exdqlmMCMC: exDQLM - MCMC algorithm
In exdqlm: Extended Dynamic Quantile Linear Models

exdqlmMCMC

R Documentation

exDQLM - MCMC algorithm

Description

The function applies a Markov chain Monte Carlo (MCMC) algorithm to sample the posterior of an exDQLM.

Usage

exdqlmMCMC(
  y,
  p0,
  model,
  df,
  dim.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  Sig.mh,
  joint.sample = FALSE,
  n.burn = 2000,
  n.mcmc = 1500,
  init.from.isvb = TRUE,
  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`.
`Sig.mh`	Covariance matrix used in the random walk MH step to jointly sample sigma and gamma.
`joint.sample`	Logical value indicating whether or not to recompute `Sig.mh` based off the initial burn-in samples of gamma and sigma. Default is `FALSE`.
`n.burn`	Number of MCMC iterations to burn. Default is `n.burn = 2000`.
`n.mcmc`	Number of MCMC iterations to sample. Default is `n.mcmc = 1500`.
`init.from.isvb`	Logical value indicating whether or not to initialize the MCMC using the ISVB algorithm. Default is `TRUE`.
`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.
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.
samp.theta - Posterior sample of the state vector.
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.
samp.vts - Posterior sample of latent parameters, v_t.
theta.out - List containing the distributions of the state vector including filtered distribution parameters (fm and fC) and smoothed distribution parameters (sm and sC).

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

samp.gamma - Posterior sample of skewness parameter gamma.
samp.sts - Posterior sample of latent parameters, s_t.
init.log.sigma - Burned samples of log sigma from the random walk MH joint sampling of sigma and gamma.
init.logit.gamma - Burned samples of logit gamma from the random walk MH joint sampling of sigma and gamma.
accept.rate - Acceptance rate of the MH step.
Sig.mh - Covariance matrix used in MH step to jointly sample sigma and gamma.

Examples


y = scIVTmag[1:100]
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)
M2 = exdqlmMCMC(y,p0=0.85,model,df=c(1,1),dim.df = c(1,6),
                gam.init=-3.5,sig.init=15,
                n.burn=100,n.mcmc=150)

exdqlm documentation built on Feb. 16, 2023, 7:29 p.m.