Singular spectrum analysis based on the perturbation theory

Hassani, Hossein; Xu, Zhengyuan; Zhigljavsky, Anatoly

doi:10.1016/j.nonrwa.2011.03.020

Cited by 28 publications

(16 citation statements)

References 24 publications

(42 reference statements)

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“…However, the commencement of SSA is usually associated with publications of the papers by King (1986a,1986b) and Fraedrich (1986), Vautard and Ghil (1989), Vautard et al (1992) and Allen and Smith (1996). A through review of SSA for analysis and forecasting economic and financial time series is given in Hassani and Thomakos (2010), and two new versions of SSA, based on the minimum variance estimator and perturbation theory, have been introduced in Hassani (2010) and Hassani et al (2011). For comparison of the SSA with classical methods, ARIMA, ARAR algorithm, GARCH and Holt-Winters, see Hassani et al (2009aHassani et al ( ,2009b, Hassani (2007); Patterson et al (2010) and Hassani and Zhigljavsky (2009).…”

Section: Singular Spectrum Analysismentioning

confidence: 99%

“…For a recent development see Zhigljavsky (2010). A through review of SSA for analysis and forecasting economic and financial time series is given in Hassani and Thomakos (2010), and two new versions of SSA, based on the minimum variance estimator and perturbation theory, have been introduced in Hassani (2010) and Hassani et al (2011). Here, a short description of the SSA technique is given (for more information see Golyandina et al, 2001).…”

Section: Singular Spectrum Analysismentioning

confidence: 99%

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Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

Hassani

Heravi

Zhigljavsky

2012

Journal of Forecasting

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In recent years the singular spectrum analysis (SSA) technique has been further developed and applied to many practical problems. The aim of this research is to extend and apply the SSA method, using the UK Industrial Production series. The performance of the SSA and multivariate SSA (MSSA) techniques was assessed by applying it to eight series measuring the monthly seasonally unadjusted industrial production for the main sectors of the UK economy. The results are compared with those obtained using the autoregressive integrated moving average and vector autoregressive models.We also develop the concept of causal relationship between two time series based on the SSA techniques. We introduce several criteria which characterize this causality. The criteria and tests are based on the forecasting accuracy and predictability of the direction of change. The proposed tests are then applied and examined using the UK industrial production series. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Singular Spectrum Analysismentioning

confidence: 99%

Section: Singular Spectrum Analysismentioning

confidence: 99%

Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

Hassani

Heravi

Zhigljavsky

2012

Journal of Forecasting

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“…The mathematical procedures which we specifically seek to link with nature consist of Singular Value Decomposition (SVD) based methods and signal subspace (SS) methods which form the basis of a general class of subspace-based noise reduction algorithms. The superior performance of this class of algorithms in noise reduction and forecasting has been proved by several studies [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

From nature to maths: Improving forecasting performance in subspace-based methods using genetics Colonial Theory

Hassani

Ghodsi

Silva

et al. 2016

Digital Signal Processing

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Many scientific fields consider accurate and reliable forecasting methods as important decision-making tools in the modern age amidst increasing volatility and uncertainty. As such there exists an opportune demand for theoretical developments which can result in more accurate forecasts. Inspired by Colonial Theory, this paper seeks to bring about considerable improvements to the field of time series analysis and forecasting by identifying certain core characteristics of Colonial Theory which are subsequently exploited in introducing a novel approach for the grouping step of subspace based methods. The proposed algorithm shows promising results in terms of improved performances in noise filtering and forecasting of time series. The reliability and validity of the proposed algorithm is evaluated and compared with popular forecasting models with the results being thoroughly evaluated for statistical significance and thereby adding more confidence and value to the findings of this research.

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“…The proposed method uses first-order perturbation (FOP) approach for the sample covariance matrix estimate with every new sample obtained in real time. Whereas the traditional SSA approach processes chunks of data acquired in batch mode, RSSA provides online processing of data based on rank one eigenvector updates in a recursive framework, as and when the data streams in real time (Mirmomeni et al 2013;Hassani et al 2013). It should be noted that the data covariance matrix should Prepared using sagej.cls -be strictly diagonally dominant at any instant of time, for the algorithm to work online, which is automatically satisfied by structural dynamical systems with low to moderate damping.…”

Section: Real Time Single and Multi Channel Structural Damage Detectimentioning

confidence: 99%

Real-time unified single- and multi-channel structural damage detection using recursive singular spectrum analysis

Bhowmik

Krishnan

Hazra

et al. 2018

Structural Health Monitoring

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A novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using Recursive Singular Spectral Analysis (RSSA) in conjunction with Time Varying Auto-Regressive Modeling (TVAR) is proposed in this paper. The acceleration data is used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by TVAR modeling of the first transformed response, to detect the change in the dynamic behavior of the vibrating system from its original state to contiguous linear /non-linear-states indicating damage. Most work to date deal with algorithms that require windowing of the gathered data that render them ineffective for online implementation. Algorithms focussed on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection is missing, that motivates the development of the present framework. The response from a single channel is provided as input to the algorithm in real time. The RSSA algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data without requiring any baseline data. Lower order TVAR models are applied on the transformed responses to improve detectability. Numerical simulations performed on a 5-dof nonlinear system and on an SDOF system modeled using a Duffing oscillator under white noise excitation data, with different levels of nonlinearity simulating the damage scenarios, demonstrate the robustness of the proposed algorithm. The method, further validated on results obtained from experiments performed on a cantilever beam subjected to earthquake excitation; a toy cart experiment model with springs attached to either side; demonstrate the efficacy of the proposed methodology as an appropriate candidate for real time, reference free structural health monitoring.

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Singular spectrum analysis based on the perturbation theory

Cited by 28 publications

References 24 publications

Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

From nature to maths: Improving forecasting performance in subspace-based methods using genetics Colonial Theory

Real-time unified single- and multi-channel structural damage detection using recursive singular spectrum analysis

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