Remove noise and periodic components 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.

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

Software Reference

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