[Paper Review] Detection of multiple structural breaks in multivariate time series

Philip Preuß, Ruprecht Puchstein+1 more|arXiv (Cornell University)|Sep 5, 2013

Financial Risk and Volatility Modeling28 references4 citations

TL;DR

This paper proposes a nonparametric, frequency-domain method for detecting multiple structural breaks in the autocovariance structure of multivariate time series without parametric assumptions or binary segmentation. It uses spectral distribution comparisons across segments, achieves consistent detection of break locations and affected components, and outperforms existing nonparametric methods in simulation and financial data applications with high power and accuracy as sample size increases.

ABSTRACT

We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second- order) piecewise stationary process, which also identifies the components of the series where the breaks occur. The new method is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows to prove the existence of structural breaks at a controlled type I error. Secondly, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods which have been proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point and addresses the problem of multiple structural breaks in the autocovariance function directly with no use of the binary segmentation algorithm. We prove that the new procedure detects all components and the corresponding locations where structural breaks occur with probability converging to one as the sample size increases and provide data-driven rules for the selection of all regularization parameters. The results are illustrated by analyzing financial returns, and in a simulation study it is demonstrated that the new procedure outperforms the currently available nonparametric methods for detecting breaks in the dependency structure of multivariate time series.

Motivation & Objective

• To develop a nonparametric method for detecting multiple structural breaks in the autocovariance function of multivariate time series without parametric assumptions.
• To identify not only the locations of structural breaks but also the specific components of the time series where changes occur.
• To provide a consistent, data-driven procedure that avoids binary segmentation and is directly applicable to multiple breaks.
• To offer a unified solution addressing all four key questions: existence, number, location, and component-specificity of breaks.
• To improve upon existing nonparametric methods by enhancing power and accuracy in detecting changes in dependency structure.

Proposed method

• The method operates in the frequency domain by comparing empirical spectral distributions across consecutive blocks of length N within the full sample of size T.
• It begins with a consistent bootstrap-based test to confirm the existence of structural breaks at a controlled type I error rate.
• A set of candidate break points is estimated using a nonparametric spectral comparison procedure.
• The candidate sets are then refined to identify the true structural breaks and their associated components via a thresholding procedure on spectral density differences.
• The method uses data-driven rules for selecting regularization parameters, including the block size N and critical thresholds for detection.
• It leverages empirical processes and nonparametric spectral estimates to detect changes in the full autocovariance structure without assuming a parametric model.

Experimental results

Research questions

• RQ1 Does a multivariate time series exhibit multiple structural breaks in its autocovariance function?
• RQ2 If so, how many structural breaks are present, and where are they located in the time series?
• RQ3 In which components of the multivariate process do these structural breaks occur?
• RQ4 Can a nonparametric method detect such breaks without relying on parametric models or binary segmentation?
• RQ5 How does the proposed method compare in power and accuracy to existing nonparametric approaches for detecting changes in dependency structure?

Key findings

• The proposed method detects all true structural breaks and their associated components with probability converging to one as the sample size increases.
• In simulations, the method significantly outperforms the CUSUM test of Aue et al. (2009) in power for models with multiple breaks, especially in small samples.
• For models with a single break, the method performs similarly or slightly better than Aue et al. (2009) in small samples and comparably in large samples.
• The method maintains high power even in models with switching variance, despite not being specifically designed for such alternatives.
• In the analysis of five U.S. sector ETFs (2010–2012), the test rejected the null of no structural breaks with a p-value of zero, detecting four significant break points at 29/04/2010, 03/08/2010, 03/08/2011, and 01/12/2011.
• At the 03/08/2011 break, all components of the spectral density matrix showed significant changes; at other breaks, only subsets of components were affected.