n_params: Calculate the number of parameters in a GMVAR, StMVAR, or...

In saviviro/gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

Calculate the number of parameters in a GMVAR, StMVAR, or G-StMVAR model's parameter vector

Description

n_params calculates the number of parameters in the model.

Usage

n_params(
  p,
  M,
  d,
  model = c("GMVAR", "StMVAR", "G-StMVAR"),
  constraints = NULL,
  same_means = NULL,
  weight_constraints = NULL,
  structural_pars = NULL
)

Arguments

p	a positive integer specifying the autoregressive order of the model.
M	For GMVAR and StMVAR models: a positive integer specifying the number of mixture components. For G-StMVAR models: a size (2x1) integer vector specifying the number of GMVAR type components M1 in the first element and StMVAR type components M2 in the second element. The total number of mixture components is M=M1+M2.
d	the number of time series in the system.
model	is "GMVAR", "StMVAR", or "G-StMVAR" model considered? In the G-StMVAR model, the first M1 components are GMVAR type and the rest M2 components are StMVAR type.
constraints	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 related 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.
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 M=3, the argument list(1, 2:3) restricts the mean parameters of the second and third regime to be the same but the first regime has freely estimated (unconditional) mean. Ignore or set to NULL if mean parameters should not be restricted to be the same among any regimes. This constraint is available only for mean parametrized models; that is, when parametrization="mean".
weight_constraints	a numeric vector of length M-1 specifying fixed parameter values for the mixing weight parameters \alpha_m, \ m=1,...,M-1. Each element should be strictly between zero and one, and the sum of all the elements should be strictly less than one.
structural_pars	If NULL a reduced form model is considered. Reduced models can be used directly as recursively identified structural models. For a structural model identified by conditional heteroskedasticity, should be a list containing at least the first one of the following elements: W - a (dxd) matrix with its entries imposing constraints on W: NA indicating that the element is unconstrained, a positive value indicating strict positive sign constraint, a negative value indicating strict negative sign constraint, and zero indicating that the element is constrained to zero. C_lambda - a (d(M-1) x r) constraint matrix that satisfies (\lambda_{2},..., \lambda_{M}) = C_{\lambda} \gamma where \gamma is the new (r x 1) parameter subject to which the model is estimated (similarly to AR parameter constraints). The entries of C_lambda must be either positive or zero. Ignore (or set to NULL) if the eigenvalues \lambda_{mi} should not be constrained. fixed_lambdas - a length d(M-1) numeric vector (\lambda_{2},..., \lambda_{M}) with elements strictly larger than zero specifying the fixed parameter values for the parameters \lambda_{mi} should be constrained to. This constraint is alternative C_lambda. Ignore (or set to NULL) if the eigenvalues \lambda_{mi} should not be constrained. See Virolainen (forthcoming) for the conditions required to identify the shocks and for the B-matrix as well (it is W times a time-varying diagonal matrix with positive diagonal entries).

Value

Returns the number of parameters in the parameter vector of the specified GMVAR, StMVAR, or G-StMVAR model.

Warning

No argument checks!

References

• Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.

• Virolainen S. (forthcoming). A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics.

• Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.

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saviviro/gmvarkit documentation built on March 8, 2024, 4:15 a.m.