exdqlmISVB | R Documentation |
The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM.
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 )
y |
A univariate time-series. |
p0 |
The quantile of interest, a value between 0 and 1. |
model |
List of the state-space model including |
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 |
Initial value for gamma (skewness parameter), or value at which gamma will be fixed if |
fix.sigma |
Logical value indicating whether to fix sigma at |
sig.init |
Initial value for sigma (scale parameter), or value at which sigma will be fixed if |
dqlm.ind |
Logical value indicating whether to fix gamma at |
exps0 |
Initial value for dynamic quantile. If |
tol |
Tolerance for convergence of dynamic quantile estimates. Default is |
n.IS |
Number of particles for the importance sampling of joint variational distribution of sigma and gamma. Default is |
n.samp |
Number of samples to draw from the approximated posterior distribution. Default is |
PriorSigma |
List of parameters for inverse gamma prior on sigma; shape |
PriorGamma |
List of parameters for truncated student-t prior on gamma; center |
verbose |
Logical value indicating whether progress should be displayed. |
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.
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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