Break detection in the covariance structure of multivariate time series models

By Alexander Aue, Siegfried Hormann, Lajos Horv'ath, Matthew Reimherr. 2009

380 citations recorded by the source corpus.

In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric model selection, model fitting and parameter estimation. We provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data. Extensions to multiple changes and the case of infinite fourth moments are also discussed.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/fb5b7a95fa8e913dc06c3f0c5d1e412effaa9f62

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Citations in the corpus

MGARCH models: Trade-off between feasibility and flexibility (2018, background): “Aue et al. (2009) establish a sufficient condition for strict stationarity and the existence of fourth-order moments.”
Detecting gradual changes in locally stationary processes (2013, background): “Most of the literature investigates the issue of detecting breaks in the mean or the variance of a time series [see Horváth et al. (1999) or Aue et al. (2009)], the parameters of regression models [see Andrews (1993) or Bai and Perron (1998)] or the second order characteristics of a time series…”
SEQUENTIAL TESTING FOR THE STABILITY OF HIGH-FREQUENCY PORTFOLIO BETAS (2011, methodology): “This non-trivial task has been carried out, however, for simpler models in Aue and Horváth (2004), Aue et al. (2006a, 2006b, 2009) and Černiková et al. (2011). Next, we study the behavior of the stopping rule under a one-change alternative.”
Inference for single and multiple change‐points in time series (2013, methodology): “In this review, we shall focus primarily on estimation aspect of the multiple change-point problem and refer to Bai and Perron (1998), Bai (1999) and also Aue et al. (2009) for testing the presence of multiple change-points.”
Uniform change point tests in high dimension (2015, background): “1 in [3] or [27]), but is also considerably harder from a mathematical point of view.”
Change-point detection in high-dimensional covariance structure (2016, methodology): “The classic approach to the problem is based on the asymptotic behaviour of the statistic [14] [2] [1] [28] [7] [42].”
A Survey of Methods for Time Series Change Point Detection (2016, neutral): “The most familiar change point algorithm is cumulative sum [7,10,18,33], which accumulates deviations relative to a specified target of incomingmeasurements and indicates that a change point exists when the cumulative sum exceeds a specified threshold.”
Extensions of some classical methods in change point analysis (2014, methodology): “CUSUM methodology was extended to detect the stability of the covariances of the observation vectors in Berkes et al. (2009c). The proofs in their paper are based on weighted approximations of partial sums.”
TESTING FOR A CHANGE IN CORRELATION AT AN UNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONAL DELTA METHOD (2011, methodology): “Our test will then detect such types of contagion, whereas the Aue et al. (2009) procedure might not.”
Multiple‐change‐point detection for high dimensional time series via sparsified binary segmentation (2015, methodology): “In Aue et al. (2009), a CUSUM statistic was proposed for detecting and locating a single change point in the covariance structure of multivariate time series, where its extension to the detection of multiple change points via binary segmentation was discussed heuristically.”
Tests for Error Correlation in the Functional Linear Model (2010, methodology): “We formalize the notion of dependence in functional observations using the notion of L4m-approximability advocated in other contexts by Hörmann (2008), Berkes, Hörmann, and Schauer (2009), Aue et al. (2009), and used for functional data by Hörmann and Kokoszka (2010) and Aue et al. (2010).”
Testing stationarity of functional time series (2014, background): “Assumptions similar to those stated above have been used extensively in recent theoretical work, as all stationary time series models in practical use can be represented as Bernoulli shifts, see Wu (2005), Shao and Wu (2007), Aue et al. (2009), Hörmann and Kokoszka (2010), among many other contribut”
Testing for Change Points in Time Series (2010, background): “The treatment here is restricted to univariate time series, and we expect that an extension to multivariate setting is possible; see Aue et al. (2009) for a recent work.”
Structural breaks in time series (2013, methodology): “These methods have been extended to other areas of applications, notably economics and finance in a number of recent publications, see Aue et al. (2009e), Chu et al. (1996).”
Asymptotic normality of the principal components of functional time series (2013, result): “Proofs of the results of Section 3 We begin this section with the following lemma which is a direct consequence of a much more general functional CLT for random vectors established in [2].”
GARCH Models (2010, neutral): “A sufficient condition for strict stationarity and the existence of fourth-order moments of the CCC-GARCH(p, q) is established by Aue et al. (2009).”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, methodology): “Thus { 1√ T T t=h+1 Wh,i(Xt,jXt−h,l + Xt,lXt−h,j − EXt,jXt−h,l − EXt,lXt−h,j) : 1 ≤ h ≤ k} converges to a multivariate normal distribution (Theorem A.1 of Aue et al., 2009).”