Simultaneous prediction intervals for autoregressive-integrated moving-average models: A comparative study (original) (raw)

Abstract

Multiple forecasts for autoregressive-integrated moving-average (ARIMA) models are useful in many areas such as economics and business forecasting. In recent years, approximation methods to construct simultaneous prediction intervals for multiple forecasts arc developed. These methods were based on highex-order Bonfcrroni and product-type inequalities. In this article, we compare the 'exact' method which requires the evaluation of multivariate normal probabilities to the approximation methods. It is found that the exact method is computationally far more efficient. Furthermore, the exact method can be applied to all ARIMA models while the approximation methods are limited to only a subset of ARIMA models. Illustrative examples are given to compare the performance of various procedures. (~) 1998 Elsevier Science B.V. All rights reserved.

Key takeaways

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  1. The exact method for constructing prediction intervals is computationally more efficient than approximation methods.
  2. Approximation methods only apply to a limited subset of ARIMA models, reducing their overall utility.
  3. The study provides a comparative analysis of simultaneous prediction intervals for ARIMA models.
  4. Examples demonstrate that the exact method significantly reduces CPU time, with over 78% reduction in one case.
  5. Multivariate normal probabilities can now be computed efficiently for L up to 20, enhancing practical applications.

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