A Quantile-Based Kumaraswamy-Teissier autoregressive moving average models
Abstract
This paper introduces a quantile-based Kumaraswamy-Teissier autoregressive moving average (KTARMA) model for positive-valued time series. Leveraging the flexibility of the extended Kumaraswamy-Teissier distribution within an observation-driven framework, the random component of the distribution is conditioned on the historical process and time-varying covariates, and is parameterized explicitly via its ρ-th conditional quantile, where ρ∈ (0,1). To capture temporal dependence, the systematic component maps an ARMA-type structure to this conditional quantile via an appropriate link function. For inference, we implement a conditional maximum likelihood framework and derive explicit analytical expressions for the resulting score vector and conditional information matrix, followed by the development of model diagnostic and forecasting procedures. The finite-sample performance of the developed estimators is evaluated through a Monte Carlo simulation study across various parameter configurations and quantile levels. Finally, the practical utility of the study is demonstrated by modeling monthly rainfall data over the Northwest Himalayas (2001-2025), where 525 grids are grouped into four homogeneous zones using a Self-Organizing Map and relevant atmospheric variables and large-scale climate indices are incorporated as predictive regressors. Out-of-sample forecasting evaluations reveal that the KTARMA model delivers highly competitive predictive performance, achieving consistently lower mean squared errors across all identified zones compared to KARMA and βARMA models.
Related
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BibTeX
@misc{mishra2026quantilebased,
title = {{A Quantile-Based Kumaraswamy-Teissier autoregressive moving average models}},
author = {Kamana Mishra and Tanmay Kayal and Sarita Azad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04736},
eprint = {2609.04736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04736},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Quantile-Based Kumaraswamy-Teissier autoregressive moving average models
AU - Kamana Mishra
AU - Tanmay Kayal
AU - Sarita Azad
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04736
UR - https://arxiv.org/abs/2609.04736
AB - This paper introduces a quantile-based Kumaraswamy-Teissier autoregressive moving average (KTARMA) model for positive-valued time series. Leveraging the flexibility of the extended Kumaraswamy-Teissier distribution within an observation-driven framework, the random component of the distribution is conditioned on the historical process and time-varying covariates, and is parameterized explicitly via its ρ-th conditional quantile, where ρ∈ (0,1). To capture temporal dependence, the systematic component maps an ARMA-type structure to this conditional quantile via an appropriate link function. For inference, we implement a conditional maximum likelihood framework and derive explicit analytical expressions for the resulting score vector and conditional information matrix, followed by the development of model diagnostic and forecasting procedures. The finite-sample performance of the developed estimators is evaluated through a Monte Carlo simulation study across various parameter configurations and quantile levels. Finally, the practical utility of the study is demonstrated by modeling monthly rainfall data over the Northwest Himalayas (2001-2025), where 525 grids are grouped into four homogeneous zones using a Self-Organizing Map and relevant atmospheric variables and large-scale climate indices are incorporated as predictive regressors. Out-of-sample forecasting evaluations reveal that the KTARMA model delivers highly competitive predictive performance, achieving consistently lower mean squared errors across all identified zones compared to KARMA and βARMA models.
ER -