Financial Stress Through Complexity Science

Financial markets typically undergo periods of prosperity followed by periods of stagnation, and this undulation makes it challenging to maintain market efficiency. The efficient market hypothesis (EMH) states that there exist differences in structural complexity in security prices between regular and abnormal situations. Yet, despite a clear link between market acceleration (cf. recession in security prices) and stress in physical systems, indices of financial stress still have significant scope for further development. The overarching aim of this work is therefore to determine the characteristics of financial indices related to financial stress, and to establish a robust metric for the extent of such 'stress'. This is achieved based on intrinsic multiscale analysis which quantifies the so called complexity-loss hypothesis in the context of financial stress. The multiscale sample entropy and our proposed Assessment of Latent Index of Stress methods have successfully assessed financial stress, and have served as a measure to establish an analogy between transitions from 'normal' (relaxed) to 'abnormal' (stressed) financial periods with the sympatho-vagal balance in humans. Four major stock indices of the US economy over the past 25 years are considered: (i) Dow Jones Industrial Average, (ii) NASDAQ Composite, (iii) Standard & Poor's 500, and (iv) Russell 2000, together with FTSE 100, CAC 40 and exchange rates. Our findings support the EMH theory and reveal high stress for both the periods of Internet bubble burst and sub-prime mortgage crisis.This work was supported by the Financial Signal Processing Laboratory (http://www.fsplab.com/) at Imperial College London. The guest editor coordinating the review of this manuscript and approving it for publication was Prof. Ali N. Akansu.Hemakom, A.; Chanwimalueang, T.; Carrión García, A.; Aufegger, L.; Constantinides, AG.; Mandic, DP. (2016). Financial Stress Through Complexity Science. IEEE Journal of Selected Topics in Signal Processing. 10(6):1112-1126. doi:10.1109/JSTSP.2016.2581299S1112112610

The ClassA Framework: HRV Based Assessment of SNS and PNS Dynamics Without LF-HF Controversies

The powers of the low frequency (LF) and high frequency (HF) components of heart rate variability (HRV) have become the de facto standard metrics in the assessment of the stress response, and the related activities of the sympathetic nervous system (SNS) and the parasympathetic nervous system (PNS). However, the widely adopted physiological interpretations of the LF and HF components in SNS /PNS balance are now questioned, which puts under serious scrutiny stress assessments which employ the LF and HF components. To avoid these controversies, we here introduce the novel Classification Angle (ClassA) framework, which yields a family of metrics which quantify cardiac dynamics in three-dimensions. This is achieved using a finite-difference plot of HRV, which displays successive rates of change of HRV, and is demonstrated to provide sufficient degrees of freedom to determine cardiac deceleration and/or acceleration. The robustness and accuracy of the novel ClassA framework is verified using HRV signals from ten males, recorded during standardized stress tests, consisting of rest, mental arithmetic, meditation, exercise and further meditation. Comparative statistical testing demonstrates that unlike the existing LF-HF metrics, the ClassA metrics are capable of distinguishing both the physical and mental stress epochs from the epochs of no stress, with statistical significance (Bonferroni corrected p-value ≤ 0.025); HF was able to distinguish physical stress from no stress, but was not able to identify mental stress. The ClassA results also indicated that at moderate levels of stress, the extent of parasympathetic withdrawal was greater than the extent of sympathetic activation. Finally, the analyses and the experimental results provide conclusive evidence that the proposed nonlinear approach to quantify cardiac activity from HRV resolves three critical obstacles to current HRV stress assessments: (i) it is not based on controversial assumptions of balance between the LF and HF powers; (ii) its temporal resolution when estimating parasympathetic dominance is as little as 10 s of HRV data, while only 60 s to estimate sympathetic dominance; (iii) unlike LF and HF analyses, the ClassA framework does not require the prohibitive assumption of signal stationarity. The ClassA framework is unique in offering HRV based stress analysis in three-dimensions

Fault diagnosis of bearing vibration signals based on a reconstruction algorithm with multiple side Information and CEEMDAN method

When bearing vibration of instruments is monitored, a large number of data are produced. This requires a massive capacity of storage and high bandwidth of data transmission whereby costs and complex installation are concerned. In this study, we aim to propose an effective framework to address such the amount of bearing signals to which only meaningful information is extracted. Based on the compressed sensing (CS) theory. We proposed a reconstruction algorithm based on the multiple side information signal (RAMSI) with a purpose to effectively obtain important information from recorded bearing signals. In the process of sparse optimization, the RAMSI algorithm was implemented to solve the n-11 minimization problem with the weighting adaptive multiple side information signals. Wavelet basis and Hartley matrix were applied for the reconstruction process, for which the effective sparse optimization processing of bearing signals was able to adaptively computed. The performance of our RAMSI-based CS theory was compared with the basis pursuit (BP) which is based on the alternating direction method of multiplier (ADMM) and orthogonal matching pursuit (OMP). The error indices of the reconstruction algorithms were evaluated. This proves that the performance of the sparse optimization algorithm from our proposed framework is superior to the BP based on the ADMM and OMP algorithm. After recovering vibration signals, some strong noise caused by the incipient fault characteristic of the bearing. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method was performed to extract the bearing fault component from such noise. In terms of performance, the CEEMDAN method was compared to the standard ensemble empirical mode decomposition (EEMD) method. The results show that the CEEMDAN method yields a better decomposition performance and is able to extract meaningful information of bearing fault characteristic

Stage Call: Cardiovascular Reactivity to Audition Stress in Musicians

Auditioning is at the very center of educational and professional life in music and is associated with significant psychophysical demands. Knowledge of how these demands affect cardiovascular responses to psychosocial pressure is essential for developing strategies to both manage stress and understand optimal performance states. To this end, we recorded the electrocardiograms (ECGs) of 16 musicians (11 violinists and 5 flutists) before and during performances in both low- and high-stress conditions: with no audience and in front of an audition panel, respectively. The analysis consisted of the detection of R-peaks in the ECGs to extract heart rate variability (HRV) from the notoriously noisy real-world ECGs. Our data analysis approach spanned both standard (temporal and spectral) and advanced (structural complexity) techniques. The complexity science approaches—namely, multiscale sample entropy and multiscale fuzzy entropy—indicated a statistically significant decrease in structural complexity in HRV from the low- to the high-stress condition and an increase in structural complexity from the pre-performance to performance period, thus confirming the complexity loss theory and a loss in degrees of freedom due to stress. Results from the spectral analyses also suggest that the stress responses in the female participants were more parasympathetically driven than those of the male participants. In conclusion, our findings suggest that interventions to manage stress are best targeted at the sensitive pre-performance period, before an audition begins

Bringing complexity science to real world: Quantification of stress in humans and systems

Analysing real-world data within the context of structural complexity is crucial for accurately revealing the dynamical behavior of systems, ranging from individual (human) to network (economic). Indeed, the so-called "Complexity Loss Theory" establishes that complexity measures are able to provide physically meaningful interpretation of, for example, the occurrence of stress in such systems. This theory states that organisms or systems under constraints, such as ageing illness or more generally loss of degrees of freedom, exhibit lower complexity of their observable responses. To this end, this thesis aims to model/quantify stress levels of two dynamical systems: i) autonomic nervous (in humans), and ii) economic (in financial markets). For human based scenarios, we collected Electrocardiogram (ECG) in two human activities: i) public speaking, and ii) music performance. For the assessment of the structural complexity of systems, stock indices from the four major stock markets in the US were used for studying stress in economic. This thesis introduces a novel framework for analysing physiological stress from heart rate variability (HRV) extracted from the wearable ECG. The framework includes a robust method, established based on the matched filtering method and the Hilbert transform, for detecting R-peaks in noisy ECG. We examine the physiological stress through several standard entropy measures, prior to introducing our novel “Cosine Similarity Entropy” and “Multiscale Cosine Similarity Entropy”. These new entropy measures are derived based on angular distance, Shannon entropy and the coarse-grained scale, and shown to successfully and rigorously quantify structural complexity in systems within the context of self-correlation. The analysis over numerous case studies shows that the proposed framework is capable of detecting loss of degrees of freedom, that is, ‘stress-patterns’ under different stress conditions. Furthermore, we examine economic stress through an enhanced multivariate entropy measure, “Moving-Averaged Multivariate Sample Entropy”, which is established based on a standard multivariate entropy and a novel detrended moving average scale. The MA-MSE makes it possible to capture the periods of financial stress which corresponds to the occurrence of the economic crises correctly. Overall, the novel algorithms in this thesis have resolved several limitations of the existing entropy measures, especially related to short time series, sensitivity to signal amplitudes, and undefined entropy values for data with artefacts. In addition, real world data do not obey any closed-form probability distribution and are often nonstationary, which requires non-parametric entropy estimators suitable for such scenarios - a subject of this thesis.Open Acces

Cosine Similarity Entropy: Self-Correlation-Based Complexity Analysis of Dynamical Systems

The nonparametric Sample Entropy (SE) estimator has become a standard for the quantification of structural complexity of nonstationary time series, even in critical cases of unfavorable noise levels. The SE has proven very successful for signals that exhibit a certain degree of the underlying structure, but do not obey standard probability distributions, a typical case in real-world scenarios such as with physiological signals. However, the SE estimates structural complexity based on uncertainty rather than on (self) correlation, so that, for reliable estimation, the SE requires long data segments, is sensitive to spikes and erratic peaks in data, and owing to its amplitude dependence it exhibits lack of precision for signals with long-term correlations. To this end, we propose a class of new entropy estimators based on the similarity of embedding vectors, evaluated through the angular distance, the Shannon entropy and the coarse-grained scale. Analysis of the effects of embedding dimension, sample size and tolerance shows that the so introduced Cosine Similarity Entropy (CSE) and the enhanced Multiscale Cosine Similarity Entropy (MCSE) are amplitude-independent and therefore superior to the SE when applied to short time series. Unlike the SE, the CSE is shown to yield valid entropy values over a broad range of embedding dimensions. By evaluating the CSE and the MCSE over a variety of benchmark synthetic signals as well as for real-world data (heart rate variability of three different cardiovascular pathologies), the proposed algorithms are demonstrated to be able to quantify degrees of structural complexity in the context of self-correlation over small to large temporal scales, thus offering physically meaningful interpretations and rigor in the understanding the intrinsic properties of the structural complexity of a system, such as the number of its degrees of freedom

Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE

Sparse Optimistic Based on Lasso-LSQR and Minimum Entropy De-Convolution with FARIMA for the Remaining Useful Life Prediction of Machinery

To reduce the maintenance cost and safeguard machinery operation, remaining useful life (RUL) prediction is very important for long term health monitoring. In this paper, we introduce a novel hybrid method to deal with the RUL prediction for health management. Firstly, the sparse reconstruction algorithm of the optimized Lasso and the Least Square QR-factorization (Lasso-LSQR) is applied to compressed sensing (CS), which can realize the sparse optimization for long term health monitoring data. After the sparse signal is reconstructed, the minimum entropy de-convolution (MED) is used to identify the fault characteristics and to obtain significant fault information from the machinery operation. Health indicators with Skip-over, sample entropy and approximate entropy are then performed to track the degradation of the machinery process. The performance analysis of the Skip-over is superior to other indicators. Finally, Fractal Autoregressive Integrated Moving Average model (FARIMA) is employed to predict the Skip-over using the R/S method. The analysis results evidence that the novel hybrid method yields a good performance, and such method can achieve highly accurate RUL prediction and safeguard machinery operation for long term monitoring

Scripts - readme

The file "Scripts - readme.txt" explains which MATLAB scripts are the main files and how the parameters in the header need to be set to obtain the diagrams in the paper, based on the supplied data files

Scripts

zip-folder containing the scripts to process the raw data in the folder Data.zi