Package 'DynCount'

Specify priors for a dynamic count / binomial model

Description

Builds the prior hyperparameters used by fit_dynamic_model(). Called with no arguments it returns weakly informative defaults.

Usage

dynamic_prior(
  var_shape = 2.5,
  var_rate = 0.5,
  df_min = 3,
  df_mean_excess = 6,
  mix_components = 2,
  mix_concentration = 1,
  sv_prior = NULL,
  zi_open_a = 1,
  zi_open_b = 1,
  ar_rho_mean = 0,
  ar_rho_sd = 1,
  mu_mean = 0,
  mu_sd = 1,
  init_mean = 0,
  init_var = 100
)

Arguments

var_shape	Shape of the inverse-gamma prior on the innovation variance/scale. Default 2.5.
var_rate	Rate of the inverse-gamma prior on the innovation variance/scale. Default 0.5.
df_min	Lower bound for the Student-t degrees of freedom. Default 3.
df_mean_excess	Prior mean of $\nu - \code{df\_min}$. Default 6.
mix_components	Number of components in the scale-mixture innovation structure. Default 2.
mix_concentration	Symmetric Dirichlet concentration for the mixture weights. Default 1.
sv_prior	Optional stochvol prior specification for the stochastic-volatility innovation structure. Default NULL.
zi_open_a, zi_open_b	Beta prior parameters for the gate-open probability in zero-inflated models. Default 1 and 1.
ar_rho_mean, ar_rho_sd	Mean and standard deviation of the Gaussian prior on the AR(1) coefficient $\rho$ (used only when latent_dynamics = "ar1"). The conjugate Gibbs update truncates $\rho$ to the stationary region $\rho \in (-1, 1)$. Defaults 0 and 1.
mu_mean, mu_sd	Mean and standard deviation of the Gaussian prior on the drift/intercept $\mu$ (used only when include_mu = TRUE). Defaults 0 and 1.
init_mean, init_var	Mean and variance of the Gaussian prior on the initial latent state, used under both random-walk and AR(1) dynamics. Defaults 0 and 100 (a diffuse $N(0, 100)$).

Details

The model places a GMRF latent process on the series $z_t$ (a log-rate for the Poisson family, a logit for the binomial family): either a first-order random walk (latent_dynamics = "rw") or an AR(1) process (latent_dynamics = "ar1"). The 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) are given one of four innovation distributions, each governed by some of the priors below.

Innovation variance (all structures). The baseline increment variance $\sigma^2$ (or, for the "t"/"mixture" structures, the overall scale) has an inverse-gamma prior

$\sigma^2 \sim \mathrm{InvGamma}(\code{var\_shape}, \code{var\_rate}).$

Smaller var_rate gives a smoother (more strongly shrunk) latent path.

Student-t degrees of freedom (innovations = "t"). The degrees of freedom are modelled as $\nu = \code{df\_min} + E$, where $E \sim \mathrm{Exp}(\mathrm{rate} = 1/\code{df\_mean\_excess})$. Thus $\nu \ge \code{df\_min}$ and its prior mean is $\code{df\_min} + \code{df\_mean\_excess}$. Large $\nu$ approaches the Gaussian case.

Scale mixture (innovations = "mixture"). The mixture uses mix_components variance components, each with an $\mathrm{InvGamma}(\code{var\_shape}, \code{var\_rate})$ prior, and symmetric Dirichlet weights with concentration mix_concentration.

Stochastic volatility (innovations = "sv"). The log-variance AR(1) priors are delegated to stochvol. Pass a prior specification created with stochvol::specify_priors() via sv_prior, or leave it NULL to use the stochvol defaults.

Zero inflation (zeros = "inflated"). The probability that the observation "gate" is open (i.e. that a zero is an ordinary sampling zero rather than a structural zero) has a $\mathrm{Beta}(\code{zi\_open\_a}, \code{zi\_open\_b})$ prior. The default Beta(1, 1) is uniform.

AR(1) coefficient (latent_dynamics = "ar1"). When the latent state follows $z_t = \mu + \rho\, z_{t-1} + \varepsilon_t$, the coefficient $\rho$ is given a Gaussian prior $\rho \sim \mathrm{N}(\code{ar\_rho\_mean}, \code{ar\_rho\_sd}^2)$, truncated to the stationary region $\rho \in (-1, 1)$, and is sampled jointly with $\mu$ by an exact conjugate Gibbs draw (see DynCount-package). AR(1) always carries an intercept (include_mu = TRUE). Under latent_dynamics = "rw" the coefficient is fixed at $\rho = 1$ and this prior is unused.

Drift / intercept (include_mu = TRUE). A scalar $\mu$ in the state equation $z_t = \mu + \rho\, z_{t-1} + \varepsilon_t$: a drift under the random walk ($\rho = 1$) and an intercept under AR(1) (where it is always enabled). It is given a Gaussian prior $\mu \sim \mathrm{N}(\code{mu\_mean}, \code{mu\_sd}^2)$. With include_mu = FALSE (random walk only), $\mu = 0$ and is not sampled.

Initial state. A proper, fixed $\mathrm{N}(\code{init\_mean}, \code{init\_var})$ prior (default $N(0, 100)$) anchors the otherwise-improper GMRF on the first latent state, under both "rw" and "ar1" dynamics; keeping it free of $(\mu, \rho)$ is what makes their update conjugate (see DynCount-package). With the diffuse default the initial state is effectively determined by the data.

Value

An object of class "dynamic_prior": a named list of hyperparameters.

See Also

fit_dynamic_model()

Examples

# Defaults
dynamic_prior()

# Smoother latent path and heavier-tailed t innovations
dynamic_prior(var_rate = 0.1, df_min = 2, df_mean_excess = 3)

---

Fit a Bayesian dynamic count / binomial time-series model

Description

Fits a GMRF state-space model in which a latent trajectory $z_t$ evolves as either a first-order random walk (latent_dynamics = "rw", the default) or a stationary AR(1) process (latent_dynamics = "ar1"), and the observations are linked to it through a Poisson (log link) or binomial (logit link) observation model. See DynCount-package for an overview.

Usage

fit_dynamic_model(
  y,
  family = c("poisson", "binomial"),
  trials = NULL,
  innovations = c("gaussian", "t", "mixture", "sv"),
  latent_dynamics = c("rw", "ar1"),
  include_mu = FALSE,
  zeros = c("none", "inflated", "missing"),
  zero_inflation = FALSE,
  prior = dynamic_prior(),
  nsave = 4000,
  nburn = 1000,
  thin = 1,
  horizon = 0L,
  forecast_trials = NULL,
  forecast_offset = NULL,
  offset = NULL,
  verbose = FALSE,
  seed = NULL
)

Arguments

y	Numeric vector of non-negative integer observations. For the Poisson family these are counts; for the binomial family these are the numbers of successes.
family	Observation model, "poisson" (default) or "binomial".
trials	For family = "binomial", the number of trials. Either a single number (recycled) or a vector the same length as y. Each y must not exceed its number of trials. Ignored for the Poisson family.
innovations	Distribution of the latent increments, one of "gaussian" (default), "t", "mixture", "sv". See DynCount-package for details. "sv" requires the stochvol package.
latent_dynamics	Latent state evolution: "rw" (default; a first-order random walk, $\rho = 1$ fixed) or "ar1" (a stationary AR(1) with $\rho$ sampled on $(-1, 1)$). "ar1" always includes an intercept (include_mu is forced to TRUE).
include_mu	Logical; include a scalar $\mu$ in the state equation $z_t = \mu + \rho z_{t-1} + \varepsilon_t$. It is a drift under latent_dynamics = "rw" ($\rho = 1$) and an intercept under "ar1". With FALSE (default) $\mu = 0$ and is not sampled; with TRUE it has the Gaussian prior in dynamic_prior(). When latent_dynamics = "ar1" this is forced to TRUE regardless of the value supplied: the intercept gives the process a non-zero stationary mean $\mu / (1 - \rho)$, without which the zero-mean stationary assumption is rarely appropriate for a log-rate/logit series.
zeros	Zero handling for both families: "none" (default), "inflated" (time-constant zero inflation; see structural_zero_prob()), or "missing" (observed zeros treated as missing data). zero_inflation = TRUE is shorthand for zeros = "inflated". See Details.
zero_inflation	Logical convenience flag. If TRUE, sets zeros = "inflated". Ignored if zeros is supplied explicitly.
prior	A dynamic_prior() object giving the prior hyperparameters.
nsave	Number of posterior draws to keep. Default 4000.
nburn	Number of burn-in iterations. Default 1000.
thin	Thinning interval: one draw is kept every thin iterations, so the sampler runs nburn + nsave * thin iterations in total and retains nsave draws. Default 1.
horizon	Forecast horizon H (a non-negative integer). When H >= 1, forecasts are produced inside the sampler and stored for retrieval with forecast.dynamic_fit(); when H = 0 (default) no forecast is produced.
forecast_trials	For the binomial family, the number of trials in the forecast period (length 1, recycled, or length horizon). If omitted it defaults to the last observed trials count. Ignored when horizon = 0.
forecast_offset	Known per-period offset over the forecast horizon (length 1, recycled, or length horizon). Defaults to 0. Ignored when horizon = 0.
offset	Optional known per-observation offset on the linear-predictor scale (length 1 or n). For the Poisson family this is a log-exposure term, so the mean is $\exp(\mathrm{offset}_t + z_t)$; for the binomial family it shifts the logit. Default NULL (no offset).
verbose	Logical; print a progress bar. Default FALSE.
seed	Optional integer random seed for reproducibility.

Details

Zero handling. Under zeros = "inflated" a latent gate decides, for each observed zero, whether it is structural (gate closed) or an ordinary sampling zero produced by the Poisson/binomial process (gate open); the gate-open probability is a single time-constant parameter. See structural_zero_prob().

Forecasting. Forecasts are produced during sampling: set horizon = H (a positive integer) and H extra latent states are appended to the state vector and sampled as missing values inside the MCMC. A response is drawn from the observation model at each sampled forecast state. The stored forecast draws are retrieved with forecast.dynamic_fit(). With the default horizon = 0 no forecast is produced.

Value

An object of class "dynamic_fit": a list with three elements, each holding a distinct kind of content.

draws

Posterior draws only – a list of matrices/vectors with one row (or element) per stored draw:

z, sig2

Latent states and increment variances.

fitted, yrep

Unconditional fitted means and posterior predictive replicates; under zeros = "inflated" they include the zero-inflation gate.

fitted_open, yrep_open

Their conditional-on-gate-open counterparts: the latent-implied mean, and a replicate drawn straight from the observation model.

gate, pi_open

Zero-inflation gate indicators and gate-open probability. For fits without zero inflation these are stored as placeholders: gate is the constant indicator y > 0 and pi_open is 1.

rho, mu, nu, innov_var

AR(1) coefficient, drift/intercept, Student-t degrees of freedom, and a representative innovation variance whose definition depends on innovations: the estimated constant increment variance $\sigma^2$ for "gaussian"; the marginal increment variance for "t" ($\sigma^2 \nu / (\nu - 2)$) and "mixture" ($\sigma^2 \sum_h \eta_h \sigma_h^2$); and the average of the per-increment variances $\exp(h_t)$ over the series for "sv". For "t", if a draw has $\nu \le 2$ (possible only when df_min <= 2), the undefined variance factor is replaced by the convention 3.

forecast_z, forecast_y

Latent and response forecasts when horizon >= 1 (NULL otherwise); forecast_y is unconditional, i.e. includes the gate.

Use yrep, not yrep_open, for posterior predictive checks; without zero inflation the conditional and unconditional pairs are identical. See predict.dynamic_fit().

data

The observed inputs: y, trials, the series length n, and the resolved per-observation offset.

spec

The model and MCMC specification: family, innovations, latent_dynamics, include_mu, zeros, prior, nsave, nburn, thin, horizon, and the fixed forecast-period inputs forecast_offset / forecast_trials (NULL when not applicable).

See Also

dynamic_prior(), forecast.dynamic_fit(), plot_fitted(), structural_zero_prob()

Examples

set.seed(1)
sim <- simulate_dynamic_poisson(n = 60, sigma = 0.2, log_rate0 = 2)
fit <- fit_dynamic_model(sim$y, family = "poisson", nsave = 300, nburn = 200)
summary(fit)

---

Generic forecast function

Description

Generic for extracting forecasts from a fitted model. See forecast.dynamic_fit() for the method for "dynamic_fit" objects.

Usage

forecast(object, ...)

Arguments

object	A fitted model object.
...	Passed to methods.

Value

The value returned by the method dispatched on object; for "dynamic_fit" objects a "dynamic_forecast" object (see forecast.dynamic_fit()).

---

Forecast a fitted dynamic model

Description

Returns the forecast draws that were produced during MCMC sampling. Forecasts are generated inside the sampler when the model is fitted with horizon = H >= 1. This method extracts and summarises those stored draws.

Usage

## S3 method for class 'dynamic_fit'
forecast(object, probs = c(0.025, 0.5, 0.975), ...)

Arguments

object	A "dynamic_fit" object that was fitted with horizon >= 1.
probs	Quantile probabilities for the summary. Default c(0.025, 0.5, 0.975).
...	Unused.

Details

Zero inflation. For fits with zeros = "inflated" the response forecast is unconditional: each draw includes the zero-inflation gate, so structural zeros are reproduced and the draws are directly comparable to future observations (like the in-sample yrep, unlike yrep_open). The latent forecast summary in ⁠$latent⁠ is gate-free by construction.

Value

An object of class "dynamic_forecast": a list with summary (one row per horizon $1, \dots, H$, on the response scale), latent (summary of the forecast latent path), draws (the predictive draws, draws x H), final (the single-row summary of the final H-step-ahead forecast), final_draws (the predictive draws at horizon H), and the forecast horizon horizon.

Examples

sim <- simulate_dynamic_poisson(60, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 300, nburn = 200, horizon = 8)
fc <- forecast(fit)
fc$summary

---

Weekly Mediterranean crossings (Mediterranean example)

Description

A longer weekly count series of irregular sea crossings on the Mediterranean route, beginning in autumn 2015. The counts are larger in magnitude with fewer zeros than uk_weekly, which makes the series useful for the plain Poisson model and the robust (Student-t) and stochastic-volatility innovation structures. The series is used in the irregular-migration application of Zens and Bijak (2026).

Usage

med_weekly

Format

A data frame with 494 rows and 2 variables:

week

ISO week label, e.g. "2015-W40".

count

Non-negative integer count of weekly crossings.

Source

Weekly aggregates of detected irregular Mediterranean crossings, compiled from operational/agency records as described in Zens and Bijak (2026), doi:10.1214/26-AOAS2171.

References

Zens, G. and Bijak, J. (2026). Dynamic Count Models with Flexible Innovation Processes for Irregular Maritime Migration. The Annals of Applied Statistics. doi:10.1214/26-AOAS2171.

Examples

data(med_weekly)
summary(med_weekly$count)

---

Plot observed versus fitted values

Description

Observed series with the posterior median fitted mean and a credible band on the response scale.

Usage

plot_fitted(object, level = 0.95, ...)

Arguments

object	A "dynamic_fit" object.
level	Credible level. Default 0.95.
...	Passed to graphics::plot().

Value

Invisibly, the fitted summary.

Examples

sim <- simulate_dynamic_poisson(60, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 300, nburn = 200)
plot_fitted(fit)

---

Plot observed history, fitted values and forecast with uncertainty

Description

Shows the observed series together with the in-sample fitted mean (median and credible band) and the forecast (median and credible band) over the forecast horizon. The forecast draws are those produced during sampling, so the model must have been fitted with horizon >= 1 (see forecast.dynamic_fit()).

Usage

plot_forecast(object, level = 0.95, ...)

Arguments

object	A "dynamic_fit" object fitted with horizon >= 1.
level	Credible level. Default 0.95.
...	Passed to graphics::plot().

Value

Invisibly, the "dynamic_forecast" object.

Examples

sim <- simulate_dynamic_poisson(60, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 300, nburn = 200, horizon = 12)
plot_forecast(fit)

---

Plot the fitted latent trajectory

Description

Shows the posterior median of the latent state (log-rate for the Poisson family, logit for the binomial family) with a credible band.

Usage

plot_latent(object, level = 0.95, ...)

Arguments

object	A "dynamic_fit" object.
level	Credible level for the band. Default 0.95.
...	Passed to graphics::plot().

Value

Invisibly, the summary data frame used for plotting.

Examples

sim <- simulate_dynamic_poisson(60, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 300, nburn = 200)
plot_latent(fit)

---

Plot zero-inflation diagnostics

Description

Bar chart of the posterior probability that each observed zero is a structural zero. Requires a model fitted with zeros = "inflated".

Usage

plot_zero_inflation(object, ...)

Arguments

object	A "dynamic_fit" object.
...	Passed to graphics::barplot().

Value

Invisibly, the structural_zero_prob() data frame.

Examples

sim <- simulate_dynamic_poisson(80, 0.2, 2, zero_inflation = 0.3, seed = 1)
fit <- fit_dynamic_model(sim$y, zero_inflation = TRUE, nsave = 300, nburn = 200)
plot_zero_inflation(fit)

---

Plot method for fitted dynamic models

Description

A convenience wrapper that dispatches to the dedicated plotting functions.

Usage

## S3 method for class 'dynamic_fit'
plot(x, which = c("fitted", "latent", "forecast", "zeros"), ...)

Arguments

x	A "dynamic_fit" object.
which	One of "fitted" (default), "latent", "forecast", "zeros".
...	Passed to the underlying plotting function.

Value

Invisibly, the result of the underlying plotting function.

---

In-sample fitted values and posterior predictive replicates

Description

In-sample fitted values and posterior predictive replicates

Usage

## S3 method for class 'dynamic_fit'
predict(
  object,
  type = c("mean", "response"),
  conditional = FALSE,
  probs = c(0.025, 0.5, 0.975),
  ...
)

Arguments

object	A "dynamic_fit" object.
type	"mean" (default) returns the posterior of the mean of y; "response" returns posterior predictive replicates of y.
conditional	Logical. Leave FALSE (the default) for anything compared against observed data – posterior predictive checks, calibration – and set TRUE only to inspect the latent intensity process. With FALSE, means and replicates come from the full zero-inflated model (the gate is included, so structural zeros are reproduced); with TRUE, they are conditional on the gate being open, i.e. drawn straight from the Poisson/binomial observation model, and show systematically too few zeros under zero inflation. Without zero inflation the two versions are identical. See DynCount-package for the gate notation.
probs	Quantile probabilities for the summary. Default c(0.025, 0.5, 0.975).
...	Unused.

Value

A list with summary (a data frame, one row per observation) and draws (the underlying draws matrix, draws x time).

Examples

sim <- simulate_dynamic_poisson(40, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 200, nburn = 100)
head(predict(fit)$summary)

---

Simulate a binomial dynamic series

Description

Generates a latent logit process (random walk or AR(1)) and binomial counts, optionally with structural (zero-inflation) zeros.

Usage

simulate_dynamic_binomial(
  n,
  sigma,
  trials,
  logit0 = 0,
  zero_inflation = 0,
  rho = 1,
  mu = 0,
  offset = 0,
  seed = NULL
)

Arguments

n	Number of observations.
sigma	Standard deviation of the latent increments (Gaussian).
trials	Number of trials: a single number (recycled) or a length-n vector.
logit0	Initial logit $z_1$. Default 0.
zero_inflation	Structural-zero probability. With probability zero_inflation an observation is forced to a structural zero (gate closed) regardless of the binomial draw. Default 0 (no inflation).
rho	AR(1) coefficient of the latent process $z_t = \mu + \rho z_{t-1} + \varepsilon_t$. Default 1 (a random walk).
mu	Drift (random walk) / intercept (AR(1)) of the latent process. Default 0.
offset	Known offset on the logit scale (length 1 or n); the success probability is $\mathrm{logit}^{-1}(\mathrm{offset}_t + z_t)$. Default 0.
seed	Optional random seed.

Value

A list with components y (successes), trials, logit (latent path $z_t$), prob (plogis(offset + logit)), offset, and structural (logical, TRUE for structural zeros).

Examples

sim <- simulate_dynamic_binomial(n = 50, sigma = 0.15, trials = 40, seed = 1)
head(sim$y)
# with structural zeros:
zi <- simulate_dynamic_binomial(50, 0.15, trials = 40, zero_inflation = 0.2, seed = 1)
mean(zi$structural)

---

Simulate a Poisson dynamic series

Description

Generates a latent log-rate process (random walk or AR(1)) and Poisson counts, optionally with zero inflation.

Usage

simulate_dynamic_poisson(
  n,
  sigma,
  log_rate0 = 1,
  zero_inflation = 0,
  rho = 1,
  mu = 0,
  offset = 0,
  seed = NULL
)

Arguments

n	Number of observations.
sigma	Standard deviation of the latent increments (Gaussian).
log_rate0	Initial log-rate $z_1$. Default 1.
zero_inflation	Probability that the gate is closed (i.e. the probability of a structural zero) at each time point. 0 (default) gives an ordinary Poisson series.
rho	AR(1) coefficient of the latent process $z_t = \mu + \rho z_{t-1} + \varepsilon_t$. Default 1 (a random walk).
mu	Drift (random walk) / intercept (AR(1)) of the latent process. Default 0.
offset	Known log-exposure offset (length 1 or n); the Poisson mean is $\exp(\mathrm{offset}_t + z_t)$. Default 0.
seed	Optional random seed.

Value

A list with components y (observed counts), log_rate (the latent log-rate path $z_t$), rate (the mean exp(offset + log_rate)), offset, and structural (logical, TRUE where a structural zero was forced).

Examples

sim <- simulate_dynamic_poisson(n = 50, sigma = 0.2, log_rate0 = 2,
                           zero_inflation = 0.2, seed = 1)
table(sim$y == 0, sim$structural)

---

Posterior probability that each observed zero is structural

Description

For a zero-inflated fit (Poisson or binomial), returns for every observed zero the posterior probability that it is a structural zero (gate closed) rather than an ordinary sampling zero generated by the observation process. The zero inflation is time-constant: a single gate-open probability governs all observations (it does not vary over time or with covariates).

Usage

structural_zero_prob(object, zeros_only = TRUE)

Arguments

object	A "dynamic_fit" object fitted with zeros = "inflated".
zeros_only	If TRUE (default), return only the rows where the observation is zero.

Details

The model introduces a latent gate indicator $v_t \in \{0, 1\}$: when the gate is open ($v_t = 1$) the count comes from the observation model (Poisson or binomial); when closed ($v_t = 0$) the count is a structural zero. The sampler stores $v_t$ for each draw, so the structural-zero probability is

$\Pr(\text{structural} \mid y_t = 0) = 1 - \overline{v_t},$

the posterior mean of the gate being closed. Non-zero observations are always sampling observations and have structural probability 0.

Value

A data frame with columns time, observed, p_structural (posterior probability the zero is structural) and p_sampling (1 - p_structural).

Examples

sim <- simulate_dynamic_poisson(60, 0.2, 2, zero_inflation = 0.25, seed = 1)
fit <- fit_dynamic_model(sim$y, zero_inflation = TRUE, nsave = 300, nburn = 200)
structural_zero_prob(fit)

---

Summarise a fitted dynamic model

Description

Summarise a fitted dynamic model

Usage

## S3 method for class 'dynamic_fit'
summary(object, probs = c(0.025, 0.5, 0.975), ...)

Arguments

object	A "dynamic_fit" object.
probs	Quantile probabilities. Default c(0.025, 0.5, 0.975).
...	Unused.

Value

An object of class "summary.dynamic_fit" containing posterior summaries of the global parameters (the innovation standard deviation innov_sd – the estimated SD for "gaussian" innovations, the marginal SD for "t" and "mixture", and the series-average SD for "sv" – and where relevant the t degrees of freedom, the AR(1) coefficient, the drift/intercept, and the zero-inflation gate-open probability) and the fitted-value summary.

Examples

sim <- simulate_dynamic_poisson(50, 0.2, 2, seed = 1)
fit <- fit_dynamic_model(sim$y, nsave = 200, nburn = 100)
summary(fit)

---

Weekly English Channel crossings (UK example)

Description

A weekly count series of irregular small-boat crossings of the English Channel towards the United Kingdom, beginning in early 2018. The series has frequent zeros in its early weeks, which makes it a useful example for zero inflation with the Poisson model. The series is used in the irregular-migration application of Zens and Bijak (2026).

Usage

uk_weekly

Format

A data frame with 376 rows and 2 variables:

week

ISO week label, e.g. "2018-W01".

count

Non-negative integer count of weekly crossings.

Source

Weekly aggregates of detected irregular English Channel crossings, compiled from operational/agency records as described in Zens and Bijak (2026), doi:10.1214/26-AOAS2171.

References

Zens, G. and Bijak, J. (2026). Dynamic Count Models with Flexible Innovation Processes for Irregular Maritime Migration. The Annals of Applied Statistics. doi:10.1214/26-AOAS2171.

Examples

data(uk_weekly)
plot(uk_weekly$count, type = "h")
mean(uk_weekly$count == 0)

---