Multiple prediction intervals for time series: Comparison of simultaneous and marginal intervals (original) (raw)
Related papers
Computational Statistics & Data Analysis, 1998
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.
Forecasting models and prediction intervals for the multiplicative Holt–Winters method
International Journal of Forecasting, 2001
A new class of models for data showing trend and multiplicative seasonality is presented. The models allow the forecast error variance to depend on the trend and/or the seasonality. It can be shown that each of these models has the same updating equations and forecast functions as the multiplicative Holt-Winters method, regardless of whether the error variation in the model is constant or not. While the point forecasts from the different models are identical, the prediction intervals will, of course, depend on the structure of the error variance and so it is essential to be able to choose the most appropriate form of model. Two methods for making this choice are presented and examined by simulation.
On the Comparison of Interval Forecasts
Social Science Research Network, 2018
We explore interval forecast comparison when the nominal confidence level is specified, but the quantiles on which intervals are based are not specified. It turns out that the problem is difficult, and perhaps unsolvable. We first consider a situation where intervals meet the Christoffersen conditions (in particular, where they are correctly calibrated), in which case the common prescription, which we rationalize and explore, is to prefer the interval of shortest length. We then allow for mis-calibrated intervals, in which case there is a calibration-length tradeoff. We propose two natural conditions that interval forecast loss functions should meet in such environments, and we show that a variety of popular approaches to interval forecast comparison fail them. Our negative results strengthen the case for abandoning interval forecasts in favor of density forecasts: Density forecasts not only provide richer information, but also can be readily compared using known proper scoring rules like the log predictive score, whereas interval forecasts cannot.
Prediction Intervals for ARIMA Models
Journal of Business & Economic Statistics, 2001
The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals which incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationarity and invertibility conditions is also incorporated. Two new methods, based to varying degrees on first-order Taylor approximations, are proposed. These are compared in a simulation study to two existing methods: a heuristic approach and the `plug-in' method whereby parameter values are set equal to their maximum likelihood estimates
M1 and M2 indicators- new proposed measures for the global accuracy of forecast intervals
This is an original scientific paper that proposes the introduction in literature of two new accuracy indicators for assessing the global accuracy of the forecast intervals. Taking into account that there are not specific indicators for prediction intervals, point forecasts being associated to intervals, we consider an important step to propose those indicators whose function is only to identify the best method of constructing forecast intervals on a specific horizon. This research also proposes a new empirical method of building intervals for maximal appreciations of inflation rate made by SPF's (Survey of Professional Forecasters) experts. This method proved to be better than those of the historical errors methods (those based on RMSE (root mean square error)) for the financial services providers on the horizon Q3:2012-Q2:2013 .
Multiple forecasts with autoregressive time series models: case studies
Mathematics and Computers in Simulation, 2004
It is indisputable that accurate forecasts of economic activities are vital to successful business and government policies. In many circumstances, instead of a single forecast, simultaneous prediction intervals for multiple forecasts are more useful to decision-makers. For example, based on previous monthly sales records, a production manager would be interested in the next 12 interval forecasts of the monthly sales using for the annual inventory and manpower planning. For Gaussian autoregressive time series processes, several procedures for constructing simultaneous prediction intervals have been proposed in the literature. These methods assume a normal error distribution and can be adversely affected by departures from normality which are commonly encountered in business and economic time series. In this article, we explore the bootstrap methods for the construction of simultaneous multiple interval forecasts. To understand the mechanisms and characteristics of the proposed bootstrap procedures, several macroeconomic time series are selected for illustrative purposes. The selected series are fitted reasonably well with autoregressive models which form an important class in time series. As a matter of fact, the major ideas discussed in this paper with autoregressive processes can be extended to other more complicated time series models.