exdqlmISVB: 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
)

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.

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.

Examples

Run this code

# \donttest{
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)
# }

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