发表机构
Indian Institute of Technology Mandi（印度技术学院曼迪分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出KTARMA模型，以正数值时间序列为研究对象，采用条件最大似然推断，经模拟与西北喜马拉雅降雨数据验证，其预测性能优于KARMA、βARMA模型。
AI 中文摘要
本文针对正数值时间序列，提出了一种基于分位数的Kumaraswamy-Teissier自回归移动平均（KTARMA）模型。该模型利用扩展Kumaraswamy-Teissier分布在观测驱动框架内的灵活性，将分布的随机分量以历史过程和时变协变量为条件，并通过其ρ阶条件分位数进行显式参数化，其中ρ∈(0,1)。为捕捉时间依赖性，系统分量通过合适的连接函数将ARMA型结构映射至该条件分位数。在推断方面，本文实现了条件最大似然框架，推导了所得得分向量和条件信息矩阵的显式解析表达式，随后开发了模型诊断与预测程序。通过蒙特卡洛模拟研究，在不同参数配置和分位数水平下评估了所开发估计量的有限样本性能。最后，通过模拟2001-2025年西北喜马拉雅地区的月度降雨数据，验证了该研究的实际效用：使用自组织映射将525个网格划分为四个同质区域，并纳入相关大气变量和大尺度气候指数作为预测回归因子。样本外预测评估显示，KTARMA模型表现出极具竞争力的预测性能，在所有已识别区域中，与KARMA和βARMA模型相比，其均方误差始终更低。
英文摘要
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 $ρ\in (0,1)$. 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 $β$ARMA models.
