Break detection in the covariance structure of multivariate time series models

Aue, Alexander; Hörmann, Siegfried; Horváth, Lajos; Reimherr, Matthew

doi:10.1214/09-aos707

Cited by 307 publications

(391 citation statements)

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“…Davidson (1994), p. 273. Assumption 4 is a stationarity condition which is in line with Aue et al (2009) and that can be slightly relaxed to allow for some fluctuations in the first and second moments. However, we do not consider this situation for ease of exposition and because the procedure would remain exactly the same.…”

Section: The Proceduresmentioning

confidence: 99%

Dating multiple change points in the correlation matrix

Galeano

Wied

2016

TEST

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We propose a nonparametric procedure for detecting and dating multiple change points in the correlation matrix of a sequence of random variables. The procedure is based on a test for changes in correlation matrices at an unknown point in time recently proposed by Wied (2014). Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. We show the validity of the procedure including the convergence rate of the change point estimators. Moreover, we illustrate its performance in finite samples by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the proposed algorithm has large power in finite samples.

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Section: The Proceduresmentioning

confidence: 99%

Dating multiple change points in the correlation matrix

Galeano

Wied

2016

TEST

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“…In order to detect change points in the (variance-) covariance structure of a d-dimensional time series , … , , where , , … , , , ∈ , we apply below a nonparametric test based on [19]. The associated test statistic is given by, …”

Section: Change Point Detection For Nasdaqmentioning

confidence: 99%

Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter

Theodosiadou

Skaperas

Tsaklidis

2017

Risks

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Abstract:In the first part of the paper, the positive and negative jumps of NASDAQ daily (log-) returns and three of its stocks are estimated based on the methodology presented by Theodosiadou et al. 2016, where jumps are assumed to be hidden random variables. For that reason, the use of stochastic state space models in discrete time is adopted. The daily return is expressed as the difference between the two-sided jumps under noise inclusion, and the recursive Kalman filter algorithm is used in order to estimate them. Since the estimated jumps have to be non-negative, the associated pdf truncation method, according to the non-negativity constraints, is applied. In order to overcome the resulting underestimation of the empirical time series, a scaling procedure follows the stage of truncation. In the second part of the paper, a nonparametric change point analysis concerning the (variance-) covariance is applied to the NASDAQ return time series, as well as to the estimated bivariate jump time series derived after the scaling procedure and to each jump component separately. A similar change point analysis is applied to the three other stocks of the NASDAQ index.

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“…The crucial idea is to approximate the original process with auxiliary processes whose asymptotics are known. This approach was recently used in Aue et al (2009a) and Hörmann and Kokoszka (2010) to examine, respectively, multivariate time series and functional time series. The latter paper and Aue et al (2012) also contain a number of examples of processes that satisfy Assumptions 4 and 5, these notably including functional autoregressive processes.…”

Section: Assumptionmentioning

confidence: 99%