Smoothing

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 sophistical 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.

Nonparametric Fitting Using a Smoothing Algorithm 4:08