transfn_exdqlmISVB {exdqlm} | R Documentation |
The function applies an Importance Sampling Variational Bayes (ISVB) algorithm to estimate the posterior of an exDQLM with exponential decay transfer function component.
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
)
y |
A univariate time-series. |
p0 |
The quantile of interest, a value between 0 and 1. |
model |
List of the state-space model including |
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 |
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 |
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. |
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.
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))