MAllog: log-likelihood associated with an MA(p) model
Description
This function returns the numerical value of the log-likelihood associated with a time
series and an MA(p) model in Chapter 7. It either uses the natural parameterisation of the MA(p)
model $$x_t-\mu = \varepsilon_t - \sum_{j=1}^p \psi_{j} \varepsilon_{t-j}$$
or the parameterisation via the lag-polynomial roots
$$x_t - \mu = \prod_{i=1}^p (1-\lambda_i B) \varepsilon_t$$
where $B^j \varepsilon_t = \varepsilon_{t-j}$.
number of complex roots in the lag polynomial, necessarily even
lr
real roots
lc
complex roots, stored as real part for odd indices and
imaginary part for even indices. (lc is either 0 when
pc=0 or a vector of even length when pc>0.)
mu
drift parameter $\mu$ such that $(X_t-\mu)_t$ is a standard MA$(p)$ 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 (if TRUE) or not (if FALSE)
pepsi
potential coefficients $\psi_i$, computed by the function if compsi is TRUE
eps
white noise terms $(\varepsilon_t)_{t\le 0}$ with negative indices
Value
llvalue of the log-likelihood
psvector of the $\psi_i$'s, similar to the entry if compsi is FALSE