partialCI (version 1.2.0)

likelihood_ratio.pci: Computes the likelihood ratio of the partially cointegrated model vs the null model

Description

Computes the likelihood ratio of the partially cointegrated model vs the null model

Usage

likelihood_ratio.pci(Y, X, 
  robust = FALSE, 
  null_model = c("rw", "ar1"), 
  pci_opt_method = c("jp", "twostep"), 
  nu = 5)

Arguments

Y

The time series that is to be modeled. A plain or zoo vector of length n.

X

A (possibly zoo) matrix of dimensions n x k. If k=1, then this may be a plain or zoo vector.

robust

If TRUE, then the residuals are assumed to follow a t-distribution with nu degrees of freedom. Default: FALSE.

null_model

This specifies the model that is assumed under the null hypothesis.

• rwRandom walk. Assumes sigma_M = rho = 0. Default.

• ar1Autoregressive of order one. Assumes sigma_R=0.

pci_opt_method

Method to be used for fitting Y to X.

• jpThe coefficients of Y are jointly optimized with the parameters of the AAR fit of the residuals. Default.

• twostepA modified Engle-Granger procedure is used, where the coefficients of Y are first estimated, and then an AAR model is fit to the residuals.

nu

If robust is TRUE, then this is the degrees of freedom parameter used in fitting the t-distribution. Default: 5.

Value

The log of the ratio of the likelihoods of the two models.

Details

First searches for the optimal fit under the null model, and computes the log of the likelihood score of this fit. Then, searches for the optimal fit under the full model, and computes the log of the likelihood score of this fit. Returns the difference of the two likelihood scores. Since the null model is nested in the full model, the log likelihood ratio score is guaranteed to be negative.

References

Clegg, Matthew, 2015. Modeling Time Series with Both Permanent and Transient Components using the Partially Autoregressive Model. Available at SSRN: http://ssrn.com/abstract=2556957

See Also

fit.pci Fitting partially cointegrated models

Examples

# NOT RUN {
YX <- rpci(n=1000, beta=c(2,3,4), sigma_C=c(1,1,1), rho=0.9, sigma_M=0.1, sigma_R=0.2)
likelihood_ratio.pci(YX[,1], YX[,2:ncol(YX)])
# }