Robust Spectral Analysis

Hagemann, Andreas

doi:10.48550/arxiv.1111.1965

Cited by 9 publications

(29 citation statements)

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“…Further development in the Fourier domain approach has been made by Hagemann (2013) and Dette et al (2015). See also Li (2014) and Kley et al (2016).…”

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confidence: 99%

The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series

Han

Linton

Oka

et al. 2016

Journal of Econometrics

377

324

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This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross-quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ a stationary bootstrap procedure; we establish consistency of this bootstrap. Also, we consider a self-normalized approach, which yields an asymptotically pivotal statistic under the null hypothesis of no predictability. We provide simulation studies and two empirical applications. First, we use the cross-quantilogram to detect predictability from stock variance to excess stock return. Compared to existing tools used in the literature of stock return predictability, our method provides a more complete relationship between a predictor and stock return. Second, we investigate the systemic risk of individual financial institutions, such as JP Morgan Chase, Morgan Stanley and AIG.

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“…Further development in the Fourier domain approach has been made by Hagemann (2013) and Dette et al (2015). See also Li (2014) and Kley et al (2016).…”

mentioning

confidence: 99%

The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series

Han

Linton

Oka

et al. 2016

Journal of Econometrics

377

324

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“…If the objective is a locally stationary extension of classical spectral analysis, only the autocovariances Cov(X t,T , X s,T ) have to be approximated. In the quantile-related context considered here, the joint distributions of X t,T and X s,T are the feature of interest, and traditional autocovariances are to be replaced with autocovariances of indicators, of the form Cov(I {X t,T ≤q t,T (τ 1 )} , I {X s,T ≤q s,T (τ 2 )} ), where q t,T (τ 1 ) and q s,T (τ 2 ) stand for the τ 1 -quantile of X t,T and the τ 2 -quantile of X s,T , respectively, with τ 1 , τ 2 ∈ (0, 1); see Li (2008Li ( , 2012, Hagemann (2013), or Dette et al (2015). Such covariances only depend on the bivariate copulas of X t,T and X s,T .…”

Section: Locally Strictly Stationary Processesmentioning

confidence: 99%

“…Pioneering contributions in that direction are Hong (1999) and Li (2008), who coined the names of Laplace spectrum and Laplace periodogram. The Laplace spectrum concept was further studied by Hagemann (2013), and extended into cross-spectrum and spectral kernel concepts by Dette et al (2015), who also introduced copula-based versions of the same. Those copula spectral quantities are indexed by couples (τ 1 , τ 2 ) of quantile levels, and their collections (for (τ 1 , τ 2 ) ∈ [0, 1] 2 ) account for any features of the joint distributions of pairs (X t , X t−k ) in a strictly stationary process {X t }, without requiring any distributional assumptions such as the existence of finite moments.…”

Section: Introductionmentioning

confidence: 99%

Quantile Spectral Analysis for Locally Stationary Time Series

Birr

Volgushev

Kley

et al. 2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Classical spectral methods are subject to two fundamental limitations: they can account only for covariance-related serial dependences, and they require second-order stationarity. Much attention has been devoted lately to quantile-based spectral methods that go beyond covariance-based serial dependence features. At the same time, covariance-based methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time series models. Here, we combine those two approaches by proposing quantilebased spectral methods for locally stationary processes. We therefore introduce a time varying version of the copula spectra that have been recently proposed in the literature, along with a suitable local lag window estimator.We propose a new definition of local strict stationarity that allows us to handle completely general non-linear processes without any moment assumptions, thus accommodating our quantile-based concepts and methods. We establish a central limit theorem for the new estimators and illustrate the power of the proposed methodology by means of a simulation study. Moreover, in two empirical studies (namely of the Standard & Poor's 500 series and a temperature data set recorded in Hohenpeissenberg), we demonstrate that the new approach detects important variations in serial dependence structures both across time and across quantiles. Such variations remain completely undetected and are actually undetectable, via classical covariance-based spectral methods.

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“…Similarly to the behavior of the ordinary spectrum and periodogram (Brockwell and Davis, 1984), the quantile periodogram has an asymptotic exponential distribution but the mean function, called the quantile spectrum, is a scaled version of the ordinary spectrum of the level-crossing process. Related works include Hagemann (2013), Li (2013), Dette et al (2015) Lim and Oh (2016), Birr et al (2017Birr et al ( , 2019, and Baruník and Kley (2019).…”

Section: Introductionmentioning

confidence: 99%

“…To estimate the copula rank-based quantile spectrum, Zhang (2019) produced an automatically smoothed estimator for the copula spectral density kernel (CSDK), along with samples from the posterior distributions of the parameters via a Hamiltonian Monte Carlo (HMC) step. Hagemann (2013) applied the Parzen (1957) class of kernel spectral density estimators to the quantile periodogram and characterized the asymptotic properties of the quantile and smoothed quantile periodograms. Dette et al (2015) showed that the quantile spectrum can be estimated consistently by a window smoother of the quantile periodogram.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Parametric Estimation Method for the Quantile Spectrum with an Application to Earthquake Classification Using Convolutional Neural Network

Chen

Sun

Li³

2019

Preprint

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In this paper, a new estimation method is introduced for the quantile spectrum, which uses a parametric form of the autoregressive (AR) spectrum coupled with nonparametric smoothing. The method begins with quantile periodograms which are constructed by trigonometric quantile regression at different quantile levels, to represent the serial dependence of time series at various quantiles. At each quantile level, we approximate the quantile spectrum by a function in the form of an ordinary AR spectrum. In this model, we first compute what we call the quantile autocovariance function (QACF) by the inverse Fourier transformation of the quantile periodogram at each quantile level. Then, we solve the Yule-Walker equations formed by the QACF to obtain the quantile partial autocorrelation function (QPACF) and the scale parameter. Finally, we smooth QPACF and the scale parameter across the quantile levels using a nonparametric smoother, convert the smoothed QPACF to AR coefficients, and obtain the AR spectral density function.Numerical results show that the proposed method outperforms other conventional smoothing techniques. We take advantage of the two-dimensional property of the estimators and train a convolutional neural network (CNN) to classify smoothed quantile periodogram of earthquake data and achieve a higher accuracy than a similar classifier using ordinary periodograms.

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Robust Spectral Analysis

Cited by 9 publications

References 0 publications

The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series

The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series

Quantile Spectral Analysis for Locally Stationary Time Series

A Semi-Parametric Estimation Method for the Quantile Spectrum with an Application to Earthquake Classification Using Convolutional Neural Network

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