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Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: . curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one;
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor.
The formula for a given N-Day period and for a given data series is: [2] [3] = = + (()) = (,) The idea is do a regular exponential moving average (EMA) calculation but on a de-lagged data instead of doing it on the regular data.
ARMA is appropriate when a system is a function of a series of unobserved shocks (the MA or moving average part) as well as its own behavior. For example, stock prices may be shocked by fundamental information as well as exhibiting technical trending and mean-reversion effects due to market participants. [citation needed]
Exponentially weighted moving average (EWMA) is an alternative model in a separate class of exponential smoothing models. As an alternative to GARCH modelling it has some attractive properties such as a greater weight upon more recent observations, but also drawbacks such as an arbitrary decay factor that introduces subjectivity into the ...
Smoothing (estimation) and smoothing (convolution) despite being labelled with the same name in English language, can mean totally different mathematical procedures. The requirements of problems they solve are different. These concepts are distinguished by the context (signal processing versus estimation of stochastic processes).
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [6] [2] However, the term Hanning function is also conventionally used, [7] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.