Simultaneous prediction intervals for autoregressive-integrated moving-average models: A comparative study (original) (raw)
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Multiple prediction intervals for time series: Comparison of simultaneous and marginal intervals
Journal of Forecasting, 1991
Simultaneous prediction intervals for forecasts from time series models that contain L ( L 2 1) unknown future observations with a specified probability are derived. Our simultaneous intervals are based on two types of probability inequalities, i.e. the Bonferroni-and product-types. These differ from the marginal intervals in that they take into account the correlation structure between the forecast errors. For the forecasting methods commonly used with seasonal time series data, we show how to construct forecast error correlations and evaluate, using an example, the simultaneous and marginal prediction intervals. For all the methods, the simultaneous intervals are accurate with the accuracy increasing with the use of higher-order probability inequalities, whereas the marginal intervals are far too short in every case. Also, when L is greater than the seasonal period, the simultaneous intervals based on improved probability inequalities will be most accurate.
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.
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
Confidence intervals for linear combinations of forecasts from dynamic econometric models
Journal of Policy Modeling, 1992
This paper derives the approximate distribution of a vector of forecast errors from a dynamic simultaneous equations econometric model. The system may include exogenous variables with known and/or unknown future values. For the latter set of exogenous variables, a stationary and invertible ARMAX process is assumed. Confidence regions are derived for vectors of linear combinations of forecasts. These confidence regions are particularly useful for designing tests of super exogeneity via tests of predictive failure. To illustrate the use of confidence intervals, forecasts are generated for an oil price and for a Venezuelan consumer price index.
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 .
This paper proposes a strategy to increase the efficiency of forecast combining methods. Given the availability of a wide range of forecasting models for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, an algorithm procedure based on a widely used encompassing test (Harvey, Leybourne, Newbold, 1998) is developed. First, forecasting models are ranked according to a measure of predictive accuracy (RMSFE) and, in a consecutive step, each prediction is chosen for combining only if it is not encompassed by the competing models. To assess the robustness of this procedure, an empirical application to Italian monthly industrial production using ISAE short-term forecasting models is provided.
Expert Systems with Applications, 2012
Forecast combination is a method that allows the improvement of accuracy of forecasts. The literature presents several studies that assess the methods of forecast combination existent in relation to its accuracy, but there is no unanimity in the results. The combination method by arithmetic mean is the one most widely used, although some authors consider the minimum variance method as more accurate. The latter allows to consider whether or not the correlation between the errors of individual forecasts, a situation in which is attributed, in this study, the nomenclature of simplified method of minimum variance. This study aims at identifying differences in the accuracy of quantitative forecasts, obtained by these methods. The individual modeling that support the combinations are SARIMA and ANN, and measures of accuracy used to choose the best method are MAPE, MSE and MAE. As the main result, there is a superior performance of the simplified combination method by minimum variance.