exdqlmTransferLDVB: Transfer Function exDQLM - LDVB algorithm
In exdqlm: Extended Dynamic Quantile Linear Models

exdqlmTransferLDVB

R Documentation

Transfer Function exDQLM - LDVB algorithm

Description

The function applies a Laplace-Delta Variational Bayes (LDVB) algorithm to estimate the posterior of an exDQLM with an exponential-decay transfer function component. For multivariate transfer inputs, each column of X has its own instantaneous coefficient state in \psi_t, while a single scalar decay rate lam controls persistence of the accumulated transfer effect \zeta_t.

Usage

exdqlmTransferLDVB(
  y,
  p0,
  model,
  X,
  df,
  dim.df,
  lam,
  tf.df,
  fix.gamma = FALSE,
  gam.init = NA,
  fix.sigma = FALSE,
  sig.init = NA,
  dqlm.ind = FALSE,
  exps0,
  tol = 0.1,
  n.samp = 200,
  PriorSigma = NULL,
  PriorGamma = NULL,
  tf.m0 = NULL,
  tf.C0 = NULL,
  verbose = TRUE,
  debug_shapes = FALSE,
  debug_every = 5
)

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 numeric vector or matrix of transfer-function inputs. Vectors are treated as a univariate input series. Matrices should have one row per time point and one column per covariate.
`df`	Discount factors for each block.
`dim.df`	Dimension of each block of discount factors.
`lam`	Single transfer-function decay-rate parameter `\lambda`, a value between 0 and 1. This scalar is shared across all transfer inputs and controls propagation of the accumulated transfer effect `\zeta_t`.
`tf.df`	Discount factor specification for the transfer function component. These discount factors control the evolution variances of the transfer states, separately from the deterministic decay rate `lam`. If `length(tf.df) = 1`, the value is shared by the `\zeta_t` state and the whole `\psi_t` block. If `length(tf.df) = 2`, it is interpreted as `c(df_zeta, df_psi_shared)`. If `length(tf.df) = k + 1`, where `k = ncol(X)`, the values are applied componentwise to `(\zeta_t, \psi_{1,t}, \dots, \psi_{k,t})`.
`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 `FALSE`.
`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.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. Defaults to a zero vector of length `k+1`, where `k = ncol(X)`.
`tf.C0`	Prior covariance of the transfer function component. Defaults to the `(k+1)\times(k+1)` identity matrix.
`verbose`	Logical value indicating whether progress should be displayed.
`debug_shapes`	Logical; if TRUE, print KF input/output shapes every `debug_every` iterations.
`debug_every`	Integer; frequency (in iterations) for shape prints when `debug_shapes=TRUE`.

Value

An object of class "exdqlmLDVB" containing the following:

y - Time-series data used to fit the model.
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.
fix.sigma Logical value indicating whether sigma was fixed at sig.init.
diagnostics - List containing ELBO trace, standardized VB iteration trace diagnostics$vb_trace (iteration-wise ELBO / sigma / gamma / convergence deltas), and convergence diagnostics (joint stopping status, deltas for state/sigma/gamma/ELBO, and criteria used).

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 LD (Laplace-Delta) approximation for the variational distribution of sigma and gamma (means, transformed Hessian, and ELBO components).
sts.out - List containing the variational distributions of latent parameters s_t.
fix.gamma Logical value indicating whether gamma was fixed at gam.init.

Or if dqlm.ind=TRUE, the list also contains:

sig.out - As above but for the DQLM case (gamma = 0), the LD approximation for sigma.

Transfer-function return fields

In addition to the standard exdqlmLDVB() return values, the returned model, df, and dim.df entries correspond to the transfer-function-augmented state-space model, with appended \zeta_t and \psi_t states. The object also contains:

lam - Single transfer-function decay-rate parameter \lambda.
median.kt - Median number of time steps until the aggregated transfer effect |x_t^\top \psi_{t-1}| is less than or equal to 1e-3.
transfer_input_names - Column names of the transfer inputs after normalization of X.

Examples


data("scIVTmag", package = "exdqlm")
data("ELIanoms", package = "exdqlm")
old = options(exdqlm.max_iter = 20L)
y = scIVTmag[1:120]
X = ELIanoms[1:120]
trend.comp = polytrendMod(1, stats::quantile(y, 0.85), 10)
seas.comp = seasMod(365, c(1,2), C0 = 10*diag(4))
model = trend.comp + seas.comp
M1 = exdqlmTransferLDVB(
  y, p0 = 0.85, model = model, X = X,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97,0.97),
  n.samp = 20, tol = 0.2, verbose = FALSE
)
X_multi = cbind(ELIanoms[1:120], scale(scIVTmag[1:120])[, 1])
M2 = exdqlmTransferLDVB(
  y, p0 = 0.85, model = model, X = X_multi,
  df = c(1,1), dim.df = c(1,4),
  gam.init = -3.5, sig.init = 15,
  lam = 0.38, tf.df = c(0.97, 0.99),
  n.samp = 20, tol = 0.2, verbose = FALSE
)
options(old)

exdqlm documentation built on June 5, 2026, 1:06 a.m.