标题： 双变量广义自回归模型用于预测双变量非高斯时间序列 显示英文标题

标题： Bivariate generalized autoregressive models for forecasting bivariate non-Gaussian times series

摘要： 本文介绍了一种新方法，即双变量广义自回归（BGAR）模型，用于建模和预测双变量时间序列数据。 BGAR模型通过允许数据不一定遵循正态分布，从而推广了双变量向量自回归（VAR）模型。 我们考虑一个由两个时间序列组成的随机向量，并假设每个时间序列都属于规范指数族，类似于单变量广义自回归移动平均（GARMA）模型。 我们将一个序列的自回归项包含在另一个序列的动力结构中，反之亦然。 模型参数使用条件最大似然（CML）方法进行估计。 我们提供了条件得分向量和条件费舍尔信息矩阵的一般闭式表达式，涵盖了所有规范指数族分布。 我们开发了渐近置信区间和假设检验。 我们讨论了模型选择技术、残差诊断分析和预测方法。 我们进行了蒙特卡洛模拟研究，以评估有限样本CML推断的性能，包括点估计和区间估计。 对真实数据的应用分析了巴西圣保罗州因钩端螺旋体病住院的钩端螺旋体病病例数。 为了比较目的，考虑了竞争模型，如GARMA、自回归积分移动平均（ARIMA）和VAR模型。 新模型通过提供更准确的样本外预测并能够量化病例数序列对因钩端螺旋体病住院的滞后效应，优于竞争模型。 显示英文摘要

摘要： This paper introduces a novel approach, the bivariate generalized autoregressive (BGAR) model, for modeling and forecasting bivariate time series data. The BGAR model generalizes the bivariate vector autoregressive (VAR) models by allowing data that does not necessarily follow a normal distribution. We consider a random vector of two time series and assume each belongs to the canonical exponential family, similarly to the univariate generalized autoregressive moving average (GARMA) model. We include autoregressive terms of one series into the dynamical structure of the other and vice versa. The model parameters are estimated using the conditional maximum likelihood (CML) method. We provide general closed-form expressions for the conditional score vector and conditional Fisher information matrix, encompassing all canonical exponential family distributions. We develop asymptotic confidence intervals and hypothesis tests. We discuss techniques for model selection, residual diagnostic analysis, and forecasting. We carry out Monte Carlo simulation studies to evaluate the performance of the finite sample CML inferences, including point and interval estimation. An application to real data analyzes the number of leptospirosis cases on hospitalizations due to leptospirosis in S\~ao Paulo state, Brazil. Competing models such as GARMA, autoregressive integrated moving average (ARIMA), and VAR models are considered for comparison purposes. The new model outperforms the competing models by providing more accurate out-of-sample forecasting and allowing quantification of the lagged effect of the case count series on hospitalizations due to leptospirosis.