arspectrum(Y,P [,nfreq:nfreq] [,nospec:T]), Y a REAL vector, integer P > 0, integer nfreq > 0. |

arspectrum(Y,P) estimates the spectrum of Y considered as a discrete parameter AR(P) (order P autoregressive) time series. Y must be a REAL vector with no MISSING elements and P > 0 an integer. The value returned is a structure(phi:Phi,var:Var, spectrum:Sy) Phi REAL vector of length P containing estimated AR coefficients V REAL scalar containing the estimated variance of the residuals (innovations) Sy 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. The default value for Nfreq is determined as follows: 1. If variable S is defined and is an integer > 2, Nfreq = S. It is an error if S has a prime factor > 29. 2. Otherwise, Nfreq is the smallest integer >= 2*nrows(y) which has no prime factor > 29, that is Nfreq = goodfactors(2*nrows(y)) arspectrum(Y,P,nfreq:Nfreq) or arspectrum(Y,P,Nfreq), where Nfreq > 0 is an integer, does the same, computing the spectrum at Nfreq frequencies. It is an error if Nfreq has a prime factor > 29. arspectrum(Y,P,nospec:T) computes phi and var but not spectrum, returning structure(phi,var). Estimated AR coefficients Phi are computed from the first P sample autocorrelations by solving the Yule-Walker equations. See yulewalker(). The variance V = gammahat(0)*prod(1 - pacf^2), where gammahat(0) = sum((y - ybar)^2)/n and pacf is the vector of P partial autocorrelations associated with Phi. See also burg(), yulewalker().

Gary Oehlert 2003-01-15