VLSTAR {starvars} | R Documentation |
VLSTAR- Estimation
Description
This function allows the user to estimate the coefficients of a VLSTAR model with m regimes through maximum likelihood or nonlinear least squares. The set of starting values of Gamma and C for the convergence algorithm can be either passed or obtained via searching grid.
Usage
VLSTAR(
y,
exo = NULL,
p = 1,
m = 2,
st = NULL,
constant = TRUE,
starting = NULL,
method = c("ML", "NLS"),
n.iter = 500,
singlecgamma = FALSE,
epsilon = 10^(-3),
ncores = NULL
)
Arguments
y |
|
exo |
(optional) |
p |
lag order |
m |
number of regimes |
st |
single transition variable for all the equation of dimension |
constant |
|
starting |
set of intial values for Gamma and C, inserted as a list of length |
method |
Fitting method: maximum likelihood or nonlinear least squares. |
n.iter |
number of iteration of the algorithm until forced convergence |
singlecgamma |
|
epsilon |
convergence check measure |
ncores |
Number of cores used for parallel computation. Set to |
Details
The multivariate smooth transition model is an extension of the smooth transition regression model introduced by Bacon and Watts (1971) (see also Anderson and Vahid, 1998). The general model is
where and
are the
vectors of intercepts,
and
are square
matrices of parameters for lags
, A_0 and A_1 are
matrices of parameters,
x_t is the
vector of exogenous variables and
is the innovation. Finally,
is a
diagonal matrix of transition function at time t, such that
Each diagonal element is specified as a logistic cumulative density functions, i.e.
for and
, so that the first model is a Vector Logistic Smooth Transition AutoRegressive
(VLSTAR) model.
The ML estimator of
is obtained by solving the optimization problem
where is the log-likelihood function of VLSTAR model, given by
The NLS estimators of the VLSTAR model are obtained by solving the optimization problem
Generally, the optimization algorithm may converge to some local minimum. For this reason, providing valid starting values of is crucial. If there is no clear indication on the initial set of parameters,
, this can be done by implementing a grid search. Thus, a discrete grid in the parameter space of
and C is create to obtain the estimates of B conditionally on each point in the grid. The initial pair of
and C producing the smallest sum of squared residuals is chosen as initial values, then the model is linear in parameters.
The algorithm is the following:
Construction of the grid for
and C, computing
for each poin in the grid
Estimation of
in each equation, calculating the residual sum of squares,
Finding the pair of
and C providing the smallest
Once obtained the starting-values, estimation of parameters, B, via nonlinear least squares (NLS)
Estimation of
and C given the parameters found in step 4
Repeat step 4 and 5 until convergence.
Value
An object of class VLSTAR
, with standard methods.
Author(s)
Andrea Bucci
References
Anderson H.M. and Vahid F. (1998), Testing multiple equation systems for common nonlinear components. Journal of Econometrics. 84: 1-36
Bacon D.W. and Watts D.G. (1971), Estimating the transition between two intersecting straight lines. Biometrika. 58: 525-534
Terasvirta T. and Yang Y. (2014), Specification, Estimation and Evaluation of Vector Smooth Transition Autoregressive Models with Applications. CREATES Research Paper 2014-8
Examples
data(Realized)
y <- Realized[-1,1:10]
y <- y[-nrow(y),]
st <- Realized[-nrow(Realized),1]
st <- st[-length(st)]
stvalues <- startingVLSTAR(y, p = 1, n.combi = 3,
singlecgamma = FALSE, st = st, ncores = 1)
fit.VLSTAR <- VLSTAR(y, p = 1, singlecgamma = FALSE, starting = stvalues,
n.iter = 1, st = st, method ='NLS', ncores = 1)
# a few methods for VLSTAR
print(fit.VLSTAR)
summary(fit.VLSTAR)
plot(fit.VLSTAR)
predict(fit.VLSTAR, st.num = 1, n.ahead = 1)
logLik(fit.VLSTAR, type = 'Univariate')
coef(fit.VLSTAR)