estim_LS {sstvars} | R Documentation |
Internal estimation function for estimating autoregressive and threshold parameters of TVAR models by the method of least squares.
Description
estim_LS
estimates the autoregressive and threshold parameters of TVAR models
by the method of least squares.
Usage
estim_LS(
data,
p,
M,
weight_function = c("relative_dens", "logistic", "mlogit", "exponential", "threshold",
"exogenous"),
weightfun_pars = NULL,
cond_dist = c("Gaussian", "Student", "ind_Student", "ind_skewed_t"),
parametrization = c("intercept", "mean"),
AR_constraints = NULL,
mean_constraints = NULL,
weight_constraints = NULL,
penalized = TRUE,
penalty_params = c(0.05, 0.2),
min_obs_coef = 3,
use_parallel = TRUE,
ncores = 2
)
Arguments
data |
a matrix or class |
p |
a positive integer specifying the autoregressive order |
M |
a positive integer specifying the number of regimes |
weight_function |
What type of transition weights
See the vignette for more details about the weight functions. |
weightfun_pars |
|
cond_dist |
specifies the conditional distribution of the model as |
parametrization |
|
AR_constraints |
a size |
mean_constraints |
Restrict the mean parameters of some regimes to be identical? Provide a list of numeric vectors
such that each numeric vector contains the regimes that should share the common mean parameters. For instance, if
|
weight_constraints |
a list of two elements, |
penalized |
Perform penalized LS estimation that minimizes penalized RSS in which estimates close to breaking or not satisfying the
usual stability condition are penalized? If |
penalty_params |
a numeric vector with two positive elements specifying the penalization parameters: the first element determined how far from the boundary of the stability region the penalization starts (a number between zero and one, smaller number starts penalization closer to the boundary) and the second element is a tuning parameter for the penalization (a positive real number, a higher value penalizes non-stability more). |
min_obs_coef |
the smallest accepted number of observations (times variables) from each regime relative to the number of parameters in the regime. |
use_parallel |
employ parallel computing? If |
ncores |
the number CPU cores to be used in parallel computing. |
Details
Used internally in the multiple phase estimation procedure proposed by Koivisto, Luoto, and Virolainen (2025). Mean constraints are not supported. Only weight constraints that specify the threshold parameters as fixed values are supported. Only intercept parametrization is supported.
Value
Returns the estimated parameters in a vector of the form
(\phi_{1,0},...,\phi_{M,0},\varphi_1,...,\varphi_M,\alpha
, where
\phi_{m,0} =
the(d \times 1)
intercept vector of them
th regime.\varphi_m = (vec(A_{m,1}),...,vec(A_{m,p}))
(pd^2 \times 1)
.\alpha = (r_1,...,r_{M-1})
the(M-1\times 1)
vector of the threshold parameters.
For models with...
- AR_constraints:
Replace
\varphi_1,...,\varphi_M
with\psi
as described in the argumentAR_constraints
.- weight_constraints:
If linear constraints are imposed, replace
\alpha
with\xi
as described in the argumentweigh_constraints
. If weight functions parameters are imposed to be fixed values, simply drop\alpha
from the parameter vector.
References
Hubrich K., Teräsvirta. T. 2013. Thresholds and Smooth Transitions in Vector Autoregressive Models. CREATES Research Paper 2013-18, Aarhus University.
Koivisto T., Luoto J., Virolainen S. 2025. Unpublished working paper.
Tsay R. 1998. Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93:443, 1188-1202.
Virolainen S. 2024. Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models. Unpublished working paper, available as arXiv:2404.19707.