A Note on Prediction with Misspecified Models
DOI:
https://doi.org/10.5614/itbj.sci.2012.44.3.2Abstract
Suppose that a time series model is fitted. It is likely that the fitted model is not the true model. In other words, the model has been misspecified. In this paper, we consider the prediction interval problem in the case of a misspecified first-order autoregressive or AR(1) model. We have calculated the coverage probability of an upper one-step-ahead prediction interval for both properly specified and misspecified models through Monte Carlo simulation. It was found that dealing with prediction interval for misspecified model is complicated: the distribution of a future observation conditional on the last observation and the parameter estimator is not identical to the distribution of this future observation conditional on the last observation alone.References
Barndorff-Nielsen, O.E. & Cox, D.R., Prediction and Asymptotics, Bernoulli, 2, pp. 319-340, 1996.
Kabaila, P., The Relevance Property for Prediction Intervals, Journal of Time Series Analysis, 20(6), pp. 655-662, 1999.
Kabaila, P. & Syuhada, K., The Relative Efficiency of Prediction Intervals, Communication in Statistics: Theory and Methods, 36(15), pp. 2673-2686, 2007.
Kabaila, P. & Syuhada, K., Improved Prediction Limits for AR( p ) and ARCH( p ) Processes, Journal of Time Series Analysis, 29, pp. 213-223, 2008.
Vidoni, P., Improved Prediction Intervals for Stochastic Process Models, Journal of Time Series Analysis, 25, pp. 137-154, 2004.
Davies, N. & Newbold, P., Forecasting with Misspecified Models, Applied Statistics, 29, pp. 87-92, 1980.
Kunitomo, N. & Yamamoto, T., Properties of Predictors in Misspecified Autoregressive Time Series Models, Journal of the American Statistical Association, 80, pp. 941-950, 1985.
de Luna, X., Prediction Intervals Based on Autoregression Forecasts, The Statistician, 49, pp. 87-93, 2000.
Graybill, F.A., Theory and Application of The Linear Model, North Scituate, Mass: Duxbury Press, 1976.
