Perform Durbin-Levinson recursion on a vector or matrix.
levinson(x, p = NULL)
The denominator filter coefficients.
Variance of the white noise = square of the numerator constant.
Reflection coefficients = coefficients of the lattice implementation of the filter.
Input signal.
Lag (defaults to length(x) or nrow(x)).
Original Octave version by Paul Kienzle pkienzle@users.sf.net based on yulewalker.m by Friedrich Leisch Friedrich.Leisch@boku.ac.at. Conversion to R by Sebastian Krey krey@statistik.tu-dortmund.de.
Use the Durbin-Levinson algorithm to solve:
toeplitz(acf(1:p)) * y = -acf(2:p+1).
The solution [1, y'] is the denominator of an all pole filter approximation to the signal x which generated the autocorrelation function acf.
acf is the autocorrelation function for lags 0 to p.
Steven M. Kay and Stanley Lawrence Marple Jr.: Spectrum analysis -- a modern perspective, Proceedings of the IEEE, Vol 69, pp 1380-1419, Nov., 1981