exdqlmISVB: exDQLM - ISVB algorithm

In exdqlm: Extended Dynamic Quantile Linear Models

exDQLM - ISVB algorithm

Description

The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM.

Usage

exdqlmISVB(
  y,
  p0,
  model,
  df,
  dim.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = TRUE,
  sig.init = NA,
  dqlm.ind = FALSE,
  exps0,
  tol = 0.1,
  n.IS = 500,
  n.samp = 200,
  PriorSigma = NULL,
  PriorGamma = NULL,
  verbose = TRUE
)

Arguments

y	A univariate time-series.
p0	The quantile of interest, a value between 0 and 1.
model	List of the state-space model including 'GG', 'FF', prior parameters 'm0' and 'C0'.
df	Discount factors for each block.
dim.df	Dimension of each block of discount factors.
fix.gamma	Logical value indicating whether to fix gamma at 'gam.init'. Default is 'FALSE'.
gam.init	Initial value for gamma (skewness parameter), or value at which gamma will be fixed if 'fix.gamma=TRUE'.
fix.sigma	Logical value indicating whether to fix sigma at 'sig.init'. Default is 'TRUE'.
sig.init	Initial value for sigma (scale parameter), or value at which sigma will be fixed if 'fix.sigma=TRUE'.
dqlm.ind	Logical value indicating whether to fix gamma at '0', reducing the exDQLM to the special case of the DQLM. Default is 'FALSE'.
exps0	Initial value for dynamic quantile. If 'exps0' is not specified, it is set to the DLM estimate of the 'p0' quantile.
tol	Tolerance for convergence of dynamic quantile estimates. Default is 'tol=0.1'.
n.IS	Number of particles for the importance sampling of joint variational distribution of sigma and gamma. Default is 'n.IS=500'.
n.samp	Number of samples to draw from the approximated posterior distribution. Default is 'n.samp=200'.
PriorSigma	List of parameters for inverse gamma prior on sigma; shape 'a_sig' and scale 'b_sig'. Default is an inverse gamma with mean 1 (or 'sig.init' if provided) and variance 10.
PriorGamma	List of parameters for truncated student-t prior on gamma; center 'm_gam', scale 's_gam' and degrees of freedom 'df_gam'. Default is a standard student-t with 1 degree of freedom, truncated to the support of gamma.
verbose	Logical value indicating whether progress should be displayed.

Value

A list of the following is returned:

• 'run.time' - Algorithm run time in seconds.

• 'iter' - Number of iterations until convergence was reached.

• 'dqlm.ind' - Logical value indicating whether gamma was fixed at '0', reducing the exDQLM to the special case of the DQLM.

• 'model' - List of the state-space model including 'GG', 'FF', prior parameters 'm0' and 'C0'.

• 'p0' - The quantile which was estimated.

• 'df' - Discount factors used for each block.

• 'dim.df' - Dimension used for each block of discount factors.

• 'sig.init' - Initial value for sigma, or value at which sigma was fixed if 'fix.sigma=TRUE'.

• 'seq.sigma' - Sequence of sigma estimated by the algorithm until convergence.

• 'samp.theta' - Posterior sample of the state vector variational distribution.

• 'samp.post.pred' - Sample of the posterior predictive distributions.

• 'map.standard.forecast.errors' - MAP standardized one-step-ahead forecast errors.

• 'samp.sigma' - Posterior sample of scale parameter sigma variational distribution.

• 'samp.vts' - Posterior sample of latent parameters, v_t, variational distributions.

• 'theta.out' - List containing the variational distribution of the state vector including filtered distribution parameters ('fm' and 'fC') and smoothed distribution parameters ('sm' and 'sC').

• 'vts.out' - List containing the variational distributions of latent parameters v_t.

If 'dqlm.ind=FALSE', the list also contains:

• 'gam.init' - Initial value for gamma, or value at which gamma was fixed if 'fix.gamma=TRUE'.

• 'seq.gamma' - Sequence of gamma estimated by the algorithm until convergence.

• 'samp.gamma' - Posterior sample of skewness parameter gamma variational distribution.

• 'samp.sts' - Posterior sample of latent parameters, s_t, variational distributions.

• 'gammasig.out' - List containing the IS estimate of the variational distribution of sigma and gamma.

• 'sts.out' - List containing the variational distributions of latent parameters s_t.

Or if 'dqlm.ind=TRUE', the list also contains:

• 'sig.out' - List containing the IS estimate of the variational distribution of sigma.

Examples

y = scIVTmag[1:1095]
trend.comp = polytrendMod(1,mean(y),10)
seas.comp = seasMod(365,c(1,2,4),C0=10*diag(6))
model = combineMods(trend.comp,seas.comp)
M0 = exdqlmISVB(y,p0=0.85,model,df=c(1,1),dim.df = c(1,6),
                 gam.init=-3.5,sig.init=15,tol=0.05)

exdqlm documentation built on Sept. 11, 2025, 9:09 a.m.