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Formes nouvelles du hasard dans les sciences
... Some of these texts are translated in English, modified, and reprinted in his 1997 Fractals and Scaling in Finance. In this chapter, I term "Mandelbrot's program" the research program described in these papers corresponding to Mandelbrot (1966Mandelbrot ( , 1967Mandelbrot ( , 1973aMandelbrot ( , 1973bMandelbrot ( , 1973c (2015): fat tails, long-range dependence, and intrinsic time. A second strand of papers came after his 1997 book, corresponding to Mandelbrot (2001aMandelbrot ( , 2001bMandelbrot ( , 2001c, which built on the generalized multifractal model put forward in 1997, outside the IID framework. ...
FULL-TEXT HERE: https://hal.science/hal-04561141
... D'autres conceptions de l'instabilité existent pourtant. Mandelbrot (1973a) distingue le hasard bénin, gaussien, qui disparaît lorsque l'échelle d'observation est suffisamment grossière, du « hasard sauvage ». Le hasard bénin est celui dont il a été question ci-dessus mais Mandelbrot souligne la fréquence du « hasard sauvage » dans les séries économiques et en particulier dans les séries de prix, « (…) la raison, à priori est que l'offre et la demande, qui en principe doivent déterminer un prix, résultent toute deux à la fois de facteurs objectifs et d'anticipations. ...
Alors que les gains à attendre suite à la libéralisation des échanges, en particulier pour les PED, sont généralement présentés comme essentiels aux progrès de la lutte contre la pauvreté, cette étude souligne leur faiblesse lorsqu'ils sont exprimés en termes relatifs et leur sensibilité aux hypothèses réalisées sur le fonctionnement des marchés. En effet, alors que l'imperfection de l'information est largement admise, parmi les spécialistes, comme caractéristiques des marchés agricoles, sa prise en compte dans le modèle transforme des gains extrêmement faibles en pertes parfois importantes, soulignant ainsi l'utilité sociale des politiques agricoles.
... ***************** 9C1 **j************** **************** C6 **************** *************** 3B *************** ************ ******** 23 ***** 69T 75 153 ***** 24 **** 67 73 5 38**** 25 **** 9C5 166 *ï 68788**** 26 *** 7Al!i 73 68757 788808*** 27 *** 1 AT 11 53 1 700760888878*** 28 *-** 9G 19CECrA6 55 85 l 101 **** 77 **** 06QCD077BD96560A771315 **** 70 ***** 589DEDB989BLC90BBBDEBC93 6 "**** 79 ****** 19EGCFA78ABCDB9CCEEGD6 3 ****** 80 ****** 675BCBEBAA9EGEFFDC9951 1 ****** 81 *******5 3 898CCBCEEDFFFEB1 **..***** 82 ******** 1BDD9BDEDBCDB 5 ******** 03 ******** 618CECCB9EFCB1 11 ******** 04 ********* 398BEDEDBD7I 3 ********* 85 ********** 13 7A78BDB3 ********** 86 *********** 5683 ******~**** 87 ************ 3 J***J******* 88 ************ ************ flQ ************** ************** have given rise to a large specialist literature concerning the nature and phenomenology of these "fronts" and "bands". Erratic or "intermittent" behaviour was tackled by Mandelbrot (1973Mandelbrot ( , 1977Mandelbrot ( , 1982 and Mandelbrot & Wallis (1968), who, by incorporating such behaviour in the notion of fractals, suggested ...
Rain areas as seen by radar show a complex of bands, lines and other structures. Fluctuations in both time and space can occasionally be very large. Radar and satellite data from Canada, Spain, France and the tropical Atlantic on scales from 1 to 1000 km are analysed in the context of fractals, i.e. objects with structure at all scales. It is possible to construct fractal rainfall models of the evolution of rainfields that are fairly realistic both visually and statistically. In particular, the models presented have the following properties: realistic "complexity" of shapes (as measured by the fractal dimension); realistic distribution of fluctuations; realistic distribution of rainfronts; and, realistic distribution of rain areas.
... Instead, it showed the characteristics of discontinuity and durability . Based on the empirical findings of Hurst, B B Mandelbrot (1968 Mandelbrot ( , 1973) made a breakthrough regarding fundamental theories of traditional statistical methods. He found many time series no longer present a random Brownian movement unrelated to the past, but show a characteristic of long-term correlation (Comte et al., 1996 ), which he called " fractal " . ...
This paper attempted to identify fractal and chaotic characteristics of the annual runoff processes in headwaters of the Tarim River. Methods of fractal analyses were used to explore several aspects of the temporal changes from 1957 to 2002. The main findings are as follows: (1) The annual runoff processes of the three headwaters of the Tarim River are complex nonlinear systems with fractal as well as chaotic dynamics. (2) The correlation dimensions of attractor derived from the time series of the annual runoff for the Hotan, Yarkand and Aksu rivers are all greater than 3.0 and non-integral, implying that all three rivers are chaotic dynamical systems that are sensitive to initial conditions, and the dynamic modeling of their annual runoff process requires at least four independent variables. (3) The time series of annual runoff in each river presents a long-term correlation characteristic. The Hurst exponent for the period of 1989 to 2002 suggests that we may expect to see an increasing trend in the annual runoff of the Aksu and Yarkand rivers in the years after 2002, but a decreasing tendency for the Hotan River in the same period.
... And there shall arise after them seven years of famine" showing the periodical occurrence of humidity and aridity with a characteristic of durability. The idea was proposed in his speech named "New forms of chance in the sciences" and recorded in references of MANDELBROT and WALLIS (1968) and MANDELBROT (1973). Under the effect of Noah Effects and Joseph Effects, time series no longer presents a random Brownian movement unrelated to the past, XU Jian-hua, LU Yah, but shows a characteristic of long-term correlation (COMTE and RENAULT, 1996), which was called fBM (fractional Brownian Movement) by B B MAN-DELBROT and could be studied by rescaled range statistic (R/S) analysis. ...
This paper shows the dynamic process of regional disparity of economic development in China in the past 50 years from a new insight by using the rescaled range statistic (R/S) analysis and wavelet analysis of the Theil index sequence with different time scales. The main conclusions are: 1) The regional disparity of economic development in China, including the inter-provincial disparity, inter-regional disparity and intra-regional disparity, has existed for many years. Theil index by the comparative price has revealed the true trend for comparative disparity of regional economic development from 1952 to 2000. 2) Decomposition of Theil index indicates that the dynamic trend of comparative inter-provincial disparity in the coastal region is in line
with dynamic trend of inter-provincial disparity in the whole China. 3) The R/S analysis results tell us that during 1966–1978, the Hurst exponent H=0.504≈0.5, which indicates that in that period the evolution of comparative inter-provincial disparity of economic development showed a random characteristic, and in the other periods, i.e. 1952–1965, 1979–1990 and 1991–2000, the Hurst exponent H>0.5, which indicates that in those periods the evolution of the comparative inter-provincial disparity of economic development in China had a long-enduring characteristic. 4) By using wavelet analysis at different time scale, we arrived at a conclusion that the evolutionary process of the disparity of economic development of China is not a simple inverted U shape but a compound of several U shapes. The result tells us that the evolutionary plot of inter-provincial disparity in China follows the inverted U on the whole at the higher scale, 24 (16 years). That is to say, the disparity tends to rise in the first stage of economic development, and fall slowly over the peak in the second stage of economic development. However, if we shorten the time scale to 23 (8 years), then a link of several U shapes will appear.
... When H E Hurst et al. analyzed water levels of the Nile River, he found that such time series of variables such as river water level were not fit for Gauss distribution, showing a characteristics of discontinuity and durability (Hurst, 1951; Hurst et al., 1965 ). Based on the empirical findings of Hurst, B B Mandelbrot made a breakthrough regarding fundamental theories of traditional statistical methods (Mandelbrot, 1973; Mandelbrot and Wallis, 1968) . He found many time series no longer present a random Brownian movement unrelated to the past, but show a characteristic of long-term correlation (Comte and Renault, 1996), which he called " fractal " . ...
Based on the time series data from the Aral hydrological station for the period of 1958–2005, the paper reveals the long-term trend and fractal of the annual runoff process in the mainstream of the Tarim River by using the wavelet analysis method and the fractal theory. The main conclusions are as follows: 1) From a large time scale point of view, i.e. the time scale of 16 (24) years, the annual runoff basically shows a slightly decreasing trend as a whole from 1958 to 2005. If the time scale is reduced to 8 (23) or 4 (22) years, the annual runoff still displays the basic trend as the large time scale, but it has fluctuated more obviously during
the period. 2) The correlation dimension for the annual runoff process is 3.4307, non-integral, which indicates that the process has both fractal and chaotic characteristics. The correlation dimension is above 3, which means that at least four independent variables are needed to describe the dynamics of the annual runoff process. 3) The Hurst exponent for the first period (1958–1973) is 0.5036, which equals 0.5 approximately and indicates that the annual runoff process is in chaos. The Hurst exponents for the second (1974–1989) and third (1990–2005) periods are both greater than 0.50, which indicate that the annual runoff process
showed a long-enduring characteristic in the two periods. The Hurst exponent for the period from 1990 to 2005 indicates that the annual runoff will show a slightly increasing trend in the 16 years after 2005.
... In 1973, Benoît Mandelbrot, who first worked in economics, wrote an article about new forms of randomness in science.26 He listed situations where, in contrast to the classical paradigm, incidents do not compensate for each other, but are additive, and where statistical predictions become invalid. ...
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.
Through an examination of the work of great scholars from fields including philosophy, literature, philology, semiology, quantum physics, history, and anthropology, this book argues that building on the contribution of non-economists can open new areas of reflection in economics beyond the usual schools of thought.
The purpose of the book is twofold. First, it offers a critique and discussion of the limits of contemporary economic discourse, both mainstream and self-styled alternative theories. The central theme on which the book is built is that the discipline of economics fails to examine the nature of social reality in a systematic way. This prompts the economists to become fully aware of the methodology on which they base their representation, analysis, and argumentation in a way that economists currently are not. Second, the book proposes alternative ways of thinking that can help readers of economics to overcome the current limitations of their discipline. This means going beyond various dominant dualities – orthodox/heterodox, micro/ macro, epistemology/ontology – because it is not a question of doing ‘the economy’ differently, but of overcoming the economy as a representation of the world that strives to submit everything to its realm. Thus, the book does not simply propose a broader conceptual framework than that portrayed by mainstream economists or those who propose an alternative approach but raises questions that do not usually come from the minds of economists at all.
The book will be of particular interest to readers of economic methodology and pluralism, philosophers of science, and other social scientists interested in methodological issues.
The subject of this presentation is the relation between the uncertainty of the second kind and the limits of knowledge. Scientific research, music and communication. Fractal models of phenomena. Strange attractors. How far could science go in practice? How far should science go? How far could science go in principle? External disabilities and internal disabilities. Two types of learning: phylogenetic and ontogenic. Inadequacy of the two categories to deal with uncertainty of the second kind: the problem of the meaning of black swans.
FULL-TEXT HERE: https://hal.science/hal-04561125
The purpose of this study is to analyse the time series of the eurodollar exchange rate. This exchange rate is studied as if it was a continuous-time physical process, which implies that we systematically make use of different degrees of time resolution. The analysis takes into account various statistical indicators, but puts a special emphasis on the spectrum of the process. In other words, we consider the process of the returns of the euro-dollar exchange rate as produced by a superposition of oscillations with different frequencies and we try to determine the relative weight of those frequencies within the returns process. The spectrum of this process is the function giving those relative weights. We find that this spectrum has an identifiable pattern and we claim that this pattern is a core characteristic of the process. We simulate then a process having the same spectrum and compare the behaviours of actual process and of the simulated process in terms of various statistical indicators. We find that the simulated process provides a good, but not perfect, replication of the behaviour of the actual euro-dollar exchange rate.
When applying the statistical theory of long range dependent (LRD) processes to economics, the strong complexity of macroeconomic and financial variables, compared to standard LRD processes, becomes apparent. In order to get a better understanding of the behaviour of some economic variables, the book assembles three different strands of long memory analysis: statistical literature on the properties of, and tests for, LRD processes; mathematical literature on the stochastic processes involved; models from economic theory providing plausible micro foundations for the occurence of long memory in economics. Each chapter of the book will give a comprehensive survey of the state of the art and the directions that future developments are likely to take. Taken as a whole the book provides an overview of LRD processes which is accessible to economists, econometricians and statisticians.
Diversity and complementarity of multi-agent models in the social sciences
Multi-agent systems have been used for fifteen years to simulate the dynamics of social phenomena. They help conceptualize interactions between an organized set of agents and to explore the structures that emerge through the formalization of complex situations where heterogeneous agents operate at various levels. This paper presents and discusses a framework of thought which articulates the relevant fields (empirical, conceptual, model) in a general way, and in the case of multi-agent systems. It then develops an analytical framework to capture the various uses of these systems, exploring in particular the methodological opposition between parsimonious models (KISS) and descriptive models (KIDS), which in fact reflect different stages in scientific investigation. Finally, it uses this framework and grid to analyse several examples from sociology, economics and geography (residential segregation, educational inequality, the emergence of norms, market operation, urban hierarchy) and concludes with methodological proposals based on an abductive approach to the use of multi-agent systems in social science.
L’objet de cet article est de presenter quelques reflexions sur ce mouvement de la science, qualifie de « finance scientifique » par ses promoteurs, en mettant l’accent sur les differences qui la distinguent tant de la finance traditionnelle qui l’a precedee, que des enjeux contemporains ; cet essai de comparaison etant effectue a la lumiere de l’actuelle crise financiere mondiale dont l’ampleur et les dereglements qu’elle decele nous amenent a nous demander si l’analyse de la crise financiere qui est souvent demandee par l’opinion ne reflete pas plutot une crise de l’analyse financiere. Dans un premier temps, nous dresserons un tableau des traits qui nous paraissent caracteriser la « finance scientifique », en en mettant en relief les principales caracteristiques. Dans un second temps, nous illustrerons cette analyse en prenant comme exemple la crise dite des « subprimes », laquelle – comme on le sait – a ete le fait declencheur de la crise bancaire, boursiere et economique mondiale. En conclusion provisoire, sous forme de propos d’etape, nous evoquerons le souhait de voir emerger un nouveau paradigme en finance et son corollaire : la necessaire reforme de la formation des financiers.
Investigations into the patterns of schizophrenia reveal evidence of scaling properties in temporal behaviour. This is shown in the spectral properties of mid-range and long-range (up to two years) daily recordings from a sample of patients drawn at the therapeutic dwelling SOTERIA (Ambühl et al., in: Springer Series in Synergetics, Vol. 58, eds. Tschacher et al. (Springer, Berlin, 1992) pp. 195–203 and references therein) of the Psychiatric University Hospital in Bern. The therapeutic setting is unique in that it tries to avoid treatment by medication.Power law behaviour has been found within fractal walk analysis and Fourier spectra for the daily fluctuations. A simple dynamic principle, based on a generic intermittency model, is put in relation to these time series thus predicting an additional scaling law for the distribution P(T) of time spans T between successive hospitalizations. Testing this hypothesis with our data shows only insignificant deviations. A possible role of this dynamic principle in the risk assignment of psychotic phases is explored with the help of an example.
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