Abstract

Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.

摘要

潜在时间序列模型，例如 ARMA( p , q的独立和) 具有附加随机过程的模型越来越多地用于生物学、生态学、工程学和经济学的数据分析。从这些模型进行推断和/或预测可能极具挑战性：(i) 数据可能包含异常值，可能会对估计过程产生不利影响；(ii) 当时间序列非常大时，计算复杂度会变得高得令人望而却步；(iii) 模型选择增加了另一层（计算）复杂性；(iv) 同时解决 (i)、(ii) 和 (iii) 的解决方案在实践中并不存在。本文旨在通过基于小波方差的有界影响 M 估计量提出鲁棒两步估计的通用框架来共同应对这些挑战。我们首先为后一个估计量的联合渐近正态性开发条件，从而提供必要的工具来执行（直接）推理以进行基于尺度的信号分析。利用第一步估计器的模型无关权重，然后我们使用广义小波矩 (GMWM) 方法的框架开发两步稳健估计器的渐近特性。仿真研究说明了稳健的 GMWM 估计器的良好有限样本性能，应用示例突出了所提出方法的实际相关性。然后，我们使用小波矩广义方法 (GMWM) 的框架开发两步稳健估计量的渐近特性。仿真研究说明了稳健的 GMWM 估计器的良好有限样本性能，应用示例突出了所提出方法的实际相关性。然后，我们使用小波矩广义方法 (GMWM) 的框架开发两步稳健估计量的渐近特性。仿真研究说明了稳健的 GMWM 估计器的良好有限样本性能，应用示例突出了所提出方法的实际相关性。