Autoregressive models for time series of random sums of positive variables: application to tree growth as a function of climate and insect outbreaks
正变量随机和时间序列的自回归模型：气候与虫害下的树木生长应用AI 解读 ↓
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正变量随机和时间序列的自回归模型：气候与虫害下的树木生长应用
- 研究问题
- 当时间序列观测值是正变量的随机和，且求和项数随时间变化时，如何建立稳定模型并有效估计气候和虫害相关关系？
- 方法与思路
- 作者提出一类半参数自回归模型，研究稳定性与统计推断，采用准极大似然估计，并用模拟及魁北克白云杉生长序列作说明。
- 材料陈述的贡献
- 摘要称估计量具有一致性和渐近正态性，应用发现虫害与滞后生长下降相关，且加入气候与落叶交互项未改善该数据上的表现。
- 阅读关注点
- 应核对随机项数与正变量过程的设定、稳定性及渐近条件，以及树木数据的站点差异、滞后选择和模型表现评价方式。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未经核实；摘要未展开定理条件或应用效应大小，气候与虫害系数不能直接作为因果效应。
原文摘要
We present a broad class of semi-parametric models for time series of random sums of positive variables. Our methodology allows the number of terms inside the sum to be time-varying and is therefore well suited to many examples encountered in the natural sciences. We study the stability properties of the models and provide a valid statistical inference procedure to estimate the model parameters. It is shown that the proposed quasi-maximum likelihood estimator is consistent and asymptotically normally distributed. This work is complemented by simulation results and applied to annual growth rate time series of white spruce (Picea glauca) trees from a few dozen sites in Quebec spanning 41 years, including one major spruce budworm (Choristoneura fumiferana) outbreak from around 1968 to 1991. We found significant growth reductions due to budworm-induced by defoliation up to two years in the past. Our results also revealed positive effects of maximum temperature, precipitation and the climate moisture index in the summer, as well as negative effects of the climate moisture index in the spring and the maximum temperature in the previous summer. However, considering the interaction of climate and defoliation on growth did not improve the model's performance on this dataset. This study represent a major advances and our result represent an useful tool in the understanding of the combined effects of climate and insect defoliation on tree growth in the face of climate change, where the frequency and the severity of outbreaks, as well as an increase of temperature is expected.