TSA AR Modeling VI

Owning Palette: Modeling and Prediction VIs

Requires: Advanced Signal Processing Toolkit

Estimates the autoregressive (AR) 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.

Select an instance TSA AR Modeling (Waveform)TSA AR Modeling (Array)TSA Vector AR Modeling (Waveform)TSA Vector AR Modeling (Array)

TSA AR Modeling (Waveform)

	Xt specifies the univariate time series.
	AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average.
	AR order specifies the order of the autoregressive (AR) model. The value of AR order must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	AR coefficients returns the estimated coefficients of the autoregressive model.
	noise returns the estimated white noise series in the autoregressive model.
	error out contains error information. This output provides standard error out functionality.

TSA AR Modeling (Array)

	Xt specifies the univariate time series.
	AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average.
	AR order specifies the order of the autoregressive (AR) model. The value of AR order must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	AR coefficients returns the estimated coefficients of the autoregressive model.
	noise returns the disturbance e(t) in the estimated system model.
	error out contains error information. This output provides standard error out functionality.

TSA Vector AR Modeling (Waveform)

	Xt specifies the multivariate (vector) time series.
	AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average.
	AR order specifies the order of vector autoregressive model to estimate. The value of AR order must be greater than 0.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	AR coefficients returns the estimated coefficients of the vector autoregressive model.
	noise returns the estimated multivariate white noise series in the vector autoregressive model.
	error out contains error information. This output provides standard error out functionality.

TSA Vector AR Modeling (Array)

	Xt specifies the multivariate (vector) time series. Each column of the 2D array represents a vector at certain time.
	AR method specifies the method this VI uses to estimate the autoregressive (AR) model. 0 Forward-Backward (default)—Computes the AR coefficients by minimizing the least-square errors of the forward and backward predictions. 1 Least-Squares—Computes the AR coefficients by minimizing the least-square errors of the forward predictions. 2 Yule-Walker—Computes the AR coefficients by solving the Yule-Walker functions based on the forward predictions. 3 Burg-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the arithmetic average. 4 Geometric-Lattice—Computes the AR coefficients using the Levinson-Durbin recursion based on the forward and backward predictions. The Levinson-Durbin recursion uses the geometric average.
	AR order specifies the order of the autoregressive (AR) model. The value of AR order must be greater than 0. The default is 4.
	error in describes error conditions that occur before this node runs. This input provides standard error in functionality.
	AR coefficients returns the estimated coefficients of the vector autoregressive model.
	noise returns the estimated multivariate white noise series in the vector autoregressive model. Each column of the 2D array represents a vector at certain time.
	error out contains error information. This output provides standard error out functionality.

TSA AR Modeling Details

This VI estimates the AR model according to the following equation:

X_t + a₁X_t–1 + ,…, + a_nX_t–n = e_t

where n is the AR order. X_t is a univariate or multivariate (vector) time series. e_t is a Gaussian white noise series with a mean of zero.

For univariate time series, AR coefficients is a 1D array of [1, a₁, a₂, …, a_n], where each coefficient a_i is a real number.

For multivariate time series, AR coefficients is a 1D array of [I, a₁, a₂, …, a_n], where each coefficient a_i is a cluster of 2D arrays.

The minimum length requirement for the input time series needs to be at least two times the AR order.

Examples

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

• Power Line Monitor VI: labview\examples\Time Series Analysis\TSAApplications
• Fault Detection with Pattern Recognition VI: labview\examples\Time Series Analysis\TSAApplications
• AR Model Estimation VI: labview\examples\Time Series Analysis\TSAGettingStarted