aryule function

Autoregressive model coefficients - Yule-Walker method

compute autoregressive all-pole model parameters using the Yule-Walker method.

aryule(x, p)

Arguments

• x: input data, specified as a numeric or complex vector or matrix. In case of a vector it represents a single signal; in case of a matrix each column is a signal.
• p: model order; number of poles in the AR model or limit to the number of poles if a valid criterion is provided. Must be smaller than the length of x minus 1.

Returns

A list containing the following elements:

• a: vector or matrix containing (p + 1) autoregression coefficients. If x is a matrix, then each row of a corresponds to a column of x. a has p + 1 columns.
• e: white noise input variance, returned as a vector. If x is a matrix, then each element of e corresponds to a column of x.
• k: Reflection coefficients defining the lattice-filter embodiment of the model returned as vector or a matrix. If x is a matrix, then each column of k corresponds to a column of x. k has p rows.

Details

aryule uses the Levinson-Durbin recursion on the biased estimate of the sample autocorrelation sequence to compute the parameters.

Note

The power spectrum of the resulting filter can be plotted with pyulear(x, p), or you can plot it directly with ar_psd(a,v,...).

Examples

a <- Arma(1, c(1, -2.7607, 3.8106, -2.6535, 0.9238))
y <- filter(a, rnorm(1024))
coefs <- aryule(y, 4)

See Also

ar_psd, arburg

Author(s)

Paul Kienzle, pkienzle@users.sf.net ,

Peter V. Lanspeary, pvl@mecheng.adelaide.edu.au .

Conversion to R by Geert van Boxtel, gjmvanboxtel@gmail.com .