Exponential Smoothing

Exponential smoothing is a technique that can be applied to time series data, either to produce smoothed data for presentation, or to make forecasts. The time series data themselves are a sequence of observations. The observed phenomenon may be an essentially random process, or it may be an orderly, but noisy, process. Whereas in the simple moving average the past observations are weighted equally, exponential smoothing assigns exponentially decreasing weights over time.

Exponential smoothing is commonly applied to financial market and economic data, but it can be used with any discrete set of repeated measurements. The raw data sequence is often represented by {xt}, and the output of the exponential smoothing algorithm is commonly written as {st}, which may be regarded as a best estimate of what the next value of x will be. When the sequence of observations begins at time t = 0, the simplest form of exponential smoothing is given by the formulae:

\begin{align} s_1& = x_0\\ s_{t}& = \alpha x_{t-1} + (1-\alpha)s_{t-1}, t>1 \end{align}

where α is the smoothing factor, and 0 < α < 1.

Read more about Exponential Smoothing:  The Exponential Moving Average, Double Exponential Smoothing, Triple Exponential Smoothing

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