arguments.model {BTSR}R Documentation

Available models in BTSR package

Description

The BTSR package supports a variety of models, including

This documentation describes

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.

Regression models: the argument error.scale and all entries but g11 in linkg are ignored

ARMA-like models

ARFIMA-like models

Chaotic models

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


[Package BTSR version 1.0.0 Index]