Description Usage Arguments Details Value References See Also Examples
View source: R/loglikelihood.R
loglikelihood
compute conditional regimewise means, conditional means, and conditional covariance matrices
of a GMVAR, StMVAR, or GStMVAR model.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  cond_moments(
data,
p,
M,
params,
model = c("GMVAR", "StMVAR", "GStMVAR"),
parametrization = c("intercept", "mean"),
constraints = NULL,
same_means = NULL,
structural_pars = NULL,
to_return = c("regime_cmeans", "regime_ccovs", "total_cmeans", "total_ccovs",
"arch_scalars"),
minval = NA,
stat_tol = 0.001,
posdef_tol = 1e08,
df_tol = 1e08
)

data 
a matrix or class 
p 
a positive integer specifying the autoregressive order of the model. 
M 

params 
a real valued vector specifying the parameter values.
Above, φ_{m,0} is the intercept parameter, A_{m,i} denotes the ith coefficient matrix of the mth
mixture component, Ω_{m} denotes the error term covariance matrix of the m:th mixture component, and
α_{m} is the mixing weight parameter. The W and λ_{mi} are structural parameters replacing the
error term covariance matrices (see Virolainen, 2020). If M=1, α_{m} and λ_{mi} are dropped.
If In the GMVAR model, M1=M and ν is dropped from the parameter vector. In the StMVAR model, M1=0.
In the GStMVAR model, the first The notation is similar to the cited literature. 
model 
is "GMVAR", "StMVAR", or "GStMVAR" model considered? In the GStMVAR model, the first 
parametrization 

constraints 
a size (Mpd^2 x q) constraint matrix C specifying general linear constraints
to the autoregressive parameters. We consider constraints of form
(φ_{1},...,φ_{M}) = C ψ,
where φ_{m} = (vec(A_{m,1}),...,vec(A_{m,p}) (pd^2 x 1), m=1,...,M,
contains the coefficient matrices and ψ (q x 1) contains the related parameters.
For example, to restrict the ARparameters to be the same for all regimes, set C=
[ 
same_means 
Restrict the mean parameters of some regimes to be the same? Provide a list of numeric vectors
such that each numeric vector contains the regimes that should share the common mean parameters. For instance, if

structural_pars 
If
See Virolainen (2020) for the conditions required to identify the shocks and for the Bmatrix as well (it is W times a timevarying diagonal matrix with positive diagonal entries). 
to_return 
should the regimewise conditional means, total conditional means, or total conditional covariance matrices be returned? 
minval 
the value that will be returned if the parameter vector does not lie in the parameter space (excluding the identification condition). 
stat_tol 
numerical tolerance for stationarity of the AR parameters: if the "bold A" matrix of any regime
has eigenvalues larger that 
posdef_tol 
numerical tolerance for positive definiteness of the error term covariance matrices: if the error term covariance matrix of any regime has eigenvalues smaller than this, the model is classified as not satisfying positive definiteness assumption. Note that if the tolerance is too small, numerical evaluation of the loglikelihood might fail and cause error. 
df_tol 
the parameter vector is considered to be outside the parameter space if all degrees of
freedom parameters are not larger than 
The first p values are used as the initial values, and by conditional we mean conditioning on the past. Formulas for the conditional means and covariance matrices are given in equations (3) and (4) of KMS (2016).
If 
an 
If 
an 
If 
a 
If 
an 
If 
a 
Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485498.
Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.
McElroy T. 2017. Computation of vector ARMA autocovariances. Statistics and Probability Letters, 124, 9296.
Virolainen S. 2020. Structural Gaussian mixture vector autoregressive model. Unpublished working paper, available as arXiv:2007.04713.
Virolainen S. 2021. Gaussian and Student's t mixture vector autoregressive model. Unpublished working paper, available as arXiv:2109.13648.
Other moment functions:
get_regime_autocovs()
,
get_regime_means()
,
uncond_moments()
1 2 3 4 5 6 7  # GMVAR(2, 2), d=2 model;
params22 < c(0.36, 0.121, 0.223, 0.059, 0.151, 0.395, 0.406, 0.005,
0.083, 0.299, 0.215, 0.002, 0.03, 0.484, 0.072, 0.218, 0.02, 0.119,
0.722, 0.093, 0.032, 0.044, 0.191, 1.101, 0.004, 0.105, 0.58)
cond_moments(data=gdpdef, p=2, M=2, params=params22, to_return="regime_cmeans")
cond_moments(data=gdpdef, p=2, M=2, params=params22, to_return="total_cmeans")
cond_moments(data=gdpdef, p=2, M=2, params=params22, to_return="total_ccovs")

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