Discrimination and Clustering for Multivariate Time Series

Kakizawa, Yoshihide; Shumway, Robert H.; Taniguchi, Masanobu

doi:10.1080/01621459.1998.10474114

Cited by 219 publications

(133 citation statements)

References 25 publications

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“…Discrimination and clustering for time series based on their spectral density functions (or matrices) has been discussed in Ref 40, see also [Ref 8, Ch. 7] and [Ref 41, Ch.…”

Section: Topics On Spectral Estimationmentioning

confidence: 99%

Spectral estimation

Fokianos

2010

WIREs Computational Stats

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We review spectral analysis and its application in inference for stationary processes. As can be seen from the list of references, the practice of spectral analysis is widespread in diverse scientific and engineering fields, particularly in signal processing and communications. One of the most striking characteristics of time series is their oscillatory behavior. This behavior is manifested, for example, in electroencephalogram (EEG) records, weekly sales, monthly environmental data, hourly financial indices, and in numerous economic data observed periodically in time. When observing such data the intuitive notion of periodicity is inescapable, and this led to the statistical problem of estimation of 'hidden periodicities' in time series. Schuster [47] was among the first who studied the problem seriously, and is credited with the invention of the so-called periodogram, a tool for discovering periodicities in oscillatory data. Consequently, spectral analysis and its ramification was further advanced by the pioneering works of Slutsky, Yule, Khintchine, Wiener, Cramer, Kolmogorov, Bartlett, Tukey, Parzen, Rosenblatt, Grenander, Koopmans, Brillinger, and Hannan. The goal of this communication is to introduce the reader to the topic of spectral analysis, and to review some state-of-the-art developments. It is of course not possible to give a full account of the literature on spectral analysis within this limited space. The selection of the references has been influenced by my own personal research interests .  PRELIMINARIES S uppose that {X t , t = 0, ±1, ±2, . . .} is a complexvalued stationary stochastic process. Equivalently, E(X t ) is independent of t, E|X t | 2 < ∞ and E(X t+h X t ) depends only on h, where denotes complex conjugate. Then, the autocovariance function of {X t } is defined byand it is simple to check that γ (0) ≥ 0, |γ (h)| ≤ γ (0) and γ (h) = γ (−h), i.e., γ (·) is Hermitian. A useful fact about the autocovariance function of a stationary process is based on a corollary of Herglotz's theorem (see Ref 1, Thm. 4.3.1) and states that a complexvalued function γ (·), defined on the set of integers, is the autocovariance function of a stationary process if

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“…Discrimination and clustering for time series based on their spectral density functions (or matrices) has been discussed in Ref 40, see also [Ref 8, Ch. 7] and [Ref 41, Ch.…”

Section: Topics On Spectral Estimationmentioning

confidence: 99%

Spectral estimation

Fokianos

2010

WIREs Computational Stats

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“…This section examines tests for equality of autocovariances when { X t } and { Y t } are d ‐dimensional, where d ≥ 2, zero mean stationary series. This problem was considered in Kakizawa et al. (1998), where issues of clustering many series into similar groups was pursued.…”

Section: Multivariate Versionsmentioning

confidence: 99%

“…Such problems were posed by Coates and Diggle (1986), who studied the homogeneity of a single wheat price series over time and compared the wall thicknesses of a gas pipe at two different locations. Kakizawa et al. (1998) studied whether seismological series were more likely earthquakes or nuclear tests.…”

Section: Introductionmentioning

confidence: 99%

Testing equality of stationary autocovariances

Lund

Bassily

Vidaković

2009

Journal Time Series Analysis

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This article studies tests for assessing whether two stationary and independent time series have the same dynamics - specifically, whether the autocovariances of both series coincide at all lags. Frequency domain statistics previously proposed for this purpose are reviewed. A time domain statistic is then developed and investigated. The performance of these statistics are compared. Multivariate versions of the results are constructed. The methods are applied in the analysis of temperatures and precipitations from Atlanta and Athens, Georgia. Our interest here is driven by the need to identify a good climatological reference series for a given station. Copyright 2009 The Authors. Journal compilation 2009 Blackwell Publishing Ltd

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“…The problem of determining whether two multivariate time series possess the same (matrix-valued) power spectral density (PSD) at every frequency finds many diverse applications, ranging from the comparison of gas pipes [1], earthquake-explosion discrimination [2] or light-intensity emission stability determination [3], to physical-layer security [4] and spectrum sensing [5]. Thus, this problem has originated an active field of research since it was first studied by Coates and Diggle [1].…”

Section: Introductionmentioning

confidence: 99%

Locally Optimal Invariant Detector for Testing Equality of Two Power Spectral Densities

Ramírez

Romero

Vía

et al. 2018

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT does not exist. However, this proof suggests two LMPIT-inspired detectors, one of which outperforms previously proposed approaches, as computer simulations show.Index Terms-Generalized likelihood ratio test (GLRT), hypothesis test, locally most powerful invariant test (LMPIT), power spectral density (PSD), uniformly most powerful invariant test (UMPIT).

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Discrimination and Clustering for Multivariate Time Series

Cited by 219 publications

References 25 publications

Spectral estimation

Spectral estimation

Testing equality of stationary autocovariances

Locally Optimal Invariant Detector for Testing Equality of Two Power Spectral Densities

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