Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks
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Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK
systems Article How We Understand “Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK Michael C. Jackson Centre for Systems Studies, University of Hull, Hull HU6 7TS, UK; [email protected]; Tel.: +44-7527-196400 Received: 11 November 2020; Accepted: 4 December 2020; Published: 7 December 2020 Abstract: Many authors have sought to summarize what they regard as the key features of “complexity”. Some concentrate on the complexity they see as existing in the world—on “ontological complexity”. Others highlight “cognitive complexity”—the complexity they see arising from the different interpretations of the world held by observers. Others recognize the added difficulties flowing from the interactions between “ontological” and “cognitive” complexity. Using the example of the Covid-19 pandemic in the UK, and the responses to it, the purpose of this paper is to show that the way we understand complexity makes a huge difference to how we respond to crises of this type. Inadequate conceptualizations of complexity lead to poor responses that can make matters worse. Different understandings of complexity are discussed and related to strategies proposed for combatting the pandemic. It is argued that a “critical systems thinking” approach to complexity provides the most appropriate understanding of the phenomenon and, at the same time, suggests which systems methodologies are best employed by decision makers in preparing for, and responding to, such crises. Keywords: complexity; Covid-19; critical systems thinking; systems methodologies 1. Introduction No one doubts that we are, in today’s world, entangled in complexity. At the global level, economic, social, technological, health and ecological factors have become interconnected in unprecedented ways, and the consequences are immense. -
Kalman and Particle Filtering
Abstract: The Kalman and Particle filters are algorithms that recursively update an estimate of the state and find the innovations driving a stochastic process given a sequence of observations. The Kalman filter accomplishes this goal by linear projections, while the Particle filter does so by a sequential Monte Carlo method. With the state estimates, we can forecast and smooth the stochastic process. With the innovations, we can estimate the parameters of the model. The article discusses how to set a dynamic model in a state-space form, derives the Kalman and Particle filters, and explains how to use them for estimation. Kalman and Particle Filtering The Kalman and Particle filters are algorithms that recursively update an estimate of the state and find the innovations driving a stochastic process given a sequence of observations. The Kalman filter accomplishes this goal by linear projections, while the Particle filter does so by a sequential Monte Carlo method. Since both filters start with a state-space representation of the stochastic processes of interest, section 1 presents the state-space form of a dynamic model. Then, section 2 intro- duces the Kalman filter and section 3 develops the Particle filter. For extended expositions of this material, see Doucet, de Freitas, and Gordon (2001), Durbin and Koopman (2001), and Ljungqvist and Sargent (2004). 1. The state-space representation of a dynamic model A large class of dynamic models can be represented by a state-space form: Xt+1 = ϕ (Xt,Wt+1; γ) (1) Yt = g (Xt,Vt; γ) . (2) This representation handles a stochastic process by finding three objects: a vector that l describes the position of the system (a state, Xt X R ) and two functions, one mapping ∈ ⊂ 1 the state today into the state tomorrow (the transition equation, (1)) and one mapping the state into observables, Yt (the measurement equation, (2)). -
Lecture 19: Wavelet Compression of Time Series and Images
Lecture 19: Wavelet compression of time series and images c Christopher S. Bretherton Winter 2014 Ref: Matlab Wavelet Toolbox help. 19.1 Wavelet compression of a time series The last section of wavelet leleccum notoolbox.m demonstrates the use of wavelet compression on a time series. The idea is to keep the wavelet coefficients of largest amplitude and zero out the small ones. 19.2 Wavelet analysis/compression of an image Wavelet analysis is easily extended to two-dimensional images or datasets (data matrices), by first doing a wavelet transform of each column of the matrix, then transforming each row of the result (see wavelet image). The wavelet coeffi- cient matrix has the highest level (largest-scale) averages in the first rows/columns, then successively smaller detail scales further down the rows/columns. The ex- ample also shows fine results with 50-fold data compression. 19.3 Continuous Wavelet Transform (CWT) Given a continuous signal u(t) and an analyzing wavelet (x), the CWT has the form Z 1 s − t W (λ, t) = λ−1=2 ( )u(s)ds (19.3.1) −∞ λ Here λ, the scale, is a continuous variable. We insist that have mean zero and that its square integrates to 1. The continuous Haar wavelet is defined: 8 < 1 0 < t < 1=2 (t) = −1 1=2 < t < 1 (19.3.2) : 0 otherwise W (λ, t) is proportional to the difference of running means of u over successive intervals of length λ/2. 1 Amath 482/582 Lecture 19 Bretherton - Winter 2014 2 In practice, for a discrete time series, the integral is evaluated as a Riemann sum using the Matlab wavelet toolbox function cwt. -
Wavelet Entropy Energy Measure (WEEM): a Multiscale Measure to Grade a Geophysical System's Predictability
EGU21-703, updated on 28 Sep 2021 https://doi.org/10.5194/egusphere-egu21-703 EGU General Assembly 2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. Wavelet Entropy Energy Measure (WEEM): A multiscale measure to grade a geophysical system's predictability Ravi Kumar Guntu and Ankit Agarwal Indian Institute of Technology Roorkee, Hydrology, Roorkee, India ([email protected]) Model-free gradation of predictability of a geophysical system is essential to quantify how much inherent information is contained within the system and evaluate different forecasting methods' performance to get the best possible prediction. We conjecture that Multiscale Information enclosed in a given geophysical time series is the only input source for any forecast model. In the literature, established entropic measures dealing with grading the predictability of a time series at multiple time scales are limited. Therefore, we need an additional measure to quantify the information at multiple time scales, thereby grading the predictability level. This study introduces a novel measure, Wavelet Entropy Energy Measure (WEEM), based on Wavelet entropy to investigate a time series's energy distribution. From the WEEM analysis, predictability can be graded low to high. The difference between the entropy of a wavelet energy distribution of a time series and entropy of wavelet energy of white noise is the basis for gradation. The metric quantifies the proportion of the deterministic component of a time series in terms of energy concentration, and its range varies from zero to one. One corresponds to high predictable due to its high energy concentration and zero representing a process similar to the white noise process having scattered energy distribution. -
Dissipative Structures, Complexity and Strange Attractors: Keynotes for a New Eco-Aesthetics
Dissipative structures, complexity and strange attractors: keynotes for a new eco-aesthetics 1 2 3 3 R. M. Pulselli , G. C. Magnoli , N. Marchettini & E. Tiezzi 1Department of Urban Studies and Planning, M.I.T, Cambridge, U.S.A. 2Faculty of Engineering, University of Bergamo, Italy and Research Affiliate, M.I.T, Cambridge, U.S.A. 3Department of Chemical and Biosystems Sciences, University of Siena, Italy Abstract There is a new branch of science strikingly at variance with the idea of knowledge just ended and deterministic. The complexity we observe in nature makes us aware of the limits of traditional reductive investigative tools and requires new comprehensive approaches to reality. Looking at the non-equilibrium thermodynamics reported by Ilya Prigogine as the key point to understanding the behaviour of living systems, the research on design practices takes into account the lot of dynamics occurring in nature and seeks to imagine living shapes suiting living contexts. When Edgar Morin speaks about the necessity of a method of complexity, considering the evolutive features of living systems, he probably means that a comprehensive method should be based on deep observations and flexible ordering laws. Actually designers and planners are engaged in a research field concerning fascinating theories coming from science and whose playground is made of cities, landscapes and human settlements. So, the concept of a dissipative structure and the theory of space organized by networks provide a new point of view to observe the dynamic behaviours of systems, finally bringing their flowing patterns into the practices of design and architecture. However, while science discovers the fashion of living systems, the question asked is how to develop methods to configure open shapes according to the theory of evolutionary physics. -
Alternative Tests for Time Series Dependence Based on Autocorrelation Coefficients
Alternative Tests for Time Series Dependence Based on Autocorrelation Coefficients Richard M. Levich and Rosario C. Rizzo * Current Draft: December 1998 Abstract: When autocorrelation is small, existing statistical techniques may not be powerful enough to reject the hypothesis that a series is free of autocorrelation. We propose two new and simple statistical tests (RHO and PHI) based on the unweighted sum of autocorrelation and partial autocorrelation coefficients. We analyze a set of simulated data to show the higher power of RHO and PHI in comparison to conventional tests for autocorrelation, especially in the presence of small but persistent autocorrelation. We show an application of our tests to data on currency futures to demonstrate their practical use. Finally, we indicate how our methodology could be used for a new class of time series models (the Generalized Autoregressive, or GAR models) that take into account the presence of small but persistent autocorrelation. _______________________________________________________________ An earlier version of this paper was presented at the Symposium on Global Integration and Competition, sponsored by the Center for Japan-U.S. Business and Economic Studies, Stern School of Business, New York University, March 27-28, 1997. We thank Paul Samuelson and the other participants at that conference for useful comments. * Stern School of Business, New York University and Research Department, Bank of Italy, respectively. 1 1. Introduction Economic time series are often characterized by positive -
Time Series: Co-Integration
Time Series: Co-integration Series: Economic Forecasting; Time Series: General; Watson M W 1994 Vector autoregressions and co-integration. Time Series: Nonstationary Distributions and Unit In: Engle R F, McFadden D L (eds.) Handbook of Econo- Roots; Time Series: Seasonal Adjustment metrics Vol. IV. Elsevier, The Netherlands N. H. Chan Bibliography Banerjee A, Dolado J J, Galbraith J W, Hendry D F 1993 Co- Integration, Error Correction, and the Econometric Analysis of Non-stationary Data. Oxford University Press, Oxford, UK Time Series: Cycles Box G E P, Tiao G C 1977 A canonical analysis of multiple time series. Biometrika 64: 355–65 Time series data in economics and other fields of social Chan N H, Tsay R S 1996 On the use of canonical correlation science often exhibit cyclical behavior. For example, analysis in testing common trends. In: Lee J C, Johnson W O, aggregate retail sales are high in November and Zellner A (eds.) Modelling and Prediction: Honoring December and follow a seasonal cycle; voter regis- S. Geisser. Springer-Verlag, New York, pp. 364–77 trations are high before each presidential election and Chan N H, Wei C Z 1988 Limiting distributions of least squares follow an election cycle; and aggregate macro- estimates of unstable autoregressive processes. Annals of Statistics 16: 367–401 economic activity falls into recession every six to eight Engle R F, Granger C W J 1987 Cointegration and error years and follows a business cycle. In spite of this correction: Representation, estimation, and testing. Econo- cyclicality, these series are not perfectly predictable, metrica 55: 251–76 and the cycles are not strictly periodic. -
Biostatistics for Oral Healthcare
Biostatistics for Oral Healthcare Jay S. Kim, Ph.D. Loma Linda University School of Dentistry Loma Linda, California 92350 Ronald J. Dailey, Ph.D. Loma Linda University School of Dentistry Loma Linda, California 92350 Biostatistics for Oral Healthcare Biostatistics for Oral Healthcare Jay S. Kim, Ph.D. Loma Linda University School of Dentistry Loma Linda, California 92350 Ronald J. Dailey, Ph.D. Loma Linda University School of Dentistry Loma Linda, California 92350 JayS.Kim, PhD, is Professor of Biostatistics at Loma Linda University, CA. A specialist in this area, he has been teaching biostatistics since 1997 to students in public health, medical school, and dental school. Currently his primary responsibility is teaching biostatistics courses to hygiene students, predoctoral dental students, and dental residents. He also collaborates with the faculty members on a variety of research projects. Ronald J. Dailey is the Associate Dean for Academic Affairs at Loma Linda and an active member of American Dental Educational Association. C 2008 by Blackwell Munksgaard, a Blackwell Publishing Company Editorial Offices: Blackwell Publishing Professional, 2121 State Avenue, Ames, Iowa 50014-8300, USA Tel: +1 515 292 0140 9600 Garsington Road, Oxford OX4 2DQ Tel: 01865 776868 Blackwell Publishing Asia Pty Ltd, 550 Swanston Street, Carlton South, Victoria 3053, Australia Tel: +61 (0)3 9347 0300 Blackwell Wissenschafts Verlag, Kurf¨urstendamm57, 10707 Berlin, Germany Tel: +49 (0)30 32 79 060 The right of the Author to be identified as the Author of this Work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. -
Fractal Curves and Complexity
Perception & Psychophysics 1987, 42 (4), 365-370 Fractal curves and complexity JAMES E. CUTI'ING and JEFFREY J. GARVIN Cornell University, Ithaca, New York Fractal curves were generated on square initiators and rated in terms of complexity by eight viewers. The stimuli differed in fractional dimension, recursion, and number of segments in their generators. Across six stimulus sets, recursion accounted for most of the variance in complexity judgments, but among stimuli with the most recursive depth, fractal dimension was a respect able predictor. Six variables from previous psychophysical literature known to effect complexity judgments were compared with these fractal variables: symmetry, moments of spatial distribu tion, angular variance, number of sides, P2/A, and Leeuwenberg codes. The latter three provided reliable predictive value and were highly correlated with recursive depth, fractal dimension, and number of segments in the generator, respectively. Thus, the measures from the previous litera ture and those of fractal parameters provide equal predictive value in judgments of these stimuli. Fractals are mathematicalobjectsthat have recently cap determine the fractional dimension by dividing the loga tured the imaginations of artists, computer graphics en rithm of the number of unit lengths in the generator by gineers, and psychologists. Synthesized and popularized the logarithm of the number of unit lengths across the ini by Mandelbrot (1977, 1983), with ever-widening appeal tiator. Since there are five segments in this generator and (e.g., Peitgen & Richter, 1986), fractals have many curi three unit lengths across the initiator, the fractionaldimen ous and fascinating properties. Consider four. sion is log(5)/log(3), or about 1.47. -
Measures of Complexity a Non--Exhaustive List
Measures of Complexity a non--exhaustive list Seth Lloyd d'Arbeloff Laboratory for Information Systems and Technology Department of Mechanical Engineering Massachusetts Institute of Technology [email protected] The world has grown more complex recently, and the number of ways of measuring complexity has grown even faster. This multiplication of measures has been taken by some to indicate confusion in the field of complex systems. In fact, the many measures of complexity represent variations on a few underlying themes. Here is an (incomplete) list of measures of complexity grouped into the corresponding themes. An historical analog to the problem of measuring complexity is the problem of describing electromagnetism before Maxwell's equations. In the case of electromagnetism, quantities such as electric and magnetic forces that arose in different experimental contexts were originally regarded as fundamentally different. Eventually it became clear that electricity and magnetism were in fact closely related aspects of the same fundamental quantity, the electromagnetic field. Similarly, contemporary researchers in architecture, biology, computer science, dynamical systems, engineering, finance, game theory, etc., have defined different measures of complexity for each field. Because these researchers were asking the same questions about the complexity of their different subjects of research, however, the answers that they came up with for how to measure complexity bear a considerable similarity to eachother. Three questions that researchers frequently ask to quantify the complexity of the thing (house, bacterium, problem, process, investment scheme) under study are 1. How hard is it to describe? 2. How hard is it to create? 3. What is its degree of organization? Here is a list of some measures of complexity grouped according to the question that they try to answer. -
Big Data for Reliability Engineering: Threat and Opportunity
Reliability, February 2016 Big Data for Reliability Engineering: Threat and Opportunity Vitali Volovoi Independent Consultant [email protected] more recently, analytics). It shares with the rest of the fields Abstract - The confluence of several technologies promises under this umbrella the need to abstract away most stormy waters ahead for reliability engineering. News reports domain-specific information, and to use tools that are mainly are full of buzzwords relevant to the future of the field—Big domain-independent1. As a result, it increasingly shares the Data, the Internet of Things, predictive and prescriptive lingua franca of modern systems engineering—probability and analytics—the sexier sisters of reliability engineering, both statistics that are required to balance the otherwise orderly and exciting and threatening. Can we reliability engineers join the deterministic engineering world. party and suddenly become popular (and better paid), or are And yet, reliability engineering does not wear the fancy we at risk of being superseded and driven into obsolescence? clothes of its sisters. There is nothing privileged about it. It is This article argues that“big-picture” thinking, which is at the rarely studied in engineering schools, and it is definitely not core of the concept of the System of Systems, is key for a studied in business schools! Instead, it is perceived as a bright future for reliability engineering. necessary evil (especially if the reliability issues in question are safety-related). The community of reliability engineers Keywords - System of Systems, complex systems, Big Data, consists of engineers from other fields who were mainly Internet of Things, industrial internet, predictive analytics, trained on the job (instead of receiving formal degrees in the prescriptive analytics field). -
Volatility Estimation of Stock Prices Using Garch Method
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by International Institute for Science, Technology and Education (IISTE): E-Journals European Journal of Business and Management www.iiste.org ISSN 2222-1905 (Paper) ISSN 2222-2839 (Online) Vol.7, No.19, 2015 Volatility Estimation of Stock Prices using Garch Method Koima, J.K, Mwita, P.N Nassiuma, D.K Kabarak University Abstract Economic decisions are modeled based on perceived distribution of the random variables in the future, assessment and measurement of the variance which has a significant impact on the future profit or losses of particular portfolio. The ability to accurately measure and predict the stock market volatility has a wide spread implications. Volatility plays a very significant role in many financial decisions. The main purpose of this study is to examine the nature and the characteristics of stock market volatility of Kenyan stock markets and its stylized facts using GARCH models. Symmetric volatility model namly GARCH model was used to estimate volatility of stock returns. GARCH (1, 1) explains volatility of Kenyan stock markets and its stylized facts including volatility clustering, fat tails and mean reverting more satisfactorily.The results indicates the evidence of time varying stock return volatility over the sampled period of time. In conclusion it follows that in a financial crisis; the negative returns shocks have higher volatility than positive returns shocks. Keywords: GARCH, Stylized facts, Volatility clustering INTRODUCTION Volatility forecasting in financial market is very significant particularly in Investment, financial risk management and monetory policy making Poon and Granger (2003).Because of the link between volatility and risk,volatility can form a basis for efficient price discovery.Volatility implying predictability is very important phenomenon for traders and medium term - investors.