The penalty is determined by the prior on the evolution errors, which include:
the dynamic horseshoe prior ('DHS');
the static horseshoe prior ('HS');
the Bayesian lasso ('BL');
the normal-inverse-gamma prior ('NIG').
In each case, the evolution error is a scale mixture of Gaussians. Sampling is accomplished with a (parameter-expanded) Gibbs sampler, mostly relying on a dynamic linear model representation.
fit_ASV(
y,
beta = 0,
evol_error = "DHS",
D = 1,
nsave = 1000,
nburn = 1000,
nskip = 4,
mcmc_params = list("h", "logy2hat", "sigma2", "evol_sigma_t2", "dhs_phi", "dhs_mean"),
nugget = FALSE,
computeDIC = TRUE,
verbose = TRUE
)A named list of the nsave MCMC samples for the parameters named in mcmc_params
the T x 1 vector of time series observations.
the mean of the observed process y. If not provided, they are assumed to be 0.
the evolution error distribution; must be one of 'DHS' (dynamic horseshoe prior), 'HS' (horseshoe prior), 'BL' (Bayesian lasso), or 'NIG' (normal-inverse-gamma prior)
degree of differencing (D = 1, or D = 2)
number of MCMC iterations to record
number of MCMC iterations to discard (burin-in)
number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
named list of parameters for which we store the MCMC output; must be one or more of:
"h" (Log variance)
"h_smooth" (smooth estimate of log variances. Only used when nugget_asv = TRUE)
"logy2hat" (posterior predictive distribution of log(y^2))
"sigma2" (Variance, i.e. exp(h))
"evol_sigma_t2" (evolution error variance)
"dhs_phi" (DHS AR(1) coefficient)
"dhs_mean" (DHS AR(1) unconditional mean)
logical; if TRUE, fits the nugget variant of the ASV model
logical; if TRUE, compute the deviance information criterion DIC
and the effective number of parameters p_d
logical; should R report extra information on progress?