btsr-package {BTSR}R Documentation

Bounded Time Series Regression

Description

The BTSR package provides a unified framework for simulating, fitting, and forecasting bounded time series regression models. It supports a wide range of models, including i.i.d., regression, ARMA-like, and ARFIMA-like models, with a focus on bounded time series data.

Key features of the BTSR package include

Mathematical Notation

The BTSR package is based on the following mathematical framework

The BTSR Structure

Let \{Y_t\}_{t\in \mathbb{Z}} be a stochastic process for which Y_t \in (a, b) with probability 1 (a and b not necessarily finite), for all t \in \mathbb{Z}, and let \mathcal{F}_{t} denote the \sigma-field generated by the information observed up to time t. The general structure of a BTSR model is as follows

\begin{aligned} Y_t | \mathcal{F}_{t-1} & \sim f(\cdot |\mu_t, \nu_t), \quad \vartheta_t = g_2(\nu_t)\\ \eta_{1t} = g_{11}(\mu_t) & =\alpha_1 + \boldsymbol{X}_{1t}'\boldsymbol{\beta}_1 + \sum_{i=1}^{p_1} \phi_{1i}[g_{12}(Y_{t-i})-I_{X_1}\boldsymbol{X}_{1(t-i)}'\boldsymbol{\beta}_1] + \xi_t, \quad \text{(part 1)}\\ \eta_{2t} = g_{21}(\vartheta_t) & =\alpha_2 + \boldsymbol{X}_{2t}' \boldsymbol{\beta}_2 + \sum_{i=1}^{p_2} \phi_{2i}[g_{22}(\vartheta_{t-i})-I_{X_2}\boldsymbol{X}_{2(t-i)}'\boldsymbol{\beta}_2] + \sum_{k=1}^\infty c_{2k} e_{2,t-k}, \quad \text{(part 2)} \end{aligned}

with \xi_t depending on the model, controlled by the argument model,

\xi_t = \begin{cases} h(T^{t-1}(U_0)), & \text{if } \code{model = "BARC"},\\ \sum_{k=1}^\infty c_{1k} e_{1,t-k}, & \text{otherwise}, \end{cases}

e_{1,t} depending on the error.scale adopted

e_{1,t} = g_{13}(Y_t, \mu_t) = \begin{cases} Y_t - \mu_t, & \text{if } \code{error.scale = 0} \text{ (data scale)},\\ g_{11}(Y_t) - g_{11}(\mu_t), & \text{if } \code{error.scale = 1} \text{ (predictive scale)} \end{cases}

and e_{2,t} = g_{23}(e_{1,t}), where

Author(s)

Taiane Schaedler Prass taianeprass@gmail.com, Guilherme Pumi guipumi@gmail.com

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.

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.

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, Prass TS, Taufemback CG (2024). “Unit-Weibull autoregressive moving average models.” TEST, 33, 204–229. doi:10.1007/s11749-023-00893-8.

Pumi G, Prass TS, Taufemback CG (2024). “Publisher Correction: Unit-Weibull autoregressive moving average models.” TEST, 33, 358–359. doi:10.1007/s11749-023-00905-7.

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.

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.

See Also

For detailed examples and usage instructions, see the documentation for individual functions

Examples

#----------------------------
# Quickstart examples.
#----------------------------

# Example 1: Simulate i.i.d. samples
set.seed(1234)
y1 <- btsr.sim(model = "BETA", n = 1000, coefs = list(alpha = 0.2, nu = 20))
hist(y1)

# Example 2: Simulate ARMA-like model with fixed nu
y2 <- btsr.sim(
  model = "BARMA", n = 100, link = "logit",
  coefs = list(alpha = 0.2, phi = 0.5, theta = 0.3, nu = 20)
)
plot(y2, type = "l")


[Package BTSR version 1.0.0 Index]