By Rob Hyndman, Anne B. Koehler, J. Keith Ord, Ralph D. Snyder
Exponential smoothing tools were round because the Fifties, and are nonetheless the most well-liked forecasting equipment utilized in company and undefined. even though, a modeling framework incorporating stochastic versions, probability calculation, prediction periods and tactics for version choice, used to be no longer constructed till lately. This publication brings jointly the entire very important new effects at the kingdom house framework for exponential smoothing. it is going to be of curiosity to humans desirous to observe the tools of their personal niche in addition to for researchers desirous to take the information in new instructions. half 1 presents an advent to exponential smoothing and the underlying types. the fundamental info are given partly 2, which additionally offer hyperlinks to crucial papers within the literature. extra complex themes are coated partly three, together with the mathematical homes of the versions and extensions of the types for particular difficulties. functions to specific domain names are mentioned partly four.
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Extra resources for Forecasting with exponential smoothing
This general class was introduced brieﬂy in Sect. 2. As for the linear models introduced in the previous chapter, this discussion will pave the way for a general discussion of estimation and prediction methods later in the book. One of the intrinsic advantages of the innovations framework is that we preserve the ability to write down closed-form expressions for the recursive relationships and point forecasts. In addition, the time series may be represented as a weighted sum of the innovations, where the weights for a given innovation depend only on the initial conditions and earlier innovations, so that the weight and the innovation are conditionally independent.
When h = 1, we write yˆ n+1 ≡ yˆ n+1|n . 2. The forecasts may be from varying base times, and be of a consistent forecast horizon. That is, we may compute forecasts yˆ1+h|1, . . , yˆ m+h|m where each yˆ j+h| j is based on data from times t = 1, . . , j. 3. We may wish to compare the accuracy of methods between many series at a single forecast horizon. That is, we compute a single yˆ n+h|n based on data from times t = 1, . . , n for each of m different series. While these are very different situations, measuring forecast accuracy is the same in each case.
The same random number stream from a Gaussian distribution was used for the three series, so that any perceived differences can be attributed entirely to changes in α. 1, the underlying level is reasonably stable. The plot has a jagged appearance because there is a tendency for the series to switch direction between successive observations. This is a consequence of the fact, shown in Chap. 11, that successive ﬁrstdifferences of the series, ∆yt and ∆y t−1, are negatively correlated when α is restricted to the interval (0, 1).
Forecasting with exponential smoothing by Rob Hyndman, Anne B. Koehler, J. Keith Ord, Ralph D. Snyder