## Smoothing |

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™.

- 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)

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

*See also*: *random number*, *machine learning*, *data analysis*, *mathematical modeling*, *time series regression*, *kalman filter*, *smoothing videos*