loglikelihood computes log-likelihood of GMVAR model by using parameter vector
instead of object of class 'gmvar'. Exists for convenience if one wants to for example
plot profile log-likelihoods or employ other estimation algorithms than used in fitGMVAR.
Use minval to control what happens when the parameter vector is outside the parameter space.
loglikelihood(data, p, M, params, conditional = TRUE,
parametrization = c("intercept", "mean"), constraints = NULL,
minval = NA)a matrix or class 'ts' object with d>1 columns. Each column is taken to represent
a single time series. NA values are not supported.
a positive integer specifying the autoregressive order of the model.
a positive integer specifying the number of mixture components.
a real valued vector specifying the parameter values.
Should be size \(((M(pd^2+d+d(d+1)/2+1)-1)x1)\) and have form \(\theta\)\( = \)(\(\upsilon\)\(_{1}\), ...,\(\upsilon\)\(_{M}\), \(\alpha_{1},...,\alpha_{M-1}\)), where:
\(\upsilon\)\(_{m}\) \( = (\phi_{m,0},\)\(\phi\)\(_{m}\)\(,\sigma_{m})\)
\(\phi\)\(_{m}\)\( = (vec(A_{m,1}),...,vec(A_{m,p})\)
and \(\sigma_{m} = vech(\Omega_{m})\), m=1,...,M.
Should be size \(((M(d+d(d+1)/2+1)+q-1)x1)\) and have form \(\theta\)\( = (\phi_{1,0},...,\phi_{M,0},\)\(\psi\) \(,\sigma_{1},...,\sigma_{M},\alpha_{1},...,\alpha_{M-1})\), where:
\(\psi\) \((qx1)\) satisfies (\(\phi\)\(_{1}\)\(,...,\) \(\phi\)\(_{M}) =\) \(C \psi\). Here \(C\) is \((Mpd^2xq)\) constraint matrix.
Above \(\phi_{m,0}\) is the intercept parameter, \(A_{m,i}\) denotes the \(i\):th coefficient matrix of the \(m\):th
mixture component, \(\Omega_{m}\) denotes the error term covariance matrix of the \(m\):th mixture component and
\(\alpha_{m}\) is the mixing weight parameter.
If parametrization=="mean", just replace each \(\phi_{m,0}\) with regimewise mean \(\mu_{m}\).
\(vec()\) is vectorization operator that stacks columns of a given matrix into a vector. \(vech()\) stacks columns
of a given matrix from the principal diagonal downwards (including elements on the diagonal) into a vector.
The notations are in line with the cited article by Kalliovirta, Meitz and Saikkonen (2016).
a logical argument specifying whether the conditional or exact log-likelihood function
should be used. Default is TRUE.
"mean" or "intercept" determining whether the model is parametrized with regime means \(\mu_{m}\) or
intercept parameters \(\phi_{m,0}\), m=1,...,M. Default is "intercept".
a size \((Mpd^2 x q)\) constraint matrix \(C\) specifying general linear constraints
to the autoregressive parameters. We consider constraints of form
(\(\phi\)\(_{1}\)\(,...,\)\(\phi\)\(_{M}) = \)\(C \psi\),
where \(\phi\)\(_{m}\)\( = (vec(A_{m,1}),...,vec(A_{m,p}) (pd^2 x 1), m=1,...,M\)
contains the coefficient matrices and \(\psi\) \((q x 1)\) contains the constrained parameters.
For example, to restrict the AR-parameters to be the same for all regimes, set \(C\)=
[I:...:I]' \((Mpd^2 x pd^2)\) where I = diag(p*d^2).
Ignore (or set to NULL) if linear constraints should not be employed.
value that will be returned if the parameter vector does not lie in the parameter space (excluding the identification condition).
Returns log-likelihood if params is in the parameters space and minval if not.
Takes use of the function dmvn from the package mvnfast to cut down computation time.
Values extremely close to zero are handled with the package Brobdingnag.
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Lutkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.
# NOT RUN {
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
params222 <- c(-11.904, 154.684, 1.314, 0.145, 0.094, 1.292, -0.389,
-0.070, -0.109, -0.281, 0.920, -0.025, 4.839, 11.633, 124.983, 1.248,
0.077, -0.040, 1.266, -0.272, -0.074, 0.034, -0.313, 5.855, 3.570,
9.838, 0.740)
loglikelihood(data=data, p=2, M=2, params=params222, parametrization="mean")
# }
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