DynCount-package: DynCount: Bayesian Dynamic Models for Count Time Series

In DynCount: Bayesian Dynamic Models for Count Time Series

DynCount: Bayesian Dynamic Models for Count Time Series

Description

The DynCount package fits state-space models for non-Gaussian time series. A latent trajectory z_t follows flexible dynamics – a first-order random walk or a stationary AR(1) process – and the observations are linked to it through a Poisson (log link), a binomial (logit link) or a multinomial (additive-log-ratio link) observation model. An optional known offset may be added to the observation model's linear predictor (a log-exposure for the Poisson mean, a logit shift for the binomial probability, per-category ALR shifts for the multinomial shares). This is a fixed, user-supplied input and is not part of the latent process z_t.

Details

The package implements and extends the methodology of Zens and Bijak (2026, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/26-AOAS2171")}). It supports several innovation structures (Gaussian, Student-t, finite scale mixture, stochastic volatility) and, for the Poisson and binomial families, zero inflation with a time-constant gate-open probability.

Main entry points

fit_dynamic_model()

Fit a Poisson, binomial or multinomial dynamic model (random walk or stationary AR(1)).

forecast() / predict()

Posterior predictive forecasts for any horizon (by forward simulation from the posterior draws), or the in-sample fitted values and replicates.

summary()

Posterior summaries of a fitted model.

simulate_dynamic_poisson(), simulate_dynamic_binomial(), simulate_dynamic_multinomial()

Simulate data.

Plotting

plot_latent(), plot_fitted(), plot_forecast(), plot_zero_inflation().

Latent dynamics

The latent_dynamics argument of fit_dynamic_model() selects the GMRF state evolution z_t = \mu + \rho z_{t-1} + \varepsilon_t:

"rw"

A first-order random walk, i.e. \rho = 1 fixed (the default).

"ar1"

A stationary AR(1) process, always with an intercept (include_mu = TRUE).

Both share the precision P = D_\rho^\top \mathrm{diag}(1/\sigma^2) D_\rho, where D_\rho is the generalised first-difference operator; it is symmetric tridiagonal, so its bands are formed and the latent full conditionals evaluated in O(N). A scalar \mu (set include_mu = TRUE) adds a drift (RW) or intercept (AR(1)) to the state equation; it enters as a linear term in the latent full conditionals, leaving the sparse precision unchanged.

The otherwise-improper GMRF is anchored by a proper, fixed N(\code{init\_mean}, \code{init\_var}) prior on the first latent state (default N(0, 100)), under both dynamics.

Multinomial (choice-count) series

With family = "multinomial" the data are an n \times K matrix of category counts with known row totals N_t. One category b (by default the one with the largest total count) is the baseline, and each of the other K - 1 categories has its own latent additive-log-ratio series z_{t,k} = \log(p_{t,k} / p_{t,b}), so that p_t is the softmax of (z_{t,\cdot}, 0) and y_t \sim \mathrm{Multinomial}(N_t, p_t). Every ALR series follows the selected latent dynamics with the selected innovation structure, but the series share no parameters. Each series has its own innovation variance (and auxiliary innovation parameters), its own \rho and \mu, and its own copy of the prior. They are coupled only through the multinomial likelihood, and each ALR series is updated in turn with the other categories held at their current values. With K = 2 and the second column as baseline the model coincides exactly with the binomial model. The model is not invariant to the choice of baseline (the dynamics are placed on the log-ratios relative to it), so a large category with a stable share is the natural choice. Zero inflation is not available for this family currently. Rows with N_t = 0 are uninformative and handled as missing. Posterior draws carry a trailing category dimension, see fit_dynamic_model().

The four innovation structures

The innovations argument controls the distribution of the latent increments \varepsilon_t = z_t - \mu - \rho z_{t-1} (with \rho = 1 for the random walk and \mu = 0 unless a drift/intercept is included):

"gaussian"

\varepsilon_t \sim N(0, \sigma^2) with a single, constant variance.

"t"

A Student-t scale mixture: \varepsilon_t \sim t_\nu(0, \sigma^2), robust to occasional large jumps. The degrees of freedom \nu are estimated from the data.

"mixture"

A finite scale mixture of normals with mix_components components (see dynamic_prior()), resulting in a flexible increment distribution.

"sv"

Stochastic volatility: \log\sigma^2_t follows an AR(1) process (delegated to the stochvol package).

Zero inflation

Set zeros = "inflated" (or zero_inflation = TRUE) to fit zero inflation with the Poisson or the binomial family: the observed count is y_t = v_t \tilde y_t, where the gate v_t \sim \mathrm{Bernoulli}(\pi_{\mathrm{open}}) decides whether an observed zero is structural (gate closed) or a sampling zero produced by the Poisson/binomial process (gate open). The gate-open probability \pi_{\mathrm{open}} is a single parameter that does not vary over time or with covariates. See structural_zero_prob().

Every fit stores two flavours of in-sample fitted values and replicates: unconditional draws (fitted, yrep), which include the gate and are the quantities to compare with observed data (posterior predictive checks), and conditional-on-gate-open draws (fitted_open, yrep_open), which come straight from the observation model and describe the latent intensity process. Without zero inflation the pairs coincide exactly. Response forecasts are always unconditional, with the gate applied to each forecast draw. See predict.dynamic_fit().

Forecasting

Future latent states carry no likelihood, so their posterior given a draw of the parameters and of the last in-sample state is the transition law of the latent process. forecast.dynamic_fit() therefore forward-simulates the latent path from every stored posterior draw (with increments from the fitted innovation structure) and draws a response from the observation model at each simulated state. Forecasts can be requested for any horizon after fitting, e.g. forecast(fit, horizon = 8). Fitting with horizon = H stores an H-step forecast in the fit.

Author(s)

Maintainer: Gregor Zens [e-mail]

References

Zens, G. and Bijak, J. (2026). Dynamic Count Models with Flexible Innovation Processes for Irregular Maritime Migration. The Annals of Applied Statistics, 20(2), 1671–1690. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/26-AOAS2171")}.

DynCount documentation built on Sept. 28, 2026, 5:10 p.m.