Bivariate generalized autoregressive models for forecasting bivariate non-Gaussian times series
用于双变量非高斯时间序列预测的广义自回归模型AI 解读 ↓
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用于双变量非高斯时间序列预测的广义自回归模型
- 研究问题
- 如何对两个相互具有滞后关联、且不必服从正态分布的时间序列联合建模，并开展参数推断与预测？
- 方法与思路
- 作者提出双变量广义自回归模型，以典范指数族描述各序列并加入交叉滞后项，使用条件极大似然估计。
- 材料陈述的贡献
- 摘要称给出条件得分与 Fisher 信息的通式及渐近推断，并在疾病病例和住院数应用中报告样本外预测改善。
- 阅读关注点
- 应核对联合条件分布的构造、动态稳定性、条件似然推断条件，以及预测比较与交叉滞后效应的解释。
- 阅读边界
- 这是预印本，同行评审及接收未核实。摘要未说明完整分布与正则条件；滞后关联不能直接视为因果作用。
原文摘要
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 São 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.