burg(Y, P [,degree:d, nfreq:Nfreq]), Y a REAL vector, P an integer > 0, Nfreq an integer > 0 (length of DFT used). |

burg(Y,P,degree:D,nfreq:Nfreq) estimates the spectrum of Y considered as a discrete parameter AR(P) (order P autoregression) time series. The value returned is a structure with the following components: phi REAL vector of length P containing estimated AR coefficients var REAL scalar containing the estimated variance of the res- iduals (innovations) spectrum REAL vector of length Nfreq (see below) containing the estimated spectrum computed at frequencies 0, 1/Nfreq, 2/Nfreq, ..., (Nfreq-1)/Nfreq cycles per Delta-t, the interval between observations. Y must be a REAL vector and P an integer > 0. The keyword phrases are optional. See below for the default values of D and Nfreq. Before estimating the spectrum, Y is detrended by subtracting a degree D polynomial in time fit by least squares. D = 0 corresponds to subtracting the sample mean and D < 0 directs that no detrending is to be done, not even subtracting a mean. Nfreq must be an integer >= nrows(Y) + P and must have no prime factors > 29. If degree:D is omitted, the default value for D is 0 (subtract the mean). If nfreq:Nfreq is omitted, the default value for Nfreq = S if S is a positive integer variable; it is an error if S has a prime factor > 29. When such an S does not exist, Nfreq = smallest integer >= N + P that has no prime factors > 29 otherwise, that is Nfreq = goodfactors(N+P), where N = nrows(Y). The estimated AR coefficients are computed using an algorithm due to Burg which does not involve computing the sample autocorrelations. The method is sometimes called the maximum entropy method, although that can equally well describe any method of estimating a spectrum by fitting an autoregressive model. See also arspectrum(), detrend(), getmacros().

Gary Oehlert 2003-01-15