Run the MCMC for Bayesian trend filtering regression with a penalty on first (D=1) or second (D=2) differences of each dynamic regression coefficient. 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 stochastic volatility model ('SV');
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.
btf_reg(
y,
X = NULL,
evol_error = "DHS",
D = 1,
obsSV = "const",
nsave = 1000,
nburn = 1000,
nskip = 4,
mcmc_params = list("mu", "yhat", "beta", "evol_sigma_t2", "obs_sigma_t2", "dhs_phi",
"dhs_mean", "h", "h_smooth"),
use_backfitting = FALSE,
computeDIC = TRUE,
verbose = TRUE,
D_asv = 1,
evol_error_asv = "HS",
nugget_asv = 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 T x p matrix of time series predictors
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)
Options for modeling the error variance. It must be one of the following:
const: Constant error variance for all time points.
SV: Stochastic Volatility model.
ASV: Adaptive Stochastic Volatility model.
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:
"mu" (conditional mean)
"yhat" (posterior predictive distribution)
"beta" (dynamic regression coefficients)
"evol_sigma_t2" (evolution error variance)
"obs_sigma_t2" (observation error variance)
"dhs_phi" (DHS AR(1) coefficient)
"dhs_mean" (DHS AR(1) unconditional mean)
"h" (log variances or log of "obs_sigma_t2". Only used when obsSV = "ASV")
"h_smooth" (smooth estimate of log variances. Only used when obsSV = "ASV" and nugget_asv = TRUE)
logical; if TRUE, use backfitting to sample the predictors j=1,...,p (faster, but usually less MCMC efficient)
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?
integer; degree of differencing (0, 1, or 2) for the ASV model. Only used when obsSV = "ASV".
character; evolution error distribution for the ASV model. Must be one of the five options used in evol_error. Only used when obsSV = "ASV".
logical; if TRUE, fits the nugget variant of the ASV model. Only used when obsSV = "ASV".