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# detarma

Usage:
 ```detarma(phi, theta, n [,masign:Masign] [,arsign:Arsign] [,nfreq:Nfreq]), non-MISSING REAL vectors phi and theta, positive integer vector n, Masign and Arsign +1 or -1, positive integer scalar Nfreq ```

Keywords:
```Help is not complete but is taken from the comments associated with
detarma().

detarma() computes the determinant of the Toeplitz covariance associated
with ARMA process.  At present it has no provision for seasonal
processes.

Usage:
detarma(phi, theta, n [,masign:Masign] [,arsign:Arsign] [,nfreq:Nfreq])
phi      non-MISSING REAL vector defining a causal AR operator
theta    non-MISSING REAL vector defining a MA operator
n        vector of positive integers
Masign and/or Arsign must be +1 or -1; they determine sign conventions
for interpreting phi and theta.  Type arimahelp(MASIGN)
for information.
Nfreq    Number of frequencies used in DFT to compute ACFV.  Default
is the smallest integer >= 2*max(max(n), 200) that has no
prime factors > 29

The result is a REAL vector d, the same length as n, with d[i] =
det(Sigma(n[i])), where Sigma(n[i]) = Cov[(X(1),...,X(n[i]))] when X(t)
is ARMA with AR coefficients phi and MA coefficients theta

detarma() computes the autocovariance function as the inverse Fourier
transform of the spectrum computed at nfreq frequencies.  From this it
computes that partial autocorrelations which are used, together with the
variance to compute the determinant.
```

Gary Oehlert 2003-01-15