Prediction Intervals

By C. Chatfield. 1993

Computing prediction intervals (P.I.s) is an important part of the forecasting process intended s i to indicate the likely uncertainty in point forecasts. The commonest method of calculating P.I. s to use theoretical formulae conditional on a best-fitting model. If a normality assumption is t o used, it needs to be checked. Alternative computational procedures that are not so dependen n a fitted model include the use of empirically based and resampling methods. Some sos called approximate formulae should be avoided. P.I.s tend to be too narrow because out-of ample forecast accuracy is often poorer than would be expected from within-sample fit, i particularly for P.I.s calculated conditional on a model fitted to past data. Reasons for this nclude uncertainty about the model and a changing environment. Ways of overcoming these m problems include using a mixture of models with a Bayesian approach and using a forecasting ethod that is designed to be robust to changes in the underlying model. ; P

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Citations in the corpus

The Tourism Forecasting Competition (2011, background): “(1997), Hyndman et al. (2002) and Hyndman et al. (2005) (amongst others) have developed a statistical framework for the exponential smoothing methods presented in Table 1.”
Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing (2011, unknown): “Its mean E(y (ω) n+h|n) and variance V(y (ω) n+h|n) are given, after allowing for the Box-Cox transformation, by the equations (Hyndman et al. 2005): E(y n+h|n) = w ′F xn (12a) V(y n+h|n) =  σ2 if h = 1; σ2 [ 1+ h−1 ∑ j=1 c(2)j ] if h≥ 2; (12b)”