likelihood_ratio.pci: Computes the likelihood ratio of the partially cointegrated...
In partialCI: Partial Cointegration

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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

`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.

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.

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

Matthew Clegg matthewcleggphd@gmail.com

Christopher Krauss christopher.krauss@fau.de

Jonas Rende jonas.rende@fau.de

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

fit.pci Fitting partially cointegrated models