Analysis: Holt Exponential Smoothing

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Holt exponential smoothing modelling Simple exponential smoothing does not do well when there is a trend in the data, which is inconvenient. In such situations, several methods were devised under the name "double exponential smoothing" or "second-order exponential smoothing", which is the recursive application of an exponential filter twice, thus being termed "double exponential smoothing". This nomenclature is similar to quadruple exponential smoothing, which also references its recursion depth. The basic idea behind double exponential smoothing is to introduce a term to take into account the possibility of a series exhibiting some form of trend. This slope component is itself updated via exponential smoothing. Holt exponential smoothing …show more content…

In a series with a linear trend, this should equal the slope of the trend with some added noise specific for the situation at the time index t. The trend slop, which is allowed to be time varying, is denoted b_t. The idea is basically to update the true level using the present observation X_t from the previous level X ̃_(t-1) to X ̃_t by an adjustment to the previous slope element b_(t-1) using exponential smoothing. Moreover, the basic formula for exponential smoothing is applied to update from the estimate of b_(t-1) to an estimate of actual b_t as anaverage of last slop element b_(t-1) and the present observed incrementX ̃_t-X ̃_(t-1) of the estimated true level. Expressed as formulas, these two updating equations then …show more content…

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