Smoothing

Remove noise and periodic components from data sets while preserving underlying patterns

Smoothing algorithms remove noise from data sets while preserving underlying patterns. 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.

MATLAB products offer a variety of smoothing techniques for different disciplines including signal processing, statistics, and econometrics.

• The MATLAB filter command provides basic smoothing capabilities including a moving average filter.
• Signal Processing Toolbox includes more sophisticated filters such as autoregressive moving average (ARMA) models and Butterworth filters.
• Curve Fitting Toolbox includes smoothing splines, localized regression, and moving average smoothers like Savitzky-Golay filters.
• Econometrics Toolbox provides specialized tools for data series that exhibit autocorrelation, such as vector autoregressive moving average filters with exogenous variables and Hodrick-Prescott filters.

Examples and How To

• Linear Prediction and Autoregressive Modeling (Example)
• Kalman Filter Design in MATLAB (Example)
• Using Cubic Smoothing Splines to Detrend Time Series Data (Example)
• Nonparametric Fitting 4:07 (Video)

Software Reference

• filter (MATLAB Function)
• Filtering and Smoothing (Curve Fitting Toolbox Documentation)
• butter (Signal Processing Toolbox Function)
• kalman (Control Systems Toolbox Function)
• ksdensity (Statistics Toolbox Function)

See also: random number, machine learning, data analysis, mathematical modeling