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 $\rho$-th conditional quantile, where $\rho \in (0,1)$. 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 $\beta$ARMA models.