perARMA (version 1.3)

loglikec: Calculation of the logarithm of likelihood function

Description

Function loglikec, given phi, del, theta encoded in ptvec, evaluates the logarithm of likelihood function from the PARMA series. Procedure returns also values of the AIC, FPE, BIC information criteria and MSE of residuals, what enables to examine residuals and evaluate godness of model fit.

Usage

loglikec(ptvec, x, conpars)

Arguments

ptvec

vector of parameters for PARMA(p,q) model, containing matrix parameters phi (of size $T \times p$), del (of size $T \times 1$), theta (of size $T \times q$) as following ptvec = [phi[,1],...,phi[,p],del,th

x

input time series.

conpars

vector of parameters [T, p, q, stype], T period of PC-T structure, p, q maximum PAR and PMA order, respectively, stype numeric parameter connected with covariance matrix computation, so far should be eq

Value

• list of values:
• loglik
  logarithm of likehood function (nagative value).
• aicval
  value of AIC criterion.
• fpeval
  value of FPE criterion.
• bicval
  value of BIC criterion.
• mse
  value of MSE of residuals.

Details

In this procedure first series x is filtered by matrix coefficients phi, del, theta. The code to compute logarithm of likelihood function must includes the computation of covariance matrix from the parameters phi, del, theta. Since the inverse of the computed covariance is needed for computing the likelihood, and it is sometimes ill conditioned (or even singular), the condition is improved by removing rows and columns corresponding to very small eigenvalues. This corresponds to removing input data that is highly linearly dependent on the remaining input data. The procedure contains a threshold ZTHRS (which current value is 10*eps) that governs the discarding of rows and column corresponding to small eigenvalues (these are determined by a Cholesky decomposition). Any eigenvalue smaller than the threshold has its row and column deleted from the matrix. Then the inverse and the likelihood are computed from the reduced rank covariance matrix.

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. Vecchia, A., (1985), Periodic autoregressive-moving average (PARMA) modeling with applications to water resources, Water Resources Bulletin, v. 21, no. 5.

See Also

R_w_ma, parmafil

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$xd
#estimators<-perYW(volumes,24,2,NaN)
#estvec=c(estimators$phi[,1],estimators$phi[,2],estimators$del)
#loglikec(estvec,xd,c(24,2,0,0))