ARllog {bayess} R Documentation

## log-likelihood associated with an AR(p) model defined either through its natural coefficients or through the roots of the associated lag-polynomial

### Description

This function is related to Chapter 6 on dynamical models. It returns the numerical value of the log-likelihood associated with a time series and an AR(p) model, along with the natural coefficients psi of the AR(p) model if it is defined via the roots lr and lc of the associated lag-polynomial. The function thus uses either the natural parameterisation of the AR(p) model

x_t - \mu + \sum_{i=1}^p \psi_i (x_{t-i}-\mu) = \varepsilon_t

or the parameterisation via the lag-polynomial roots

\prod_{i=1}^p (1-\lambda_i B) x_t = \varepsilon_t

where B^j x_t = x_{t-j}.

### Usage

ARllog(p,dat,pr, pc, lr, lc, mu, sig2, compsi = TRUE, pepsi = c(1, rep(0, p)))


### Arguments

 p order of the AR(p) model dat time series modelled by the AR(p) model pr number of real roots pc number of non-conjugate complex roots lr real roots lc complex roots, stored as real part for odd indices and imaginary part for even indices mu drift coefficient \mu such that (x_t-\mu)_t is a standard AR(p) series sig2 variance of the Gaussian white noise (\varepsilon_t)_t compsi boolean variable indicating whether the coefficients \psi_i need to be retrieved from the roots of the lag-polynomial, i.e. if the model is defined by pepsi (when compsi is FALSE) or by lr and lc (when compsi is TRUE). pepsi potential p+1 coefficients \psi_i if compsi is FALSE, with 1 as the compulsory first value

### Value

 ll value of the log-likelihood ps vector of the \psi_i's

MAllog,ARmh
ARllog(p=3,dat=faithful[,1],pr=3,pc=0,