transfn_exdqlmISVB: Transfer Function exDQLM - ISVB algorithm

Description

The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM with exponential decay transfer function component.

Usage

transfn_exdqlmISVB(
  y,
  p0,
  model,
  X,
  df,
  dim.df,
  lam,
  tf.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,
  tf.m0 = rep(0, 2),
  tf.C0 = diag(1, 2),
  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 augmented state-space model including GG, FF, prior parameters m0 and C0.
p0 - The quantile which was estimated.
df - Discount factors used for each block, including transfer function component.
dim.df - Dimension used for each block of discount factors, including transfer function component.
lam - Transfer function rate parameter lambda.
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.
median.kt - Median number of time steps until the effect of X_t is less than or equal to 1e-3.

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.
X: A univariate time-series which will be the input of the transfer function component.
df: Discount factors for each block.
dim.df: Dimension of each block of discount factors.
lam: Transfer function rate parameter lambda, a value between 0 and 1.
tf.df: Discount factor(s) used for the transfer function component.
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.
tf.m0: Prior mean of the transfer function component.
tf.C0: Prior covariance of the transfer function component.
verbose: Logical value indicating whether progress should be displayed.

Examples

Run this code

# \donttest{
y = scIVTmag[1:1095]
X = ELIanoms[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)
M1 = transfn_exdqlmISVB(y,p0=0.85,model=model,
                          X,df=c(1,1),dim.df = c(1,6),
                          gam.init=-3.5,sig.init=15,
                          lam=0.38,tf.df=c(0.97,0.97))
# }

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