Wolfram Language & System 11.0 (2016)|Legacy Documentation

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Time Series Processes

Time series refers to a sequence of observations following each other in time, where adjacent observations are correlated. This can be used to model, simulate, and forecast behavior for a system. Time series models are frequently used in fields such as economics, finance, biology, and engineering.  The Wolfram Language provides a full suite of time series functionality, including standard models such as MA, AR, and ARMA, as well as several extensions. Time series models can be simulated, estimated from data, and used to produce forecasts of future behavior.


TimeSeriesModelFit automatically fit a time series process model to data

Basic ARMA Processes

MAProcess moving-average process (scalar and vector)

ARProcess autoregressive process (scalar and vector)

ARMAProcess autoregressive moving-average process (scalar and vector)

Integrated and Seasonal ARMA Processes

SARIMAProcess seasonal integrating ARMA for polynomial and periodic trends

ARIMAProcess  ▪  SARMAProcess  ▪  FARIMAProcess

GARCH Processes

ARCHProcess autoregressive conditionally heteroscedastic process

GARCHProcess generalized ARCH process

Process Framework »

RandomFunction simulate a time series process

EstimatedProcess estimate parameters in a time series process

TimeSeriesForecast forecast future values in a time series process

KalmanFilter filters data based on a time series model

TemporalData time series data

FindProcessParameters  ▪  AdjustTimeSeriesForecast

CovarianceFunction  ▪  CorrelationFunction  ▪  AbsoluteCorrelationFunction  ▪  PartialCorrelationFunction  ▪  PowerSpectralDensity

Model Properties and Representations

WeakStationarity conditions for a time series model to be weakly stationary

TimeSeriesInvertibility conditions for a time series model to be invertible

ToInvertibleTimeSeries gives an invertible representation of the time series

Time Series Data Processing »

UnitRootTest test whether time series data is stationary

AutocorrelationTest test whether time series data is autocorrelated

Differences detrending and deseasoning data

MovingAverage moving-average filtering