arguments.model {BTSR} | R Documentation |
Available models in BTSR package
Description
The BTSR package supports a variety of models, including
i.i.d structure,
regression models,
short- and long-memory time series models
chaotic processes.
This documentation describes
the
model
argument and available model strings,default configurations for specific models,
how to reproduce models from literature.
Arguments
model |
character string (case-insensitive) indicating the model to be fitted to the data. Must be one of the options listed in the Section Supported Models. |
Supported Models
Internally, all models are handled by the same function and all models can be
obtained from the more general case "*ARFIMAV"
. When a particular model
(e.g. "BREG"
or "BARMA"
) is invoked some default values are assumed.
The following table summarizes the available distributions and the
corresponding string to generate each model type. The character V
at
the end of the string indicates that \nu
is time-varying.
+--------------+--------+------------+---------+-----------+---------+ | Distribution | i.i.d. | Regression | Short | Long | Chaotic | | | sample | | Memory | Memory | | +--------------+--------+------------+---------+-----------+---------+ | Beta | BETA | BREG | BARMA | BARFIMA | BARC | | | | BREGV | BARMAV | BARFIMAV | | +--------------+--------+------------+---------+-----------+---------+ | Gamma | GAMMA | GREG | GARMA | GARFIMA | | | | | GREGV | GARMAV | GARFIMAV | | +--------------+--------+------------+---------+-----------+---------+ | Kumaraswamy | KUMA | KREG | KARMA | KARFIMA | | | | | KREGV | KARMAV | KARFIMAV | | +--------------+--------+------------+---------+-----------+---------+ | Matsuoka | MATSU | MREG | MARMA | MARFIMA | | +--------------+--------+------------+---------+-----------+---------+ | Unit-Lindley | UL | ULREG | ULARMA | ULARFIMA | | +--------------+--------+------------+---------+-----------+---------+ | Unit-Weibull | UW | UWREG | UWARMA | UWARFIMA | | | | | UWREGV | UWARMAV | UWARFIMAV | | +--------------+--------+------------+---------+-----------+---------+
Default values
All models are special cases of the general "*ARFIMAV"
structure. When a
specific model is selected via model = "NAME"
, the package automatically
applies these default configurations (any parameter that does not appear in
the equations below is ignored)
i.i.d samples (e.g., BETA, GAMMA,...)
\eta_{1t} = \alpha_1 = \mu, \quad \eta_{2t} = \alpha_2 = \nu.
Fixed
p <- q <- d <- 0 xreg <- NULL linkg <- list(g11 = "linear", g2 = "linear", g21 = "linear", g23 = "linear")
Regression models with \nu_t
constant over time (e.g., BREG,
GREG,...)
\eta_{1t} =
g_{11}(\mu_t) = \alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1,
\quad
\eta_{2t} = \alpha_2 = \nu.
Fixed
p <- q <- d <- 0 xreg <- list(part1 = "user's regressors", part2 = NULL) linkg <- list(g11 = "user's choice", g12 = "linear", g2 = "linear", g21 = "linear", g23 = "linear")
Regression models with \nu_t
varying on time (e.g. BREGV,
GREGV)
\eta_{1t} =
g_{11}(\mu_t) = \alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1,
\quad
\eta_{2t} =
g_{21}(g_2(\nu_t)) = \alpha_2 + \boldsymbol{X}_{2t}'\boldsymbol{\beta}_2.
Fixed
p <- q <- d <- 0 linkg <- list(g11 = "user's choice", g12 = "linear", g2 = "user's choice", g21 = "user's choice", g22 = "linear", g23 = "linear")
Short-memory models with \nu
constant over time (ARMA-like) (e.g. BARMA,
GARMA,...)
\begin{aligned}
\eta_{1t} & =
g_{11}(\mu_t) = \alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1 +
\sum_{i=1}^{p_1} \phi_{1i}\bigl(g_{12}(Y_{t-i})-
I_{X_1}\boldsymbol{X}_{1(t-i)}'\boldsymbol{\beta}_1\bigr) +
\sum_{k=1}^{q_1} \theta_{1k} e_{1,t-k}, \\
\eta_{2t} & = \alpha_2 = \nu.
\end{aligned}
Fixed
d <- 0 xreg <- list(part1 = "user's regressors", part2 = NULL) linkg <- list(g11 = "user's choice", g12 = "user's choice", g2 = "linear", g21 = "linear", g23 = "linear")
Short-memory models with \nu_t
varying on time (e.g. BARMAV,
GARMAV,...)
\begin{aligned}
\eta_{1t} & =
g_{11}(\mu_t) =\alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1 +
\sum_{i=1}^{p_1} \phi_{1i}\big(g_{12}(Y_{t-i})-
I_{X_1}\boldsymbol{X}_{1(t-i)}'\boldsymbol{\beta}_1\big) +
\sum_{k=1}^{q_1} \theta_{1k} r_{t-k},\\
\vartheta_t & = g2(\nu_t)\\
\eta_{2t} &
= g_{21}(\vartheta_t) =\alpha_2 + \boldsymbol{X}_{2t}' \boldsymbol{\beta}_2
+ \sum_{i=1}^{p_2} \phi_{2i}\big(g_{22}(\vartheta_{t-i})-
I_{X_2}\boldsymbol{X}_{2(t-i)}'\boldsymbol{\beta}_2\big) +
\sum_{k=1}^{q_2} \theta_{2k} g_{23}(e_{1,t-k}).
\end{aligned}
Fixed
d <- 0
Long-memory models with \nu
constant over time (ARFIMA-like
models) (e.g. BARFIMA, GARFIMA,...)
\begin{aligned}
\eta_{1t} & =
g_{11}(\mu_t) =\alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1 +
\sum_{i=1}^{p_1} \phi_{1i}\big(g_{12}(Y_{t-i})-
I_{X_1}\boldsymbol{X}_{1(t-i)}'\boldsymbol{\beta}_1\big) +
\sum_{k=1}^\infty c_{1k} r_{t-k},\\
\eta_{2t} & =\alpha_2 = \nu.
\end{aligned}
Fixed
p <- c("user's p", 0) q <- c("user's q", 0) d <- c("user's d", 0) xreg <- list(part1 = "user's regressors", part2 = NULL) linkg <- list(g11 = "user's choice", g12 = "user's choice", g2 = "linear", g21 = "linear", g23 = "linear")
Reproducing Models from the Literature
This section summarizes how to replicate well-known time series models from the literature using the BTSR package. For each model type, we provide the necessary parameter settings and references to the original publications. These configurations act as templates, helping users correctly apply the package to reproduce results or extend established models.
Key arguments (e.g., error.scale
, xregar
, y.lower
,
y.upper
, rho
) should be set to match the specifications in the
referenced articles. While we focus on the btsr.*
functions (see
BTSR.functions), all models can also be implemented using the corresponding
parent model functions (for details, see BTSR.parent.models).
i.i.d. samples: The arguments error.scale
and xregar
are
ignored.
Beta distribution with parameters
shape1
andshape2
compatible with the one from rbeta:model = "BETA" alpha = shape1/(shape1 + shape2) nu = shape1 + shape2
Gamma distribution with parameters
shape
andscale
compatible with the one from rgamma:model = "GAMMA" alpha = shape*scale nu = shape
Kumaraswamy distribution with shape parameters
shape1
andshape2
(respectively denoted bya
andb
in Kumaraswamy 1980):model = "KUMA" alpha = (y.lower - y.upper)*(1 - (1-rho)^1/shape2)*1/shape1 + y.lower nu = shape1
Warning: Choose
\mu
,\nu
and\rho
carefully since|\log(1-\rho)| >> |\log(1 - \mu^\nu)|
may cause numerical instability.Matsuoka distribution with shape parameter
shape
(Matsuoka et al. 2024):model = "MATSU" alpha = (shape/(shape+1))^(3/2)
Unit-Lindley distribution with parameter
theta
(Mazucheli et al. 2018):model = "UL" alpha = 1/(1 + theta)
Unit-Weibull distribution with parameter
mu
,beta
andtau
from (Mazucheli et al. 2019):model = "UW" alpha = mu nu = beta rho = tau
Regression models: the argument error.scale
and all entries but
g11
in linkg
are ignored
Beta regression (Ferrari and Cribari-Neto 2004):
model = "BREG"
Kumaraswamy regression (Mitnik and Baek 2013):
model = "KREG"
.Unit-Lindley regression (Mazucheli et al. 2018):
model = "ULREG"
.Unit-Weibull regression (Mazucheli et al. 2019):
model = "UWREG"
.
ARMA-like models
BARMA model (Rocha and Cribari-Neto 2009; Rocha and Cribari-Neto 2017):
model = "BARMA" error.scale = 1 xregar = TRUE
KARMA model (Bayer et al. 2017):
model = "KARMA" error.scale = 1 xregar = TRUE y.lower = 0 y.upper = 1 rho = 0.5
GARMA model (Prass et al. 2025):
model = "GARMA" error.scale = 0
MARMA model (Pumi et al. 2025):
model = "MARMA" error.scale = 1 xregar = TRUE
ULARMA model (Pumi et al. 2025):
model = "ULARMA" error.scale = 1 xregar = TRUE
ARFIMA-like models
BARFIMA model (Pumi et al. 2019):
model = "BARFIMA" error.scale = 1 xregar = TRUE d = TRUE (for fitting)
Chaotic models
BARC model (Pumi et al. 2021): set
model = "BARC"
anderror.scale = 1
.
References
Bayer FM, Bayer DM, Pumi G (2017).
“Kumaraswamy autoregressive moving average models for double bounded environmental data.”
Journal of Hydrology, 555, 385–396.
doi:10.1016/j.jhydrol.2017.10.006.
Ferrari SLP, Cribari-Neto F (2004).
“Beta Regression for Modelling Rates and Proportions.”
Journal of Applied Statistics, 31(7), 799–815.
doi:10.1080/0266476042000214501.
Kumaraswamy P (1980).
“A generalized probability density function for double-bounded random processes.”
Journal of Hydrology, 46(1-2), 79–88.
doi:10.1016/0022-1694(80)90036-0.
Matsuoka DH, Pumi G, Torrent HS, Valk M (2024).
“A three-step approach to production frontier estimation and the Matsuoka's distribution.”
doi:10.48550/arXiv.2311.06086.
Mazucheli J, Menezes AFB, Fernandes LB, de Oliveira RP, Ghitany ME (2019).
“The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates.”
Journal of Applied Statistics.
doi:10.1080/02664763.2019.1657813.
Mazucheli J, Menezes AJB, Chakraborty S (2018).
“On the one parameter unit-Lindley distribution and its associated regression model for proportion data.”
Journal of Applied Statistics.
doi:10.1080/02664763.2018.1511774.
Mitnik PA, Baek S (2013).
“The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation.”
Statistical Papers, 54, 177–192.
doi:10.1007/s00362-011-0417-y.
Prass TS, Pumi G, Taufemback CG, Carlos JH (2025).
“Positive time series regression models: theoretical and computational aspects.”
Computational Statistics, 40, 1185–1215.
doi:10.1007/s00180-024-01531-z.
Pumi G, Matsuoka DH, Prass TS (2025).
“A GARMA Framework for Unit-Bounded Time Series Based on the Unit-Lindley Distribution with Application to Renewable Energy Data.”
doi:10.48550/arXiv.2504.07351.
Pumi G, Matsuoka DH, Prass TS, Palm BG (2025).
“A Matsuoka-Based GARMA Model for Hydrological Forecasting: Theory, Estimation, and Applications.”
doi:10.48550/arXiv.2502.18645.
Pumi G, Prass TS, Souza RR (2021).
“A dynamic model for double bounded time series with chaotic driven conditional averages.”
Scandinavian Journal of Statistics, 48(1), 68–86.
doi:10.1111/sjos.12439.
Pumi G, Valk M, Bisognin C, Bayer FM, Prass TS (2019).
“Beta autoregressive fractionally integrated moving average models.”
Journal of Statistical Planning and Inference, 200, 196–212.
doi:10.1016/j.jspi.2018.10.001.
Rocha AV, Cribari-Neto F (2009).
“Beta autoregressive moving average models.”
Test, 18, 529–545.
doi:10.1007/s11749-008-0112-z.
Rocha AV, Cribari-Neto F (2017).
“Erratum to: Beta autoregressive moving average models.”
Test, 26, 451–459.
doi:10.1007/s11749-017-0528-4.
See Also
BTSR.models, BTSR.model.defaults, get.defaults