Bayesian Dynamic Models for Count Time Series

Fits Bayesian state-space models for count time series using a latent log-rate (Poisson), latent logit (binomial) or latent additive-log-ratio (multinomial choice counts) formulation. Each latent trajectory follows a first-order random walk or a stationary AR(1) process and is sampled by Metropolis-within-Gibbs using the implied Gaussian Markov random field full conditionals. The latent increments can be Gaussian, Student-t, a finite scale mixture of normals, or follow a stochastic volatility process, and the Poisson and binomial families support zero inflation. It implements and extends the methodology of Zens and Bijak (2026) .

DynCount

Bayesian dynamic models for count time series.

DynCount fits Bayesian state-space models to count 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, one latent series per non-baseline category) observation model. Estimation is by Metropolis-within-Gibbs MCMC using the Gaussian Markov random field full conditionals, and forecasts for any horizon are obtained by forward simulation from the posterior draws.

The package implements and extends the methodology of Zens and Bijak (2026), Dynamic Count Models with Flexible Innovation Processes for Irregular Maritime Migration, The Annals of Applied Statistics, doi:10.1214/26-AOAS2171; see citation("DynCount").

Installation

install.packages("DynCount")

Quick start

library(DynCount)

## simulate a Poisson random walk and recover the latent rate
sim <- simulate_dynamic_poisson(n = 80, sigma = 0.18, log_rate0 = 2.5, seed = 1)
fit <- fit_dynamic_model(sim$y, family = "poisson", seed = 1)  # latent_dynamics = "rw"

summary(fit)
plot_fitted(fit)

## forecast 20 steps ahead from the posterior draws
fc <- forecast(fit, horizon = 20, seed = 1)
fc$summary      # full path, one row per horizon
fc$final        # the single 20-step-ahead forecast
plot_forecast(fit, horizon = 20, seed = 1)

AR(1) dynamics

AR(1) always carries an intercept. include_mu is enabled automatically, which gives the process a non-zero stationary mean mu / (1 - rho).

# stationary AR(1) log-rate with mean 4  (mu = 4 * (1 - rho))
sim_ar <- simulate_dynamic_poisson(200, sigma = 0.2, log_rate0 = 4,
                                   rho = 0.9, mu = 0.4, seed = 3)
# include_mu is switched on automatically for AR(1)
fit_ar <- fit_dynamic_model(sim_ar$y, latent_dynamics = "ar1", seed = 3)
summary(fit_ar)            # posteriors of ar1_rho (in (-1, 1)) and intercept_mu

Drift and offset

## random-walk drift
sim_d <- simulate_dynamic_poisson(200, sigma = 0.12, log_rate0 = 1, mu = 0.03, seed = 4)
fit_d <- fit_dynamic_model(sim_d$y, include_mu = TRUE, seed = 4)   # rho = 1, mu sampled

## Poisson offset (log-exposure); supply forecast_offset for the future
expo  <- log(runif(200, 50, 200))
sim_o <- simulate_dynamic_poisson(200, sigma = 0.12, log_rate0 = -3.5,
                                  offset = expo, seed = 5)
fit_o <- fit_dynamic_model(sim_o$y, offset = expo, seed = 5)
forecast(fit_o, horizon = 8, forecast_offset = log(120))$final

Heavy-tailed and time-varying innovations

fit_t   <- fit_dynamic_model(med_weekly$count, innovations = "t", seed = 1)
fit_mix <- fit_dynamic_model(med_weekly$count, innovations = "mixture", seed = 1)
fit_sv  <- fit_dynamic_model(med_weekly$count, innovations = "sv", seed = 1)  # needs stochvol
summary(fit_t)             # t_df: degrees of freedom of the increments

Zero inflation

fit_zip <- fit_dynamic_model(uk_weekly$count, zero_inflation = TRUE, seed = 1)
summary(fit_zip)                 # gate_open_prob = P(gate open)
structural_zero_prob(fit_zip)    # P(structural) for each observed zero
plot_zero_inflation(fit_zip)

Binomial model

sim_b <- simulate_dynamic_binomial(n = 80, sigma = 0.12, trials = 50, seed = 1)
fit_b <- fit_dynamic_model(sim_b$y, family = "binomial", trials = sim_b$trials, seed = 1)
forecast(fit_b, horizon = 8, forecast_trials = 50)$final

Multinomial choice counts

# three categories, counts by week; C is the baseline of the simulation
sim_m <- simulate_dynamic_multinomial(n = 100, sigma = c(0.15, 0.1), trials = 300,
                                      alr0 = c(-1, 0.5), categories = c("A", "B", "C"),
                                      seed = 1)
fit_m <- fit_dynamic_model(sim_m$y, family = "multinomial",
                           baseline = sim_m$baseline, seed = 1)
fit_m                              # shows the categories and the baseline
summary(fit_m)                     # one innov_sd[...] row per non-baseline category
predict(fit_m, type = "prob")$summary   # posterior category shares, long format
forecast(fit_m, horizon = 8, forecast_trials = 300)$final
plot_fitted(fit_m)                 # one panel per category
plot_latent(fit_m, category = "A") # latent log-ratio of A vs the baseline

Posterior draws of multinomial fits carry a trailing category dimension, e.g. fit_m$draws$fitted_prob[, , "A"] are the draws of the share of category A. Without baseline, the fit uses the category with the largest total count. The model is not invariant to this choice, because the dynamics are placed on the log-ratios relative to the baseline, so pick a large category whose share is stable.

Example data

• uk_weekly — weekly English Channel crossings, 2018-W01 to 2025-W11.
• med_weekly — a longer weekly Mediterranean-crossings series with larger counts and few zeros, 2015-W40 to 2025-W11.

Both are weekly aggregates of detected irregular maritime crossings as used in Zens and Bijak (2026). Both data frames have the columns week (ISO week label), count and date (the Monday of the week).

Documentation

vignette("DynCount-intro", package = "DynCount")