specarma(phi ,theta [, nfreq:nf]), REAL vectors phi and theta, integer nf > 0 |

specarma(phi, theta [, nfreq:Nfreq]) computes the spectrum of an ARMA time series with AR coefficients in phi and MA coefficients in theta and innovation variance 1. phi and theta are REAL vectors with no MISSING values. To omit part of the model, use phi = 0 or theta = 0 Nfreq must be a positive integer with no prime factors > 29. The result is a vector of length nf containing the spectrum at frequencies 0, 1/Nfreq, 2/Nfreq, ..., (Nfreq-1)/Nfreq cycles per unit time. Without nfreq:Nfreq, when no positive integer scalar S exists, the default is Nfreq = 400. When S does exist and is a positive integer scalar, the default for Nfreq is S. It is an error if S has a prime factor > 29. You can use keyword phrases arsign:Arsign and masign:Masign, where Arsign and Masign are +1 or -1, to modify the interpretation of the coefficients in the ARMA model. The default for Arsign is variable ARSIGN if it exists or -1 if not. The default for Masign is variable MASIGN if it exists or -1 if not. The ARMA model assumed is defined as (1+Arsign*sum(phi*B^run(p)))X[t] = (1+Masign*sum(theta*B^run(q)))Z[t]. where B is the backshift operator and {Z[t]} is white noise with mean 0 and variance 1. Arsign = -1 and Masign = -1 correspond to the convention used by Box and Jenkins, and Arsign = -1 and Masign = +1 correspond to the convention used by Brockwell and Davis You can plot the spectrum for the ARMA model fit by arima() by Cmd> result <- arima(y,pdq:vector(p,0,q), keep:T) Cmd> ffplot(specarma(result$phi, result$theta)) See also arima(), acfarma(), ffplot().

Gary Oehlert 2003-01-15