Multivariate Singular Spectrum Analysis Research Articles

Centralized vs. Pattern-level Feature Extraction for Structural Damage Detection

The objective of this paper is to discuss two different categories on structural damage detection: One is the centralized feature extraction technique by using multi-sensor architecture and the other is the pattern-level data fusion by using the extracted features from individual sensor. The covariance-driven stochastic subspace identification and multivariate singular spectrum analysis are applied for the centralized feature extraction. For pattern-level feature recognition wavelet packet transforms and power spectral density from individual sensing record is used. Through both centralized and pattern-level feature extraction the results can not only detect the occurrence of structural damage but also can locate the damage. Finally, the dynamic finite element model updating is used for damage quantification. Verification of the proposed algorithms by using a research-scale bridge scouring test model to detect the damage occurrence and severity during scouring is presented. Finally, discussion on the computation effectiveness among different method is made.

Algorithm for the Characterization of the Cross-Correlation Structure in Multivariate Time Series

In this paper, it is shown that the block circulant matrix decomposition technique makes the multivariate singular spectrum analysis (M-SSA) a well suited tool for detecting of changes of the correlation structure in non-stationary multivariate time series in the presence of high observational noise levels. The major drawback of M-SSA, that it operates on a large covariance matrix and becomes computationally expensive, can be avoided by reordering the Toeplitz-block covariance matrix into a block Toeplitz matrix, embedding this into a block circulant matrix and efficiently block-diagonalizing this by the means of the Fast Fourier Transform (FFT) using the well known algorithm. The overall degree of synchronization among multiple-channel signals is defined by the synchronization index (the S-estimator) of the rearranged and truncated eigenvalue spectrum. Throughout the experiment, the high capability of the proposed algorithm to detect the lag-synchronized state under the influence of strong noise is validated with simulated data—a network of time series generated by autoregressive models (AR) and a network of coupled chaotic Roessler oscillators.

Automated Artifact Removal From the Electroencephalogram

Contamination of the electroencephalogram (EEG) by artifacts greatly reduces the quality of the recorded signals. There is a need for automated artifact removal methods. However, such methods are rarely evaluated against one another via rigorous criteria, with results often presented based upon visual inspection alone. This work presents a comparative study of automatic methods for removing blink, electrocardiographic, and electromyographic artifacts from the EEG. Three methods are considered; wavelet, blind source separation (BSS), and multivariate singular spectrum analysis (MSSA)-based correction. These are applied to data sets containing mixtures of artifacts. Metrics are devised to measure the performance of each method. The BSS method is seen to be the best approach for artifacts of high signal to noise ratio (SNR). By contrast, MSSA performs well at low SNRs but at the expense of a large number of false positive corrections.

MULTIVARIATE SINGULAR SPECTRUM ANALYSIS: A GENERAL VIEW AND NEW VECTOR FORECASTING APPROACH

The different forms of the multivariate singular spectrum analysis (SSA) and their associated forecasting algorithms are considered from both theoretical and practical points of view. The new multivariate vector forecasting algorithm is introduced and its uniqueness is evaluated. The performance of the new multivariate forecasting algorithm is assessed against the existent multivariate technique using various simulated and real data sets (namely European Electricity and Gas series). The forecasting results confirm that the performance of the new multivariate approach is more accurate than the current approach. The optimality of the window length and the number of eigenvalues in multivariate SSA are considered and various bounds are recommended. The effect of common components between two time series is evaluated through a simulation study. The concept of similarity and dissimilarity are also considered based on the matched components among series.

Spatio-temporal Predictions using Multivariate Singular Spectrum Analysis

In this paper, we present a method for utilizing the usually intrinsic spatial information in spatial data sets to improve the quality of temporal predictions within the framework of singular spectrum analysis (SSA) techniques. The SSA-based techniques constitute a model free approach to time series analysis and ordinarily, 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, nance, environmental sciences, mathematics, dynamical systems and economics. SSA has two broad aims: 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 structure-less noise. ii) To reconstruct the decomposed series for further analysis in the absence of the noise component. 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 situations 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. The usual question asked is whether the intrinsic location parameters in spatial data can improve data analysis of such data sets. The proposed method is based on the Inverse Distance Weighting and is exemplied on climate data. Results show that the proposed technique of incorporating spatial dependence into MSSA analysis leads to improved quality of statistical inference. Keywords: Time Series Analysis; MSSA; Inverse Distance Weighting; Spatial Dependence

Predicting Inflation Dynamics with Singular Spectrum Analysis

SummaryWe use univariate and multivariate singular spectrum analyses to predict the rate of inflation as well as changes in the direction of inflation time series for the USA. We use consumer price indices and realtime chain-weighted gross domestic product price index series in these prediction exercises. Moreover, we compare our out-of-sample, h-step-ahead moving prediction results with other prediction results based on methods such as the activity-based non-accelerating inflation rate of unemployment Phillips curve, auto-regressive AR(p) model, the dynamic factors model and random-walk models with the last as a naive forecasting method. We use short-run (quarterly) and long-run (1–6 years) time windows for predictions and find that multivariate singular spectrum analysis outperforms all other competing prediction methods. Also, we confirm the results of earlier studies that prediction of the rate of inflation in the USA during the period of the ‘Great Moderation’ is less challenging compared with the more volatile inflationary period of 1970–1985.

Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

ABSTRACTIn 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.

Impacts of Natural Disasters on a Dynamic Economy

This paper presents a modeling framework for macroeconomic growth dynamics; it is motivated by recent attempts to formulate and study 'integrated models' of the coupling between natural and socio-economic phenomena. The challenge is to describe the interfaces between human activities and the functioning of the earth system. We examine the way that this interface works in the presence of endogenous business cycle dynamics, based on a non-equilibrium dynamic model. Recent findings about the macroeconomic response to natural disasters in such a nonequilibrium setting have shown a more severe response to natural disasters during expansions than during recessions. These findings raise questions about the assessment of climate change damages or natural disaster losses that are based purely on long-term growth models. In order to compare the theoretical findings with observational data, we analyze cyclic behavior in the U.S. economy, based on multivariate singular spectrum analysis. We analyze a total of nine aggregate indicators in a 52-year interval (1954–2005) and demonstrate that the behavior of the U.S. economy changes significantly between intervals of growth and recession, with higher volatility during expansions.

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

Real-time data on national accounts statistics typically undergo an extensive revision process, leading to multiple vintages on the same generic variable. The time between the publication of the initial and final data is a lengthy one and raises the question of how to model and forecast the final vintage of data – an issue that dates from seminal articles by Mankiw et al. [51], Mankiw and Shapiro [52] and Nordhaus [57]. To solve this problem, we develop the non-parametric method of multivariate singular spectrum analysis (MSSA) for multi-vintage data. MSSA is much more flexible than the standard methods of modelling that involve at least one of the restrictive assumptions of linearity, normality and stationarity. The benefits are illustrated with data on the UK index of industrial production: neither the preliminary vintages nor the competing models are as accurate as the forecasts using MSSA.

Multivariate singular spectrum analysis and the road to phase synchronization

We show that multivariate singular spectrum analysis (M-SSA) greatly helps study phase synchronization in a large system of coupled oscillators and in the presence of high observational noise levels. With no need for detailed knowledge of individual subsystems nor any a priori phase definition for each of them, we demonstrate that M-SSA can automatically identify multiple oscillatory modes and detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. As an essential modification of M-SSA, here we introduce variance-maximization (varimax) rotation of the M-SSA eigenvectors to optimally identify synchronized-oscillator clustering.

Extracting fetal heart signal from noisy maternal ECG by multivariate singular spectrum analysis

Fetal heart rate and its beat-to-beat variability are two important indications about the health and condition of the fetus. The observed maternal electrocardiogram (ECG) signal consists of mother heart signal and fetal heart signal and is often very noisy. In this paper, we propose a multivariate singular spectrum analysis (MSSA) for extracting and separating the mother heart signal, the fetal heart signal and the noise component from the combined ECGs. The proposed method is designed to cope with noisy recordings, which is an important limitation of several approaches proposed in the literature. To validate the proposed algorithm some noisy simulated signals are used. The performance of the technique is also examined using real-life signals.

Predicting daily exchange rate with singular spectrum analysis

This paper uses univariate and multivariate singular spectrum analysis for predicting the value and the direction of changes in the daily pound/dollar exchange rate. In prediction of daily pound/dollar rate, we use the rescaled and bootstrapped daily euro/dollar rate as a guidepost for the singular spectrum analysis method. We use the random walk model as a benchmark to evaluate performances of the singular spectrum analysis as a prediction method. Empirical results show that the forecast based on the multivariate singular spectrum analysis compares favorably to the forecast of the random walk model both for predicting the value and the direction of changes in the daily pound/dollar exchange rate. We compared the prediction results based on an error correction model in the context of a restricted vector autoregressive model and compared them with the prediction results by a random walk as well as by those of singular spectrum and multiple singular spectrum models and found that the VEC results are inferior.

Patterns of temperature variability on multidecadal to centennial timescales

The spatiotemporal structure of low‐frequency temperature variability, as reflected in a paleonetwork covering the North American and European domains, is studied using a combination of statistical techniques including principal component analysis and univariate and multivariate singular spectrum analysis. On timescales τ longer than 50 years, two statistically significant modes of temperature variability are identified, one on multidecadal timescale and one on centennial timescale. The first mode is oscillatory, with τ in the narrow range 60–80 years. The spatial pattern of this multidecadal mode implies coherent oscillations over Europe and over northeastern North America, with maximum amplitudes in Europe; over northwestern North America this mode is absent. Its geographic shape suggests a connection to the North Atlantic Oscillation; a relation with solar forcing could not be detected. The second mode, which dominates low‐frequency variability at high latitudes, describes temperature variations in a wide interval of timescales (τ>100 years); in the longest records a weak ∼120 year oscillation can be identified with confidence. The temporal pattern of the centennial mode shows a multiple phase “Little Ice Age” and a prolonged “Medieval Warm Period.” The interpretation of centennial mode is difficult given its rather variable large‐scale pattern and the uncertainty associated with centennial timescales in the data. The present data set gives indications that in North America, centennial variability is independent of season, while the multidecadal mode might exhibit seasonally dependent features. In Europe, both low‐frequency modes of temperature variability are season specific.

ADAPTIVE FILTERING AND PREDICTION OF NOISY MULTIVARIATE SIGNALS: AN APPLICATION TO SUBANNUAL VARIABILITY IN ATMOSPHERIC ANGULAR MOMENTUM

Principal component analysis (PCA) in the space and time domains is applied to filter adaptively the dominant modes of subannual (SA) variability of a 12-year long multivariate time series of Northern Hemisphere atmospheric angular momentum (AAM); AAM is computed in 23 latitude bands of equal area from operational analyses of the U.S. National Meteorological Center. PCA isolates the leading empirical orthogonal functions (EOFs) of spatial dependence, while multivariate singular spectrum analysis (M-SSA) yields filtered time series that capture the dominant low-frequency modes of SA variability. The time series prefiltered by M-SSA lend themselves to prediction by the maximum entropy method (MEM). Whole-field predictions are made by combining the forecasts so obtained with the leading spatial EOFs obtained by PCA. The combination of M-SSA and MEM has predictive ability up to about a month. These methods are essentially linear but data-adaptive. They seem to perform well for short, noisy, multivariate time series, to which purely nonlinear, deterministically based methods are difficult to apply.