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the aim of smoothing is to give a general idea of relatively slow changes of value with little attention paid to the close matching of data values, while curve fitting concentrates on achieving as close a match as possible. smoothing methods often have an associated tuning parameter which is used to control the extent of smoothing.
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. It is an easily learned ...
A kernel smoother is a statistical technique to estimate a real valued function: as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter.
The "moving average filter" is a trivial example of a Savitzky–Golay filter that is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. Each subset of the data set is fit with a straight horizontal line as opposed to a higher order polynomial.
An alpha beta filter (also called alpha-beta filter, f-g filter or g-h filter [1]) is a simplified form of observer for estimation, data smoothing and control applications. It is closely related to Kalman filters and to linear state observers used in control theory. Its principal advantage is that it does not require a detailed system model.
In signal processing, Lulu smoothing is a nonlinear mathematical technique for removing impulsive noise from a data sequence such as a time series.It is a nonlinear equivalent to taking a moving average (or other smoothing technique) of a time series, and is similar to other nonlinear smoothing techniques, such as Tukey or median smoothing.
Local regression or local polynomial regression, [1] also known as moving regression, [2] is a generalization of the moving average and polynomial regression. [3] Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced / ˈ l oʊ ɛ s / LOH-ess.
is a smoothing parameter, controlling the trade-off between fidelity to the data and roughness of the function estimate. This is often estimated by generalized cross-validation, [ 3 ] or by restricted marginal likelihood (REML) [ citation needed ] which exploits the link between spline smoothing and Bayesian estimation (the smoothing penalty ...