Adaptive spectral estimation for nonstationary multivariate time series

Zhang, Shibin

doi:10.1016/j.csda.2016.05.025

Cited by 15 publications

(23 citation statements)

References 32 publications

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“…According to the analysis results, the sailing speed and/or wave‐approach angle should be adjusted to reduce fatigue damage of the hull from waves. A recommended range of wave‐approach angles under a harsh sea condition can be found in Zhang ().…”

Section: An Application To Container Ship Vibrationmentioning

confidence: 99%

Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic

Zhang

2018

Journal Time Series Analysis

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Two tests are proposed in this paper for comparing spectra of two univariate time series. One is a Pearson‐like statistic based only on periodograms of the compared time series and applicable for testing the equality of two time‐invariant spectra of two independent or dependent time series, with an asymptotic chi‐squared distribution under the null hypothesis. The other is based on the maximum of the Pearson‐like statistics. Not only does this test, again, depend only on periodograms but also approximately equals the maximum of a chi‐squared distribution of the same degrees of freedom under the null. It can be used to test the equality of spectra of two locally stationary time series regardless of whether they are dependent or independent. Multiple simulation examples show that both statistics achieve good performance. The proposed approach is illustrated by an application to longitudinal vibration data from a container ship.

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Section: An Application To Container Ship Vibrationmentioning

confidence: 99%

Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic

Zhang

2018

Journal Time Series Analysis

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“…Prior distributions for the coefficients are selected to regularize integrated squared first derivatives and formulate Bayesian linear penalized splines. As noted by Krafty and Collinge (2013) and by Zhang (2016), this Bayesian linear penalized spline model for local spectra differs somewhat from that used by Rosen and Stoffer (2007) for stationary time series. Rosen and Stoffer (2007) uses a model that is periodic, but not restricted to be odd or even.…”

Section: The Modelmentioning

confidence: 99%

“…These include methods for analyzing stationary (Carter and Kohn, 1996; Cadonna et al, 2017; Choudhuri et al, 2004; Rosen and Stoffer, 2007; Macaro and Prado, 2014; Krafty et al, 2017) and nonstationary (Rosen et al, 2012; Zhang, 2016; Bruce et al, 2017) time series. Adaptive spectral analysis was introduced by Rosen et al (2012) as a Bayesian approach to univariate nonstationary spectrum analysis, and was latter extended to the multivariate nonstationary setting by Zhang (2016). Under this approach, a time series is adaptively partitioned into a random number of approximately stationary segments, local spectra are estimated within in approximately stationary segments, and time-varying spectral estimates are obtained by averaging local estimates over the distribution of partitions.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series

Krafty

2018

Journal of the American Statistical Association

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This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood based penalized spline models of modified Cholesky components, which provide flexible nonparametric estimates that preserve positive definite structures of spectral matrices. The approach is formulated in a Bayesian framework, in which the number and location of partitions are random, and relies on reversible jump Markov chain and Hamiltonian Monte Carlo methods that can adapt to the unknown number of segments and parameters. By averaging over the distribution of partitions, the approach can approximate both abrupt and slow-varying changes in spectral matrices. Empirical performance is evaluated in simulation studies and illustrated through analyses of electroencephalography during sleep and of the El Niño-Southern Oscillation.

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“…Multi-variate time series prediction typically involves the prediction of single or multiple values from multi-variate input that are typically interconnected through some event [20,21,22]. Examples of single value prediction are the prediction of flour prices of time series obtained from different cities [20] and traffic time series [78].…”

Section: Problems In Time Series Predictionmentioning

confidence: 99%

Co-evolutionary multi-task learning for dynamic time series prediction

Chandra

Ong

Goh

2018

Applied Soft Computing

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Time series prediction typically consists of a data reconstruction phase where the time series is broken into overlapping windows known as the timespan. The size of the timespan can be seen as a way of determining the extent of past information required for an effective prediction. In certain applications such as the prediction of wind-intensity of storms and cyclones, prediction models need to be dynamic in accommodating different values of the timespan. These applications require robust prediction as soon as the event takes place. We identify a new category of problem called dynamic time series prediction that requires a model to give prediction when presented with varying lengths of the timespan. In this paper, we propose a co-evolutionary multi-task learning method that provides a synergy between multi-task learning and co-evolutionary algorithms to address dynamic time series prediction. The method features effective use of building blocks of knowledge inspired by dynamic programming and multi-task learning. It enables neural networks to retain modularity during training for making a decision in situations even when certain inputs are missing. The effectiveness of the method is demonstrated using one-step-ahead chaotic time series and tropical cyclone wind-intensity prediction.

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Adaptive spectral estimation for nonstationary multivariate time series

Cited by 15 publications

References 32 publications

Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic

Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic

Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series

Co-evolutionary multi-task learning for dynamic time series prediction

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