parmaresid function

Computing residuals of PARMA series

Procedure parmaresid, given phi (of size $T \times p$), del

(of size $T \times 1$), theta (of size $T \times q$), computes the residuals of PARMA series.

parmaresid(x, stype, del, phi,...)

Arguments

• x: input time series.
• stype: numeric parameter connected with covariance matrix computation, so far should be equal to 0 to use procedure R_w_ma (see R_w_ma description). In the future also other values of stype will be available for full covariance matrix computation.
• del: vector of coefficients of length $T$.
• phi: matrix of coefficients of size $T \times p$.
• ...: matrix of coefficients theta of size $T \times q$.

Details

This program uses parmafil to filter the series and computes the covariance matrix. This code does the Cholesky factorization and determines the residuals from the inverse of L (see the code: e=Linv*w0_r1). This allows the treatment of a deficient rank covariance and a reduction of rank. Procedure parmaresid is used in parmaf function.

Returns

Series of residuals resids.

References

Box, G. E. P., Jenkins, G. M., Reinsel, G. (1994), Time Series Analysis, 3rd Ed., Prentice-Hall, Englewood Cliffs, NJ.

Brockwell, P. J., Davis, R. A. (1991), Time Series: Theory and Methods, 2nd Ed., Springer: New York.

Vecchia, A., (1985), Maximum Likelihood Estimation for Periodic Autoregressive Moving Average Models, Technometrics, v. 27, pp.375-384.

Author(s)

Harry Hurd

See Also

R_w_ma, loglikec, loglikef

Examples

## Do not run 
## It could take a few seconds

data(volumes)
pmean<-permest(t(volumes),24, 0.05, NaN,'volumes', pp=0)
xd=pmean$xd
estimators<-perYW(volumes,24,2,NaN)

parmaresid(xd, 0, estimators$del, estimators$phi)