shrinkTVP samples from the joint posterior distribution of the parameters of a time-varying
parameter model with shrinkage, potentially including stochastiv volatility (SV), and returns the MCMC draws.
shrinkTVP(formula, data, niter = 10000, nburn = round(niter/2),
nthin = 1, learn_a_xi = TRUE, learn_a_tau = TRUE, a_xi = 0.1,
a_tau = 0.1, learn_kappa2 = TRUE, learn_lambda2 = TRUE,
kappa2 = 20, lambda2 = 20, hyperprior_param, c_tuning_par_xi = 1,
c_tuning_par_tau = 1, display_progress = TRUE, ret_beta_nc = FALSE,
sv = FALSE, sv_param, LPDS = FALSE, y_test, x_test)an object of class "formula": a symbolic representation of the model, as in the
function lm. For details, see formula.
optional data frame containing the response variable and the covariates. If not found in data,
the variables are taken from environment(formula), typically the environment from which shrinkTVP
is called. No NAs are allowed in the response variable and the covariates.
positive integer, indicating the number of MCMC iterations
to perform, including the burn-in. Has to be larger than or equal to nburn + 2. The default value is 10000.
non-negative integer, indicating the number of iterations discarded
as burn-in. Has to be smaller than or equal to niter - 2. The default value is round(niter / 2).
positive integer, indicating the degree of thinning to be performed. Every nthin draw is kept and returned.
The default value is 1, implying that every draw is kept.
logical value indicating whether to learn a_xi, the local adaptation parameter of the state variances.
The default value is TRUE.
logical value indicating whether to learn a_tau, the local adaptation parameter of the mean of the
initial values of the states. The default value is TRUE.
positive, real number, indicating the (fixed) value for a_xi. Ignored if
learn_a_xi is TRUE. The default value is 0.1.
positive, real number, indicating the (fixed) value for a_tau. Ignored if
learn_a_tau is TRUE. The default value is 0.1.
logical value indicating whether to learn kappa2, the global level of shrinkage for
the state variances. The default value is TRUE.
logical value indicating whether to learn the lambda^2 parameter,
the global level of shrinkage for the mean of the initial values of the states. The default value is TRUE.
positive, real number, indicating the (fixed) value for kappa2. Ignored if
learn_kappa2 is TRUE. The default value is 20.
positive, real number, indicating the (fixed) value for lambda2. Ignored if
learn_lambda2 is TRUE. The default value is 20.
optional named list containing hyperparameter values. Not all have to be supplied, with those missing being replaced by the default values. Any list elements that are misnamed will be ignored and a warning will be thrown. All hyperparameter values have to be positive, real numbers. The following hyperparameters can be supplied:
c0: The default value is 2.5.
g0: The default value is 5.
G0: The default value is 5 / (2.5 - 1).
cp: The default value is 1.
np: The default value is 20.
e1: The default value is 0.001.
e2: The default value is 0.001.
d1: The default value is 0.001.
d2: The default value is 0.001.
b_xi: The default value is 10.
b_tau: The default value is 10.
nu_xi: The default value is 5.
nu_tau: The default value is 5.
positive, real number. Determines the standard deviation of the proposal
distribution for the Metropolis Hastings step for a_xi. Ignored if learn_a_xi is FALSE. The default
value is 1.
positive, real number. Determines the standard deviation of the proposal
distribution for the Metropolis Hastings step for a_tau. Ignored if learn_a_tau is FALSE. The default
value is 1.
logical value indicating whether the progress bar and other informative output should be
displayed. The default value is TRUE.
logical value indicating whether to output the non-centered states in addition to the centered ones.
The default value is FALSE.
optional named list containing hyperparameter values for the stochastic volatility
parameters. Not all have to be supplied, with those missing being replaced by the default values.
Any list elements that are misnamed will be ignored and a warning will be thrown. Ignored if
sv is FALSE. The following elements can be supplied:
Bsigma_sv: positive, real number. The default value is 1.
a0_sv: positive, real number. The default value is 5.
b0_sv: positive, real number. The default value is 1.5.
bmu: real number. The default value is 0.
Bmu: real number. larger than 0. The default value is 1.
logical value indicating whether the one step ahead log predictive density score should be returned.
If LPDS is TRUE, both x_test and y_test have to be supplied. The default value is FALSE.
optional real number. If LPDS is TRUE this value will be taken to be the true one step
ahead value and will be used to calculate the log predictive density score. Ignored if LPDS is FALSE.
optional object that can be coerced to a 1 x d data frame containing the covariates for the
calculation of the one step ahead log predictive density score. The column names have to exactly match the
names of the covariates provided in the formula or an error will be thrown. An intercept will be added to
x_test if an intercept was added to the covariates by the formula interface. Ignored if LPDS is FALSE.
The value returned is a list object of class shrinkTVP_res containing
sigma2mcmc object containing the parameter draws from the posterior distribution of sigma2.
If sv is TRUE, sigma2 is additionally an mcmc.tvp object.
theta_sran mcmc object containing the parameter draws from the posterior distribution of the square root of theta.
beta_meanan mcmc object containing the parameter draws from the posterior distribution of beta_mean.
beta_nc(optional) list object containing an mcmc.tvp object for the parameter draws from the posterior
distribution of the non-centered states, one for each covariate. In the case that there is only one covariate, this becomes just
a single mcmc.tvp object. Not returned if ret_beta_nc is FALSE.
betalist object containing an mcmc.tvp object for the parameter draws from the posterior distribution of the centered
states, one for each covariate. In the case that there is only one covariate, this becomes just a single mcmc.tvp object.
xi2mcmc object containing the parameter draws from the posterior distribution of xi2.
a_xi(optional) mcmc object containing the parameter draws from the posterior distribution of a_xi.
Not returned if learn_a_xi is FALSE.
a_xi_acceptance(optional) list object containing acceptance statistics for the Metropolis Hastings algorithm for
a_xi. Not returned if learn_a_xi is FALSE.
tau2mcmc object containing the parameter draws from the posterior distribution of tau2.
a_tau(optional) mcmc object containing the parameter draws from the posterior distribution of a_tau.
Not returned if learn_a_tau is FALSE.
a_tau_acceptance(optional) list containing acceptance statistics for the Metropolis Hastings algorithm for
a_tau. Not returned if learn_a_tau is FALSE.
kappa2(optional) mcmc object containing the parameter draws from the posterior distribution of kappa2.
Not returned if learn_kappa2 is FALSE.
lambda2(optional) mcmc object containing the parameter draws from the posterior distribution of lambda2.
Not returned if learn_lambda2 is FALSE.
C0(optional) mcmc object containing the parameter draws from the posterior distribution of C0.
Not returned if sv is TRUE.
sv_mu(optional) mcmc object containing the parameter draws from the posterior distribution of the mu
parameter for the stochastic volatility model on the errors. Not returned if sv is FALSE.
sv_phi(optional) mcmc object containing the parameter draws from the posterior distribution of the phi
parameter for the stochastic volatility model on the errors. Not returned if sv is FALSE.
sv_sigma2(optional) mcmc object containing the parameter draws from the posterior distribution of the sigma2
parameter for the stochastic volatility model on the errors. Not returned if sv is FALSE.
priorvalslist object containing hyperparameter values of the prior distributions, as specified by the user.
modellist object containing the model matrix and model response used.
summarieslist object containing a collection of summary statistics of the posterior draws.
LPDS(optional) value of the log predictive density score, calculated with y_test and x_test.
For details concerning the algorithm please refer to the paper by Bitto and Fr<U+00FC>hwirth-Schnatter (2019).
Bitto, A., & Fr<U+00FC>hwirth-Schnatter, S. (2019). "Achieving shrinkage in a time-varying parameter model framework." Journal of Econometrics, 210(1), 75-97. <doi:10.1016/j.jeconom.2018.11.006>
# NOT RUN {
## Example 1, learn everything
set.seed(123)
sim <- simTVP(theta = c(0.2, 0, 0), beta_mean = c(1.5, -0.3, 0))
data <- sim$data
res <- shrinkTVP(y ~ x1 + x2, data = data)
# summarize output
summary(res)
## Example 2, hierarchical Bayesian Lasso
res <- shrinkTVP(y ~ x1 + x2, data = data,
learn_a_xi = FALSE, learn_a_tau = FALSE,
a_xi = 1, a_tau = 1)
## Example 3, non-hierarchical Bayesian Lasso
res <- shrinkTVP(y ~ x1 + x2, data = data,
learn_a_xi = FALSE, learn_a_tau = FALSE,
a_xi = 1, a_tau = 1,
learn_kappa2 = FALSE, learn_lambda2 = FALSE)
## Example 4, adding stochastic volatility
res <- shrinkTVP(y ~ x1 + x2, data = data,
sv = TRUE)
## Example 4, changing some of the default hyperparameters
res <- shrinkTVP(y ~ x1 + x2, data = data,
hyperprior_param = list(cp = 5,
nu_xi = 10))
# }
# NOT RUN {
# }
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