Package {fable.intermittent}

Title:	Forecasting Models for Intermittent Time Series
Version:	0.1.0
Description:	Extends the 'fable' framework to support forecasting methods specifically designed for intermittent time series data, where demand occurs sporadically with many zero values. All methods produce probabilistic forecasts returned as 'distributional' objects. The returned forecasts can be used to evaluate accuracy, plot and print the results seamlessly with 'fable'. The methods include: Harvey, Fernandes (1989) <doi:10.1080/07350015.1989.10509750>, Willemain, Smart, Schwarz (2004) <doi:10.1016/S0169-2070(03)00013-X>, Zhou, Viswanathan (2011) <doi:10.1016/j.ijpe.2010.09.021>, Snyder, Ord, Beaumont (2012) <doi:10.1016/j.ijforecast.2011.03.009>, Kolassa (2016) <doi:10.1016/j.ijforecast.2015.12.004>, Hasni, Aguir, Babai, Jemai (2019) <doi:10.1080/00207543.2018.1424375>, Damato, Azzimonti, Corani (2025) <doi:10.1016/j.ijforecast.2025.10.001>, Sbrana (2025) <doi:10.1080/01605682.2025.2569661>.
License:	LGPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
LinkingTo:	Rcpp, RcppArmadillo
Depends:	R (≥ 4.1.0), fabletools (≥ 0.6.0)
Imports:	tsibble (≥ 1.0.0), distributional (≥ 0.3.0), nloptr (≥ 2.0.0), rlang (≥ 1.0.0), Rcpp (≥ 1.0.0)
Suggests:	dplyr, testthat (≥ 3.3.0), tweedie, ggtime, ggplot2, tibble, knitr, rmarkdown
VignetteBuilder:	knitr
URL:	https://github.com/StefanoDamato/fable.intermittent
BugReports:	https://github.com/StefanoDamato/fable.intermittent/issues
Config/roxygen2/version:	8.0.0
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Packaged:	2026-06-09 07:19:12 UTC; stefano.damato
Author:	Stefano Damato [aut, cre, cph], Lorenzo Zambon [aut], Dario Azzimonti [aut]
Maintainer:	Stefano Damato <stefanodamato128@gmail.com>
Repository:	CRAN
Date/Publication:	2026-06-18 10:00:02 UTC

fable.intermittent: Forecasting Models for Intermittent Time Series

Description

Extends the 'fable' framework to support forecasting methods specifically designed for intermittent time series data, where demand occurs sporadically with many zero values. All methods produce probabilistic forecasts returned as 'distributional' objects. The returned forecasts can be used to evaluate accuracy, plot and print the results seamlessly with 'fable'. The methods include: Harvey, Fernandes (1989) doi:10.1080/07350015.1989.10509750, Willemain, Smart, Schwarz (2004) doi:10.1016/S0169-2070(03)00013-X, Zhou, Viswanathan (2011) doi:10.1016/j.ijpe.2010.09.021, Snyder, Ord, Beaumont (2012) doi:10.1016/j.ijforecast.2011.03.009, Kolassa (2016) doi:10.1016/j.ijforecast.2015.12.004, Hasni, Aguir, Babai, Jemai (2019) doi:10.1080/00207543.2018.1424375, Damato, Azzimonti, Corani (2025) doi:10.1016/j.ijforecast.2025.10.001, Sbrana (2025) doi:10.1080/01605682.2025.2569661.

Author(s)

Maintainer: Stefano Damato stefanodamato128@gmail.com (ORCID) [copyright holder]

Authors:

• Lorenzo Zambon lorenzo.zambon@idsia.ch (ORCID)

• Dario Azzimonti dario.azzimonti@gmail.com (ORCID)

See Also

Useful links:

• https://github.com/StefanoDamato/fable.intermittent

• Report bugs at https://github.com/StefanoDamato/fable.intermittent/issues

Beta-Negative Binomial Bayesian Dynamic Model

Description

Conjugate Bayesian dynamic model for count time series with a negative binomial observation distribution and a Beta prior on the success probability parameter. This extends the conjugate updating framework of Harvey & Fernandes (1989) to the Beta-Negative Binomial family. The Beta prior is updated at each time step using a discount factor w. Forecasts are available as samples simulating from the model forward in time.

Usage

BETANBB(formula, ...)

Arguments

Value

A model specification.

References

Harvey, A. C., & Fernandes, C. (1989). Time series models for count or qualitative observations. Journal of Business & Economic Statistics, 7(4), 407–417. doi:10.1080/07350015.1989.10509750.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(BETANBB(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Empirical Distribution Resampling

Description

Naive non-parametric baseline for intermittent demand forecasting. The predictive distribution at every horizon is simply the empirical distribution of the observed values: forecasts are produced by resampling with replacement from the historical series. Point forecasts are the sample mean.

Usage

EMPDISTR(formula, hot_start = FALSE, ...)

Arguments

Value

A model specification.

References

Hasni, M., Aguir, M. S., Babai, M. Z., & Jemai, Z. (2019). Spare parts demand forecasting: a review on bootstrapping methods. International Journal of Production Research, 57(15–16), 4791–4804. doi:10.1080/00207543.2018.1424375.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(EMPDISTR(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Gamma-Poisson Bayesian Dynamic Model

Description

Conjugate Bayesian dynamic model for count time series with a Poisson observation distribution and a Gamma prior on the rate parameter, following Harvey & Fernandes (1989). The Gamma prior is updated at each time step using a discount factor w that controls how quickly past information decays. The first-step forecast follows a Negative Binomial distribution, and multi-step forecasts are obtained by simulating from the model forward in time.

Usage

GAMPOISB(formula, ...)

Arguments

Value

A model specification.

References

Harvey, A. C., & Fernandes, C. (1989). Time series models for count or qualitative observations. Journal of Business & Economic Statistics, 7(4), 407–417. doi:10.1080/07350015.1989.10509750.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(GAMPOISB(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Hurdle-Shifted Poisson Exponential Smoothing

Description

Exponential smoothing state space model for intermittent demand with a hurdle-shifted Poisson observation distribution, following the framework of Snyder, Ord & Beaumont (2012). The model decomposes demand into two components: a Bernoulli occurrence process (probability of non-zero demand) and a shifted Poisson demand-size process. Both components are driven by independent (optionally damped) exponential smoothing state equations. The first-step forecast follows an hurdle-shifted Poisson distribution, multi-step forecasts are obtained by simulating from the model forward in time.

Usage

HSPES(formula, damped = TRUE, ...)

Arguments

Value

A model specification.

References

Snyder, R. D., Ord, J. K., & Beaumont, A. (2012). Forecasting the intermittent demand for slow-moving inventories: A modelling approach. International Journal of Forecasting, 28(2), 485–496. doi:10.1016/j.ijforecast.2011.03.009.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(HSPES(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Markov Chain Model with Random Walk dynamic

Description

A Random Walk model on the demand composed by a switching constant and an ARMA model, where the changes are controlled by a Markov Chain on the occurrence process. Parameters are estimated in closed-form on deseasonalized data, and forecasts are returned as Gaussian distributions for each time step.

Usage

MARWAL(formula, ...)

Arguments

Value

A model specification.

References

Sbrana, G. (2025). Markov Walk and Walmart sales prediction. Journal of the Operational Research Society, 1–12. doi:10.1080/01605682.2025.2569661.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(MARWAL(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Negative Binomial Exponential Smoothing

Description

Exponential smoothing state space model for intermittent demand with a negative binomial observation distribution, as proposed by Snyder, Ord & Beaumont (2012). The conditional mean of the negative binomial is governed by a (optionally damped) exponential smoothing process. The probability parameter is estimated to maximise the likelihood. The first-step forecast follows a Negative Binomial distribution, and multi-step forecasts are obtained by simulating from the model forward in time.

Usage

NEGBINES(formula, damped = TRUE, ...)

Arguments

Value

A model specification.

References

Snyder, R. D., Ord, J. K., & Beaumont, A. (2012). Forecasting the intermittent demand for slow-moving inventories: A modelling approach. International Journal of Forecasting, 28(2), 485–496. doi:10.1016/j.ijforecast.2011.03.009.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(NEGBINES(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Static Count Distribution Model

Description

Static (IID) count distribution model for intermittent demand, following Kolassa (2016). The method fits several candidate distributions — Poisson, hurdle-shifted Poisson, negative binomial, and hurdle-shifted negative binomial — to the observed series and selects the best by AIC. A mixture option that blends all four predictive distributions is also available.

Usage

STATICDISTR(
  formula,
  distr = c("auto", "pois", "hsp", "nbinom", "hsnb", "mixture"),
  hot_start = FALSE,
  criterion = c("aic", "bic"),
  ...
)

Arguments

Value

A model specification.

References

Kolassa, S. (2016). Evaluating predictive count data distributions in retail sales forecasting. International Journal of Forecasting, 32(3), 788–803. doi:10.1016/j.ijforecast.2015.12.004.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(STATICDISTR(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Tweedie Exponential Smoothing

Description

Exponential smoothing state space model for intermittent demand with a Tweedie observation distribution. The conditional mean of the Tweedie is governed by a (optionally damped) exponential smoothing process. The power and dispersion parameter are estimated to maximise the likelihood. The Tweedie family naturally models both zeros and large spikes via its compound Poisson-Gamma nature. The first-step forecast follows a Tweedie distribution, and multi-step forecasts are obtained by simulating from the model forward in time. The model parameters are estimated by

Usage

TWEES(formula, damped = TRUE, scaling = TRUE, ...)

Arguments

Value

A model specification.

References

Damato, S., Azzimonti, D., & Corani, G. (2025). Forecasting intermittent time series with Gaussian Processes and Tweedie likelihood. International Journal of Forecasting (in press). doi:10.1016/j.ijforecast.2025.10.001.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(TWEES(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Viswanathan–Zhou Bootstrap Method

Description

Non-parametric bootstrap forecasting method for intermittent demand proposed by Zhou & Viswanathan (2011). The time series is decomposed into demand sizes and inter-demand intervals via Croston's decomposition. Forecasts are generated by independently resampling from the empirical distributions of both components, preserving the marginal structure of the original series.

Usage

VZ(formula, ...)

Arguments

Value

A model specification.

References

Zhou, Chenxi, Viswanathan, S., (2011). Comparison of a new bootstrapping method with parametric approaches for safety stock determination in service parts inventory systems. International Journal of Production Economics 133(1) 481–485. doi:10.1016/j.ijpe.2010.09.021

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(VZ(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Willemain–Smart–Schwarz Bootstrap Method

Description

Markov-chain bootstrap forecasting method for intermittent demand proposed by Willemain, Smart & Schwarz (2004). Occurrence of non-zero demand is modelled with a two-state Markov chain whose transition probabilities are estimated from the observed binary occurrence sequence. Demand sizes are resampled from past non-zero observations with Gaussian jittering to smooth the empirical distribution.

Usage

WSS(formula, ...)

Arguments

Value

A model specification.

References

Willemain, T. R., Smart, C. N., & Schwarz, H. F. (2004). A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting, 20(3), 375–387. doi:10.1016/S0169-2070(03)00013-X.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)

fc_ts <- ts |>
  model(WSS(value)) |>
  forecast(h = "7 days")

fc_ts |> print()


if (requireNamespace("ggtime", quietly = TRUE)) {
  library(ggtime)
  fc_ts |> autoplot(ts)
}

Automotive Spare Parts Demand Dataset

Description

A dataset of monthly demand for automotive spare parts. The data contains 3000 intermittent time series, each spanning 24 monthly periods from January 2010 to December 2011.

Usage

auto

Format

A tsibble with 72,000 rows and 3 variables:

series_id

Character. Unique identifier for each time series.

index

Date (yearmonth). The monthly time index.

value

Numeric. The demand quantity for the given month.

Source

Turkmen, A. C., Januschowski, T., Wang, Y., & Cemgil, A. T. (2021). Forecasting intermittent and sparse time series: A unified probabilistic framework via deep renewal processes. PLOS ONE, 16(11), e0259764.

Available at https://github.com/canerturkmen/gluon-ts/tree/intermittent-datasets/datasets.

Examples

library(tsibble)
auto

Tweedie Distribution

Description

Construct a Tweedie distribution object using the compound Poisson–Gamma parameterisation with power parameter in (1, 2). The Tweedie family is a subclass of exponential dispersion models that naturally produces exact zeros (via the Poisson count component) mixed with continuous positive values (via the Gamma severity component), making it well suited to intermittent demand data.

Usage

dist_tweedie(mean = 1, dispersion = 1, power = 1.5)

Arguments

Details

The density is evaluated using the series expansion of Dunn & Smyth (2005), implemented in C++ for performance.

Value

A distributional distribution object of class dist_tweedie.

References

Dunn, P. K., & Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing, 15(4), 267–280. doi:10.1007/s11222-005-4070-y.

Examples

d <- dist_tweedie(mean = 2, dispersion = 0.8, power = 1.5)
d |> mean()
d |> quantile(c(0.5, 0.9))
d |> density(c(0, 1.5, 3))
d |> distributional::variance()
d |> distributional::generate(10)

Extract fitted values from a BETANBB model

Description

Extract fitted values from a BETANBB model

Usage

## S3 method for class 'BETANBB'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, BETANBB(value))
fitted(fit)

Extract fitted values from an EMPDISTR model

Description

Extract fitted values from an EMPDISTR model

Usage

## S3 method for class 'EMPDISTR'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, EMPDISTR(value))
fitted(fit)

Extract fitted values from a GAMPOISB model

Description

Extract fitted values from a GAMPOISB model

Usage

## S3 method for class 'GAMPOISB'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, GAMPOISB(value))
fitted(fit)

Extract fitted values from a HSPES model

Description

Extract fitted values from a HSPES model

Usage

## S3 method for class 'HSPES'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, HSPES(value))
fitted(fit)

Extract fitted values from a MARWAL model

Description

Extract fitted values from a MARWAL model

Usage

## S3 method for class 'MARWAL'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, MARWAL(value))
fitted(fit)

Extract fitted values from a NEGBINES model

Description

Extract fitted values from a NEGBINES model

Usage

## S3 method for class 'NEGBINES'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, NEGBINES(value))
fitted(fit)

Extract fitted values from a STATICDISTR model

Description

Extract fitted values from a STATICDISTR model

Usage

## S3 method for class 'STATICDISTR'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, STATICDISTR(value))
fitted(fit)

Extract fitted values from a TWEES model

Description

Extract fitted values from a TWEES model

Usage

## S3 method for class 'TWEES'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, TWEES(value))
fitted(fit)

Extract fitted values from a VZ model

Description

Extract fitted values from a VZ model

Usage

## S3 method for class 'VZ'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, VZ(value))
fitted(fit)

Extract fitted values from a WSS model

Description

Extract fitted values from a WSS model

Usage

## S3 method for class 'WSS'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, WSS(value))
fitted(fit)

Forecast a BETANBB model

Description

Produces forecast distributions from a fitted BETANBB model using simulation.

Usage

## S3 method for class 'BETANBB'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of class dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, BETANBB(value))
forecast(fit, h = "7 days")

Forecast an EMPDISTR model

Description

Produces forecast distributions by repeating the empirical distribution estimated from the training data at each forecast horizon.

Usage

## S3 method for class 'EMPDISTR'
forecast(object, new_data, specials = NULL, ...)

Arguments

Value

A distribution vector of class dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, EMPDISTR(value))
forecast(fit, h = "7 days")

Forecast a GAMPOISB model

Description

Produces forecast distributions from a fitted GAMPOISB model using simulation.

Usage

## S3 method for class 'GAMPOISB'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts: for h=1 the vector class is dist_negative_binomial; for h>1 the vector class is dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, GAMPOISB(value))
forecast(fit, h = "7 days")

Forecast a HSPES model

Description

Produces forecast distributions from a fitted HSPES model using simulation.

Usage

## S3 method for class 'HSPES'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts: for h=1 the vector class is dist_inflated (hurdle-shifted Poisson); for h>1 the vector class is dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, HSPES(value))
forecast(fit, h = "7 days")

Forecast a MARWAL model

Description

Produces forecast distributions from a fitted MARWAL model.

Usage

## S3 method for class 'MARWAL'
forecast(object, new_data, specials = NULL, ...)

Arguments

Value

A distribution vector of class dist_normal.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, MARWAL(value))
forecast(fit, h = "7 days")

Forecast a NEGBINES model

Description

Produces forecast distributions from a fitted NEGBINES model using simulation.

Usage

## S3 method for class 'NEGBINES'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts: for h=1 the vector class is dist_negative_binomial; for h>1 the vector class is dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, NEGBINES(value))
forecast(fit, h = "7 days")

Forecast a STATICDISTR model

Description

Produces forecast distributions from a fitted STATICDISTR model.

Usage

## S3 method for class 'STATICDISTR'
forecast(object, new_data, specials = NULL, ...)

Arguments

Value

A distribution vector. The class depends on the static distribution fitted by the STATICDISTR method.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, STATICDISTR(value))
forecast(fit, h = "7 days")

Forecast a TWEES model

Description

Produces forecast distributions from a fitted TWEES model using simulation.

Usage

## S3 method for class 'TWEES'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts: for h=1 the vector class is dist_tweedie; for h>1 the vector class is dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, TWEES(value))
forecast(fit, h = "7 days")

Forecast a VZ model

Description

Produces forecast distributions from a fitted VZ model using simulation.

Usage

## S3 method for class 'VZ'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts of class dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, VZ(value))
forecast(fit, h = "7 days")

Forecast a WSS model

Description

Produces forecast distributions from a fitted WSS model using simulation.

Usage

## S3 method for class 'WSS'
forecast(object, new_data, specials = NULL, times = 10000, ...)

Arguments

Value

A distribution vector of forecasts of class dist_sample.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, WSS(value))
forecast(fit, h = "7 days")

Generate sample paths from a BETANBB model

Description

Generate sample paths from a BETANBB model

Usage

## S3 method for class 'BETANBB'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, BETANBB(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from an EMPDISTR model

Description

Generate sample paths from an EMPDISTR model

Usage

## S3 method for class 'EMPDISTR'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A new_data tibble with a .sim column of simulated values.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, EMPDISTR(value))
generate(fit, h = 7)

Generate sample paths from a GAMPOISB model

Description

Generate sample paths from a GAMPOISB model

Usage

## S3 method for class 'GAMPOISB'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, GAMPOISB(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a HSPES model

Description

Generate sample paths from a HSPES model

Usage

## S3 method for class 'HSPES'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, HSPES(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a MARWAL model

Description

Generate sample paths from a MARWAL model

Usage

## S3 method for class 'MARWAL'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, MARWAL(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a NEGBINES model

Description

Generate sample paths from a NEGBINES model

Usage

## S3 method for class 'NEGBINES'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, NEGBINES(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a STATICDISTR model

Description

Generate sample paths from a STATICDISTR model

Usage

## S3 method for class 'STATICDISTR'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, STATICDISTR(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a TWEES model

Description

Generate sample paths from a TWEES model

Usage

## S3 method for class 'TWEES'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, TWEES(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a VZ model

Description

Generate sample paths from a VZ model

Usage

## S3 method for class 'VZ'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, VZ(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Generate sample paths from a WSS model

Description

Generate sample paths from a WSS model

Usage

## S3 method for class 'WSS'
generate(x, new_data, specials = NULL, ...)

Arguments

Value

A vector of future paths from a dataset using a fitted model.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, WSS(value))
generate(fit, new_data = tsibble::new_data(ts, 7))

Return model name

Description

Return model name

Usage

## S3 method for class 'BETANBB'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, BETANBB(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'EMPDISTR'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, EMPDISTR(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'GAMPOISB'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, GAMPOISB(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'HSPES'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, HSPES(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'MARWAL'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, MARWAL(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'NEGBINES'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, NEGBINES(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'STATICDISTR'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, STATICDISTR(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'TWEES'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, TWEES(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'VZ'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, VZ(value))
model_sum(fit[[1]][[1]])

Return model name

Description

Return model name

Usage

## S3 method for class 'WSS'
model_sum(x)

Arguments

Value

The model name as a string

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, WSS(value))
model_sum(fit[[1]][[1]])

Quantile method for inflated distributions

Description

Quantile method for inflated distributions

Usage

## S3 method for class 'dist_inflated'
quantile(x, p, ...)

Arguments

Value

A numeric vector of quantiles.

Examples

x <- distributional::dist_inflated(distributional::dist_normal(), 0.2, 0)
stats::quantile(x, p = c(0.25, 0.5, 0.75))

RAF Spare Parts Demand Dataset

Description

A dataset of monthly demand for spare parts from the Royal Air Force (RAF). The data contains 5000 intermittent time series, each spanning 84 monthly periods from January 1996 to December 2002. This is a widely used benchmark dataset for intermittent demand forecasting.

Usage

raf

Format

A tsibble with 420,000 rows and 3 variables:

series_id

Character. Unique identifier for each time series.

index

Date (yearmonth). The monthly time index.

value

Numeric. The demand quantity for the given month.

Source

Syntetos, A. A., & Boylan, J. E. (2005). The accuracy of intermittent demand estimates. International Journal of Forecasting, 21(2), 303–314.

Available at https://github.com/canerturkmen/gluon-ts/tree/intermittent-datasets/datasets.

Examples

library(tsibble)
raf

Extract residuals from a BETANBB model

Description

Extract residuals from a BETANBB model

Usage

## S3 method for class 'BETANBB'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, BETANBB(value))
residuals(fit)

Extract residuals from an EMPDISTR model

Description

Extract residuals from an EMPDISTR model

Usage

## S3 method for class 'EMPDISTR'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, EMPDISTR(value))
residuals(fit)

Extract residuals from a GAMPOISB model

Description

Extract residuals from a GAMPOISB model

Usage

## S3 method for class 'GAMPOISB'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, GAMPOISB(value))
residuals(fit)

Extract residuals from a HSPES model

Description

Extract residuals from a HSPES model

Usage

## S3 method for class 'HSPES'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, HSPES(value))
residuals(fit)

Extract residuals from a MARWAL model

Description

Extract residuals from a MARWAL model

Usage

## S3 method for class 'MARWAL'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, MARWAL(value))
residuals(fit)

Extract residuals from a NEGBINES model

Description

Extract residuals from a NEGBINES model

Usage

## S3 method for class 'NEGBINES'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, NEGBINES(value))
residuals(fit)

Extract residuals from a STATICDISTR model

Description

Extract residuals from a STATICDISTR model

Usage

## S3 method for class 'STATICDISTR'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, STATICDISTR(value))
residuals(fit)

Extract residuals from a TWEES model

Description

Extract residuals from a TWEES model

Usage

## S3 method for class 'TWEES'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, TWEES(value))
residuals(fit)

Extract residuals from a VZ model

Description

Extract residuals from a VZ model

Usage

## S3 method for class 'VZ'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, VZ(value))
residuals(fit)

Extract residuals from a WSS model

Description

Extract residuals from a WSS model

Usage

## S3 method for class 'WSS'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals.

Examples

ts <- tsibble::tsibble(
  time = as.Date("2026-01-01") + seq_len(40),
  value = rnbinom(40, size = 1, prob = 0.3),
  index = time
)
fit <- model(ts, WSS(value))
residuals(fit)

Tweedie Distribution Functions

Description

Density, distribution function, quantile function and random generation for the Tweedie distribution with mean equal to mean, dispersion equal to dispersion, and power equal to power.

Usage

rtweedie(n, mean = 1, dispersion = 1, power = 1.5)

dtweedie(x, mean = 1, dispersion = 1, power = 1.5, log = FALSE)

ptweedie(
  q,
  mean = 1,
  dispersion = 1,
  power = 1.5,
  lower.tail = TRUE,
  log.p = FALSE
)

qtweedie(
  p,
  mean = 1,
  dispersion = 1,
  power = 1.5,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

Details

If mean, dispersion, or power are not specified they assume the default values of 1, 1, and 1.5, respectively.

The Tweedie distribution used here follows the compound Poisson-Gamma parameterisation with power parameter in (1, 2). It has \mathbb{E}[X] = \mu and \mathrm{Var}(X) = \phi\mu^p, where \mu is mean, \phi is dispersion, and p is power.

Value

dtweedie gives the density, ptweedie gives the distribution function, qtweedie gives the quantile function, and rtweedie generates random samples.

The length of the result is determined by n for rtweedie, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

References

Dunn, P. K., & Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing, 15(4), 267–280. doi:10.1007/s11222-005-4070-y.