Multivariate singular spectrum analysis for forecasting revisions to real-time data

Patterson, Kerry; Hassani, Hossein; Heravi, Saeed; Zhigljavsky, Anatoly

doi:10.1080/02664763.2010.545371

Cited by 55 publications

(34 citation statements)

References 48 publications

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“…The matrix X is of order , see [15]. The aim of MSSA is also to decompose the initial time series into additive and interpretable components and later to reconstruct the decomposed series for further analyses.…”

Section: Multivariate Singular Spectrum Analysis Mssamentioning

confidence: 99%

In-Sample Spatio-temporal Predictions by Multivariate Singular Spectrum Analysis

Awichi

Müller

2015

Procedia Environmental Sciences

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In this paper, we present a method of utilizing spatial information, usually intrinsic in spatial data sets, to improve the quality of temporal predictions within the framework of singular spectrum analysis (SSA) techniques. Those constitute a model free approach to time series analysis and SSA can be applied to any time series with a notable structure. Indeed it has a wide area of application including social sciences, medical sciences, finance, environmental sciences, mathematics, dynamical systems and economics.The aim of SSA is twofold: i) to make a decomposition of the original series into a sum of a small number of independent and interpretable components such as a slowly varying trend, oscillatory components and a structureless noise; ii) to reconstruct the decomposed series to make a forecast in the absence of the noise component. It has two stages each with two steps. The first stage is the Decomposition Stage with steps comprising: (i) embedding -a usual procedure in time series analysis; the result of which is a called a trajectory matrix in SSA literature; (ii) singular value decomposition step that computes and arranges eigenvalues of this matrix for further analysis. The second stage is the Reconstruction Stage: it comprises two steps of (i) grouping the eigenvalues of the SVD step and (ii) diagonal averaging that works on the grouped matrices to realize a series close to the original series and this series is then used for further analysis.Multivariate Singular Spectrum Analysis (MSSA) is an extension of SSA to multivariate statistics and takes advantage of the delay procedure to obtain a similar formulation as SSA though with larger matrices for multivariate data. In environmental sciences and other areas where spatial data is an important focus of investigation, it is not uncommon to have attributes whose values change with space and time and an accurate prediction is thus important. Spatial dependence subsequently influences data analysis. The usual question asked is whether the location parameters can be of use in the analysis of such data sets. We present a method that can be used to harness the location attributes to enhance prediction of spatial data sets using an MSSA approach.

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Section: Multivariate Singular Spectrum Analysis Mssamentioning

confidence: 99%

In-Sample Spatio-temporal Predictions by Multivariate Singular Spectrum Analysis

Awichi

Müller

2015

Procedia Environmental Sciences

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“…In recurrent forecasting SSA, the time series of known measurements and unknown components is transformed to its Hankel form and the linear recurrent relation coefficients are utilized for forecasting the future values. While typical SSA considers the trajectory matrices associated with a single time series, the Multivariate Singular Spectrum Analysis (MSSA) method has been proposed for handling multiple time series [37][38][39]. In this work, we consider a simple extension of SSA where instead of analyzing a single trajectory matrix, we consider a compound trajectory matrix generated by the concatenation of S individual matri-…”

Section: Analysis Of Time Series Datamentioning

confidence: 99%

Singular spectrum-based matrix completion for time series recovery and prediction

Tsagkatakis

Beferull-Lozano

Tsakalides

2016

EURASIP J. Adv. Signal Process.

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Big data, characterized by huge volumes of continuously varying streams of information, present formidable challenges in terms of acquisition, processing, and transmission, especially when one considers novel technology platforms such as the Internet-of-Things and Wireless Sensor Networks. Either by design or by physical limitations, a large number of measurements never reach the central processing stations, making the task of data analytics even more problematic. In this work, we propose Singular Spectrum Matrix Completion (SS-MC), a novel approach for the simultaneous recovery of missing data and the prediction of future behavior in the absence of complete measurement sets. The goal is achieved via the solution of an efficient minimization problem which exploits the low rank representation of the associated trajectory matrices when expressed in terms of appropriately designed dictionaries obtained by leveraging the theory of Singular Spectrum Analysis. Experimental results in real datasets demonstrate that the proposed scheme is well suited for the recovery and prediction of multiple time series, achieving lower estimation error compared to state-of-the-art schemes.

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“…The reconstruction of the original time series is accomplished by using estimated trend and harmonic components [46]. The time series is reconstructed by selecting those components that reduce the noise in the series [47].…”

Section: Mathematical Formulation Of the Ssa Methodsmentioning

confidence: 99%

“…We can always assume m ≤ N t /2 as this value has been regarded as the most interesting case in practice. In spite of the considerable attempts and various methods that have been considered for choosing the optimal value of m, there is inadequate theoretical justification for such selection [12,40,47]. Whereas, according to [33], m can be computed as N t /4 and considered as a common practice.…”

Section: Parameters Of the Ssa Algorithmmentioning

confidence: 99%

Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

Eldwaik

2018

Technologies

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Abstract:Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.

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Multivariate singular spectrum analysis for forecasting revisions to real-time data

Cited by 55 publications

References 48 publications

In-Sample Spatio-temporal Predictions by Multivariate Singular Spectrum Analysis

In-Sample Spatio-temporal Predictions by Multivariate Singular Spectrum Analysis

Singular spectrum-based matrix completion for time series recovery and prediction

Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

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