平稳函数型时间序列的模型设定检验

中文摘要 AI 辅助

我们为平稳函数型时间序列中的模型设定检验开发了一个通用框架。该方法基于自回归近似，通过系数核表示一类广泛的平稳函数型过程，其中系数核的维数和自回归阶数可随样本量增加。不同的模型假设对这些核施加不同的结构限制，我们的检验通过测量与相应限制的偏差来构建。我们针对三个问题说明这一原理：检验函数型自回归模型的指定阶数、检验函数型自回归移动平均设定、以及检验自回归系数核的可分离性。所得统计量基于加权$\mathcal{L}^2$距离，临界值通过乘子自助法获得。我们建立了在一类权重函数上均匀的定量自助逼近，并证明了所提出检验的渐近有效性和一致性。该方法允许数据自适应加权，并通过模拟和实际数据示例加以说明。

英文摘要

We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample size. Different model assumptions induce different structural restrictions on these kernels, and our tests are constructed by measuring deviations from the corresponding restrictions. We illustrate this principle for three problems: testing a prescribed order of a functional autoregressive model, testing a functional autoregressive moving-average specification, and testing separability of autoregressive coefficient kernels. The resulting statistics are based on weighted $\mathcal{L}^2$-distances, and the critical values are obtained by a multiplier bootstrap. We establish a quantitative bootstrap approximation that is uniform over a class of weight functions and prove asymptotic validity and consistency of the proposed tests. The methodology allows for data-adaptive weighting and is illustrated by simulations and a data example.

发表机构

• Illinois State University（伊利诺伊州立大学）
• Ruhr-University Bochum（波鸿鲁尔大学）
• Zhejiang University（浙江大学）

机构由 AI 辅助整理，请以论文原文为准。