Confidence intervals for exponential smoothing I'm using exponential smoothing (Brown's method) for forecasting. The forecast can be calculated for one or more steps (time intervals). Is there any way to calculate confidence intervals for such prognosis (ex-ante)?
 A: Exponential smoothing methods as such have no underlying statistical model, so prediction intervals cannot be calculated. However, when we do want to add a statistical model, we naturally arrive at state space models, which are generalizations of exponential smoothing - and which allow calculating prediction intervals. See section 7.7 in this free online textbook using R, or look into Forecasting with Exponential Smoothing: The State Space Approach. Both books are by Rob Hyndman and (different) colleagues, and both are very good.
A: Exponential smoothing (Brown's method) is a particular variant of an ARIMA model (0,1,1) . In general the ma(1) coefficient can range from -1 to 1 allowing for both a direct response ( 0 to 1) to previous values OR both a direct and indirect response( -1 to 0). Exponential smoothing restricts the ma(1) coefficient to one half the sample space (0 to 1) see the Box-Jenkins text for the complete discussion. One could estimate the (0,1,1) ARIMA model and obtain confidence intervals for the forecast. Brown's smoothing coefficient (alpha) is equal to 1.0 minus the ma(1) coefficient. If the estimated ma(1) coefficient is >.0 e.g. .8 then alpha = .2 and you are good to go. If the ma coefficent is less than zero then Brown's method(model) is probably inadequate for the data. Tests for statistical significance of estimated parameters is often ignored using ad hoc models.  Additionly validation procedures to verify randomness of the model's residuals are ALWAYS ignored. Another useful discussion can be found at Prof. Nau's website http://people.duke.edu/~rnau/411arim.htm although he fails to point out the strong limitation imposed by Brown's Assumptions.
