishanker, N., Wu, L.S.Y., Glaz, J.: Multiple prediction intervals for time series: comparison of simultaneous and marginal intervals. Journal of Forecasting, 10, 445–463 (1991).
13. Vidoni, P.: Improved prediction intervals for stochastic process models. Journal of Time Series Analysis, 25, 137–154 (2004).
14. Wolf, M., Wunderli, D.: Bootstrap joint prediction regions. Journal of Time Series Analysis, 36, 35–376 (2015).
2. Barndorff-Nielsen, O.E., Cox, D.R.: Prediction and asymptotics. Bernoulli, 2, 319–340 (1996).
3. Beran, R.: Calibrating prediction regions. Journal of the American Statistical Association, 85, 715–723 (1990).
4. Clements, M.P., Kim, J.H.: Bootstrap prediction intervals for autoregressive time series. Computational Statistics & Data Analysis, 51, 3580–3594 (2007).
5. Corcuera, J.M., Giummolè, F.: Multivariate Prediction. Bernoulli, 12, 157–168 (2006).
6. Fonseca, G., Giummolè, F., Vidoni, P.: Bootstrap Calibrated Predictive Distributions For Time Series. In: Proceedings of S.Co. 2011: Complex Data Modeling and Computationally Intensive Statistical Methods For Estimation and Predictions, Padova, CLEUP, September 19-21, 2011.
7. Fonseca, G., Giummolè, F., Vidoni, P.: Calibrating predictive distributions. Journal of Statistical Computation and Simulation, 84, 373–383 (2014).
8. Giummolè, F., Vidoni, P.: Improved prediction limits for a general class of Gaussian models. Journal of Time Series Analysis, 31, 483–493 (2010).
9. Hall, P., Peng, L., Tajvidi, N.: On prediction intervals based on predictive likelihood or bootstrap methods. Biometrika, 86, 871–880 (1999).
10. Kabaila, P.: An efficient simulation method for the computation of a class of conditional expectations. Australian & New Zeland Journal of Statistics, 41, 331–336 (1999).
11. Kabaila, P., Syuhada, K.: Improved prediction limits for AR(p) and ARCH(p) processes. Journal of Time Series Analysis, 29, 213–223 (2007).
12. Ravishanker, N., Wu, L.S.Y., Glaz, J.: Multiple prediction intervals for time series: comparison of simultaneous and marginal intervals. Journal of Forecasting, 10, 445–463 (1991).
13. Vidoni, P.: Improved prediction intervals for stochastic process models. Journal of Time Series Analysis, 25, 137–154 (2004).
14. Wolf, M., Wunderli, D.: Bootstrap joint prediction regions. Journal of Time Series Analysis, 36, 35–376 (2015).
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