psd_varma function

VARMA(p,q) spectral density function

Evaluate the VARMA(p,q) spectral density at some frequencies freq in [0,pi). Note that no test for model stationarity is performed.

psd_varma(
  freq,
  ar = matrix(nrow = nrow(Sigma), ncol = 0),
  ma = matrix(nrow = nrow(Sigma), ncol = 0),
  Sigma
)

Arguments

• freq: numeric vector of frequencies to evaluate the psd, 0 <= freq < pi
• ar: autoregressive coeffient matrix (d times p*d) of VARMA model, defaults to empty VAR component
• ma: moving average coeffient matrix (d times p*d) of VARMA model, defaults to empty VAR component
• Sigma: positive definite innovation covariance matrix (d times d)

Returns

an array containing the values of the varma psd matrix at freq

Details

See section 11.5 in the referenced book

References

P. J. Brockwell and R. Davis (1996) Time Series: Theory and Methods (Second Edition)