GMVAR: Create object of class 'gmvar' defining a GMVAR model

Description

GMVAR creates an S3 object of class 'gmvar' that defines a GMVAR model

Usage

GMVAR(data, p, M, d, params, conditional = TRUE,
  parametrization = c("intercept", "mean"), constraints = NULL,
  calc_cond_moments, calc_std_errors = FALSE)
# S3 method for gmvar
logLik(object, ...)
# S3 method for gmvar
residuals(object, ...)
# S3 method for gmvar
summary(object, ..., digits = 2)
# S3 method for gmvar
plot(x, ...)
# S3 method for gmvar
print(x, ..., digits = 2, summary_print = FALSE)

Arguments

data

a matrix or class 'ts' object with d>1 columns. Each column is taken to represent a single times series. NA values are not supported. Ignore if defining a model without data is desired.

a positive integer specifying the autoregressive order of the model.

a positive integer specifying the number of mixture components.

number of times series in the system, i.e. ncol(data). This can be used to define GMVAR models without data and can be ignored if data is provided.

params

a real valued vector specifying the parameter values.

For regular models:

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.

For constrained models:

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).

conditional

a logical argument specifying whether the conditional or exact log-likelihood function should be used. Default is TRUE.

parametrization

"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".

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 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.

calc_cond_moments

should conditional means and covariance matrices should be calculated? Default is TRUE if the model contains data and FALSE otherwise.

calc_std_errors

should approximate standard errors be calculated?

object

object of class 'gmvar' generated by fitGMVAR or GMVAR.

...

currectly not used.

digits

number of digits to be printed.

object of class 'gmvar' generated by fitGMVAR or GMVAR.

summary_print

if set to TRUE then the print will include log-likelihood and information criteria values.

Value

Returns an object of class 'gmvar' defining the specified GMVAR model. Can be used to work with other functions provided in gmvarkit.

Remark that the first autocovariance/correlation matrix in $uncond_moments is for the lag zero, the second one for the lag one, etc.

Methods (by generic)

logLik: Log-likelihood method
residuals: residuals method to extract multivariate quantile residuals
summary: summary method
plot: plot method for class 'gmvar'
print: print method

S3 methods

Only the print method is available if data is not provided. If data is provided, then the predict method is also available.

Details

If data is provided, then also multivariate quantile residuals (Kalliovirta and Saikkonen 2010) are computed and included in the returned object.

References

Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.
Kalliovirta L. and Saikkonen P. 2010. Reliable Residuals for Multivariate Nonlinear Time Series Models. Unpublished Revision of HECER Discussion Paper No. 247.

Examples

Run this code

# NOT RUN {
# These examples use the data 'eurusd' which comes with the
# package, but in a scaled form.
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
colnames(data) <- colnames(eurusd)

# GMVAR(1,2), d=2 model:
params122 <- c(0.623, -0.129, 0.959, 0.089, -0.006, 1.006, 1.746,
 0.804, 5.804, 3.245, 7.913, 0.952, -0.037, -0.019, 0.943, 6.926,
 3.982, 12.135, 0.789)
mod122 <- GMVAR(data, p=1, M=2, params=params122)
mod122

# GMVAR(1,2), d=2 model without data
mod122_2 <- GMVAR(p=1, M=2, d=2, params=params122)
mod122_2

# GMVAR(2,2), d=2 model with mean-parametrization:
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)
mod222 <- GMVAR(data, p=2, M=2, params=params222, parametrization="mean")
mod222

# GMVAR(2,2), d=2 model with AR-parameters restricted to be
# the same for both regimes:
C_mat <- rbind(diag(2*2^2), diag(2*2^2))
params222c <- c(1.031, 2.356, 1.786, 3.000, 1.250, 0.060, 0.036,
 1.335, -0.290, -0.083, -0.047, -0.356, 0.934, -0.152, 5.201, 5.883,
 3.560, 9.799, 0.368)
mod222c <- GMVAR(data, p=2, M=2, params=params222c, constraints=C_mat)
mod222c

# GMVAR(2,2), d=2 model with AR-parameters restricted to be
# the same for both regimes and the non-diagonal elements of
# the coefficient matrices constrained to zero.
tmp <- matrix(c(1, rep(0, 10), 1, rep(0, 8), 1, rep(0, 10), 1),
 nrow=2*2^2, byrow=FALSE)
C_mat2 <- rbind(tmp, tmp)
params222c2 <- c(0.355, 3.193, -0.114, 2.829, 1.263, 1.338, -0.292,
 -0.362, 5.597, 3.456, 9.622, 0.982, -0.327, 5.236, 0.650)
mod222c2 <- GMVAR(data, p=2, M=2, params=params222c2,
  constraints=C_mat2)
mod222c2
# }

Run the code above in your browser using DataLab