TSA ARMA Modeling VI

LabVIEW 2014 Advanced Signal Processing Toolkit Help

Edition Date: June 2014

Part Number: 372656C-01

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Owning Palette: Modeling and Prediction VIs

Requires: Advanced Signal Processing Toolkit

Estimates the autoregressive-moving average (ARMA) model of a univariate or multivariate (vector) time series according to the method you specify. Wire data to the Xt input to determine the polymorphic instance to use or manually select the instance.

Details  Examples

Use the pull-down menu to select an instance of this VI.

TSA ARMA Modeling (Waveform)

Xt specifies the univariate time series.
method specifies the method to use in estimating the autoregressive-moving average model.

0Yule-Walker (default)—Computes the AR coefficients and the MA coefficients separately with the extended Yule-Walker function based on the auto-correlation matrix.
1High order AR—Computes the AR coefficients and the MA coefficients with a high-order AR model.
2Polynomial—Computes the AR coefficients and the MA coefficients by solving the model-coefficient polynomial division.
ARMA order specifies the orders of the autoregressive-moving average model.
AR specifies the AR order of the autoregressive-moving average model. The value of AR must be equal to or greater than 0. The value of AR cannot be zero if the value of MA is zero. The default is 4.
MA specifies the MA order of the autoregressive-moving average model. The value of MA must be equal to or greater than 0. The value of MA cannot be zero if the value of AR is zero. The default is 3.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
AR coefficients returns the estimated AR coefficients of the autoregressive-moving average model.
MA coefficients returns the estimated MA coefficients of the autoregressive-moving average model.
noise returns the estimated white noise of the autoregressive-moving average model.
error out contains error information. This output provides standard error out functionality.

TSA ARMA Modeling (Array)

Xt specifies the univariate time series.
method specifies the method to use in estimating the autoregressive-moving average model.

0Yule-Walker (default)—Computes the AR coefficients and the MA coefficients separately with the extended Yule-Walker function based on the auto-correlation matrix.
1High order AR—Computes the AR coefficients and the MA coefficients with a high-order AR model.
2Polynomial—Computes the AR coefficients and the MA coefficients by solving the model-coefficient polynomial division.
ARMA order specifies the orders of the autoregressive-moving average model.
AR specifies the AR order of the autoregressive-moving average model. The value of AR must be equal to or greater than 0. The value of AR cannot be zero if the value of MA is zero. The default is 4.
MA specifies the MA order of the autoregressive-moving average model. The value of MA must be equal to or greater than 0. The value of MA cannot be zero if the value of AR is zero. The default is 3.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
AR coefficients returns the estimated AR coefficients of the autoregressive-moving average model.
MA coefficients returns the estimated MA coefficients of the autoregressive-moving average model.
noise returns the estimated white noise of the autoregressive-moving average model.
error out contains error information. This output provides standard error out functionality.

TSA Vector ARMA Modeling (Waveform)

Xt specifies the multivariate (vector) time series.
ARMA order specifies the orders of the autoregressive-moving average model.
AR specifies the AR order of the autoregressive-moving average model. The value of AR must be equal to or greater than 0. The value of AR cannot be zero if the value of MA is zero. The default is 4.
MA specifies the MA order of the autoregressive-moving average model. The value of MA must be equal to or greater than 0. The value of MA cannot be zero if the value of AR is zero. The default is 3.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
AR coefficients returns the estimated AR coefficients of the vector autoregressive-moving average model.
MA coefficients returns the estimated MA coefficients of the vector autoregressive-moving average model.
noise returns the estimated multivariate white noise series of the vector autoregressive-moving average model.
error out contains error information. This output provides standard error out functionality.

TSA Vector ARMA Modeling (Array)

Xt specifies the multivariate (vector) time series. Each column of the 2D array represents a vector at certain time.
ARMA order specifies the orders of the autoregressive-moving average model.
AR specifies the AR order of the autoregressive-moving average model. The value of AR must be equal to or greater than 0. The value of AR cannot be zero if the value of MA is zero. The default is 4.
MA specifies the MA order of the autoregressive-moving average model. The value of MA must be equal to or greater than 0. The value of MA cannot be zero if the value of AR is zero. The default is 3.
error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
AR coefficients returns the estimated AR coefficients of the vector autoregressive-moving average model.
MA coefficients returns the estimated MA coefficients of the vector autoregressive-moving average model.
noise returns the estimated multivariate white noise series of the vector autoregressive-moving average model. Each column of the 2D array is a vector at certain time.
error out contains error information. This output provides standard error out functionality.

TSA ARMA Modeling Details

This VI estimates the autoregressive (AR) model according to the following equation:

Xt + a1Xt–1 + ,…, + aNaXt–Na = et + b1et–1 + ,…, + bNbet–Nb

where Na is the AR order, Nb is the MA order, Xt is a univariate or multivariate (vector) time series, and et is a Gaussian white noise series with a mean of zero.

For univariate time series, AR coefficients is a 1D array [1, a1, a2, …, aNa], where each coefficient ai is a real number. MA coefficients is a 1D array [1, b1, b2, …, bNb], where each coefficient bi also is a real number.

For multivariate time series, AR coefficients is a 1D array [I, a1, a2, …, aNa], where each coefficient ai is a 2D array cluster. MA coefficients is a 1D array [I, b1, b2, …, bNb], where each coefficient bi also is a 2D array cluster.

The minimum length requirement for the input time series differs for each method you use:

  • Yule-Walker method: minimum length ≥ AR order + MA order
  • High-Order AR method: minimum length ≥ 5 × MA order
  • Polynomial method: minimum length ≥ 5 × (AR order + MA order)

Examples

Refer to the following VIs for examples of using the TSA ARMA Modeling VI:

  • Engine Knocking Monitor VI: labview\examples\Time Series Analysis\TSAApplications
  • ARMA Prediction VI: labview\examples\Time Series Analysis\TSAGettingStarted
  • ARMA Model Estimation VI: labview\examples\Time Series Analysis\TSAGettingStarted

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