Prediction Intervals for ARIMA Models
研究如何为ARIMA模型构建考虑参数估计误差和约束条件的预测区间，提出两种基于泰勒近似的新方法，并通过模拟和实际数据验证其优于现有方法。
AbstractThe problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals that 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 on varying degrees of 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. A comparison of the four methods is also made for quarterly retail sales for 10 Organization for Economic Cooperation and Development countries. The new approaches provide a systematic improvement over existing methods.KEY WORDS: ARIMABayesianForecastingHolt-WintersSimulationState space