Multiscale Jump Testing and Estimation Under Complex Temporal Dynamics

2019/09/13 by Weichi Wu, Zhou Zhou, Wu, Weichi +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1909.06307

openalex publication_date 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed to diverge to infinity with the jump sizes possibly shrinking to zero. The method is based on a multiscale application of an optimal jump-pass filter to the time series, where the scales are dense between admissible lower and upper bounds. For a wide class of non-stationary time series models and trend functions, the proposed method is shown to be able to detect all jump points within a nearly optimal range with a prescribed probability asymptotically under mild conditions. For a time series of length n, the computational complexity of the proposed method is O(n) for each scale and O(nlog^1+ε n) overall, where ε is an arbitrarily small positive constant. Numerical studies show that the proposed jump testing and estimation method performs robustly and accurately under complex temporal dynamics.

Citations

• Optimal detection of changepoints with a linear computational cost
• Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool
• On the Volume of Tubes
• A Cluster Analysis Method for Grouping Means in the Analysis of Variance

Cited by

• Asymptotic Uniform False Discovery Rate Control for Inference of Time-varying Correlations
• Self-Normalization for CUSUM-based Change Detection in Locally Stationary Time Series

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