Smoothing algorithms are often used to remove periodic components from a data set while preserving long term trends. For example, time-series data that is sampled once a month often exhibits seasonal fluctuations. A twelve-month moving average filter will remove the seasonal component while preserving the long-term trend.

Alternatively, smoothing algorithms can be used to generate a descriptive model for exploratory data analysis. This technique is frequently used when it is impractical to specify a parameter model that describes the relationship between a set of variables.

Signal or time series smoothing techniques are used in a range of disciplines including signal processing, system identification, statistics, and econometrics.

Common smoothing algorithms include:

• LOWESS and LOESS: Nonparametric smoothing methods using local regression models
• Kernel smoothing: Nonparametric approach to modeling a smooth distribution function
• Smoothing splines: Nonparametric approach for curve fitting
• Autoregressive moving average (ARMA) filter: Filter used when data exhibits serial autocorrelation
• Hodrick-Prescott filter: Filter used to smooth econometric time series by extracting the seasonal components
• Savitzky–Golay smoothing filter: Filter used when a signal has high frequency information that should be retained
• Butterworth filter: Filter used in signal processing to remove high frequency noise

For more information on smoothing, please see Statistics and Machine Learning Toolbox™, Curve Fitting Toolbox™, Econometrics Toolbox™, System Identification Toolbox™, and Signal Processing Toolbox™.