Kaos analizi: Bir finansal sektör uygulaması /
Yazar: CAFER ERCAN BOZDAĞ
Danışman: PROF. DR. MEHMET HALUK ERKUT
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Endüstri Mühendisliği Ana Bilim Dalı
Derece: Doktora, 1998
Konu: Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering
Dizin: Kaos = Chaos

Özet:
ÖZET Doğrusal olmayan dinamikler, bir alt kümesi olan kaos teorisinin hızla gelişmesi ve popüler olması ile, dünyaya bakış açımıza yeni bir pencere açarak, yeniden gündeme gelmiştir. Kaos teorisi, yaşayan sistemlere getirdiği anlayış ve yaklaşımlarla, bilimde yeni bir paradigmanın doğuşu olarak nitelendirilmektedir. İkiden fazla gezegenin kütle çekimlerinin belirlediği makro düzeydeki davranıştan, beyin sinir hücrelerinin mikro düzeydeki davranışına, ekonomide pamuk fiyatlarındaki dalgalanmalardan kriz sırasında kalp atışlarında görülen dalgalanmalara, canlıların evrimleşmesinden, gaz içindeki moleküllerin evrimleşerek lazer ışınını oluşturmasına kadar değişik boyutlardaki bir çok örnekte kaosun gizlediği açık izlere rastlanmaktadır. Kaos teorisi, bilimsel anlayışımıza olduğu kadar yaşam felsefemize, dünya görüşümüze ve düşünce geleneklerimize karşı onları yeniden gözden geçirmemizi sağlayacak kadar güçlü eleştirel bir saldın başlatmıştır. Artık mekanistik dünya görüşünün, süprize ve bilinmezliğe yer olmayan cansız ve ruhsuz yaklaşımının yerine, neden sonuç arasındaki ilişkilerin koptuğu, geleceğin kestirilemediği, değişen ve evrimleşen bir dünya ile karşı karşıyayız. Hükmetme ve sömürmeye yönelik bilimsel anlayış, doğanın çeşitliliği karşısında onu anlamaya, güzelliklerini yeniden keşfetmeye yönelik bir anlayışa yönelmektedir. Bu çalışmanın ilk iki bölümü, dinamik sistemlere ve dinamik sistemlerin ilgi çekici bir sınıfı olan doğrusal olmayan dinamik sistemlere ayrılmıştır. Doğrusal olmayan dinamik sistemler, içlerinde doğal olarak varolan büyütme mekanizmaları ile kararsızlık yaratabilirler. Bu kararsızlığın ve dengesizliğin içinden kaotik davranışlar doğabilmektedir. Çalışmanın üçüncü bölümü kaos teorisine ve bilime getirdiği yeni yaklaşımlara ve kavramlara ayrılmıştır. Aynı bölümde kaos teorisi teknikleri olan korelasyon boyutu ve Lyapunov üslerinden söz edilmektedir. Dördüncü bölüm finansal sektörlerde uygulama alam bulan ve rassal yürüyüş varsayımından sapmaların bulunmasında kullanılan bir teknik olan R/S Analizi'ne ayrılmıştır. Çalışmanın beşinci bölümünde, uygulama alam olarak İstanbul Menkul Kıymetler Borsası alınmış, R/S Analizi ve Kaos Analizi ile incelenmiştir. Sonuçlar ve Öneriler bölümünde, analizler sonucunda elde edilen bulgular sıralanmış ve gelecekteki çalışmalara yönelik öneriler verilmiştir.

Abstract:
CHAOS ANALYSIS: AN APPLICATION OF FINANCIAL SECTOR SUMMARY For more than two centuries Newton's laws reigned supreme as the ultimate description of nature. Newton's law of gravity is a simple thing. Every two particles of matter in the universe attract each other, with a force that depends in a precise and simple manner on their masses and on the distance between them. The law can be condensed into a brief formula in algebra. When coupled with another of Newton's laws, this time the law of motion (the acceleration of a body is proportional to the force acting on it) it explains a wealth of astronomical observations ranging from the paths of the planets through the Zodiac to the wobbles of the Moon on its axis, from the resonant lacking of Jupiter's satellites to the light-curves of binary stars, from the gaps in Saturn's rings to the birth of galaxies. In the microscopic domains of the atom and the vast reaches of interstellar space, Newton has been displaced by quantum mechanics and relativity. But Newton's message remains constant: Nature has law, and we can find them. Newton sought nothing more nor less than 'the system of the world!': The theory of everything. The revolution in scientific thought that culminated in Newton led a vision of the universe as some gigantic mechanism, functioning 'like clock work', a phrase that well still use. In such a vision, a machine is above all predictable. Under identical conditions it will do identical things. Newton cast his laws in the form of mathematical equations, which relate not just quantities, but also the rates at which those quantities change. The key principle is that the solution of the equations describing the motion of same dynamical system in unique if the initial positions and velocities of all components of the system are known. This statement assumes, for simplicity, that there is no outside influence on the motion. The positions and velocities of every particle of matter in the entire universe, taken at same fixed instant, completely determine its future evolutions. The universe follows a unique, predetermined dynamical path. In the eloquent words of Pierre Simon de Laplace: an intellect which at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before its eyes.But such a machine is only capable of functioning, not of evolving. It cannot restructure itself or insert new cogs and wheels. But reality can. We can always picture a system in terms of typical components with typical interactions occurring between them. But this picture will lack the evolutionary potential that exists in real life. Evolution, then, can be said to depend on the effects of nonaverage values- fluctuations of variables and parameters, and on changes introduced by the microscopic diversity. Whether endogenous mechanisms or exogenous stochastic is the main cause of fluctuations in living systems? A stochastic approach seems to be convenient for describing the fluctuating behavior. The problem with stochastic models, however, lies in the fact that random noise with finite delay terms only explains the short-term fluctuating behavior. Actual, fluctuations may be caused by both intrinsic mechanism and external shocks. An alternative to the stochastic approach, with a large number of variables and parameters, is deterministic chaos, with a few variables or low-dimensional strange attractors. Prigogine criticized science: "What for generations had been a source of joy and amazement withers at its touch. Everything it touches is dehumanised. The echoes of another leitmotiv-domination-mingle with that of disenchantment. A disenchanted world İs, at the same time, a world liable to control and manipulation. Any science that conceives of the world as being governed according to universal theoretical plan that reduces its various riches to the drab applications of general laws thereby becomes an instrument of domination. And man, a stranger to the world, sets himself up as its master." Prigogine explains what lay behind the enthusiasm of Newton's contemporaries, their conviction that the secret of the universe, the truth about nature, had finally been revealed: "Several lines of thought, probably present from the very beginning of humanity, converge in Newton's synthesis: first of all, science as a way of acting on our environment. Newtonian science is indeed an active science, one of its sources is the knowledge of the medieval craftsmen, the knowledge of the builders of machines. The science provides the means for systematically acting on the world, for predicting and modifying the course of natural processes, for conceiving devices that can harness and exploit the forces and material sources of nature". Economists and other social scientists had long ago gotten the idea that their field had to be as "scientific" as physics, meaning that everything had to be mathematically predictable. Was Darwing unscientific because he could not predict what species would evolve in the next million years? Are geologists unscientific because they can not predict precisely where the next earthquake will come, or where the next mountain range will rise? Are astronomers unscientific because they can not predict precisely where the next star will be born? XlllNot at all. Predictions are nice, if you can make them. But the essence of science lies in explanation, laying bare the fundamental mechanisms of nature. Self-organizing structures are ubiquitous in nature. A laser is a self-organizing system in which particles of light, photons, can spontaneously group themselves into a single powerful beam that has every photon moving in lockstep. A hurricane is a self-organizing system powered by the steady stream of energy coming from the sun, which drives the winds and draws rainwater from the oceans. A living cell-although much too complicated to analyze mathematically - is a self-organizing system that survives by taking in energy in the form of food and exerting energy in the form of heat and waste. In fact, it is conceivable that the economy is a self-organizing system, in which market structures are spontaneously organized by such thing as the demand for labor and the demand for goods an services. Self-organizing depends upon self-reinforcement: a tendency for small effects to become magnified when conditions are right, instead of dying away. This is called positive feedback in engineering. Positive feedback seemed to base of change, of suprise, of life itself. Positive feedback is precisely what conventional economics did not have. Neoclassical theory assumes that the economy is entirely dominated by negative feedback: the tendency of small effects to die away. The dying-away tendency was implicit in the economic doctrine of "diminishing return": the idea that the second candy bar does not taste nearly as good as first one, that twice the fertilizer does not produce twice the yield, that the more you do of anything, the less useful, less profitable, or less enjoyable the last little bit becomes. Indeed, negative feedback/diminishing returns is what underlies the whole neoclassical vision of harmony, stability, and equilibrium in the economy. But now, positive feedback/increasing returns maybe those things did happen in the real economy. Maybe they explained the liveliness, the complexity, and the richness in the real-world economy all around us: Consider the Beta versus VHS competition in the mid- 1970 s, Even in 1979 it was clear that the VHS videotape was well on its way to concerning the market, despite the fact that many exports had originally rated it slightly inferior to Beta technologically. How could this have happened? Because the VHS vendors were lucky enough to gain a slightly bigger market share in the beginning which gave them an enormous advantage in spite of the technological differences: the video stones hated having to stock everything in two different formats, and consumers hate the idea of being stuck with obsolete VCRs. So everyone had a big incentive to go with the market leader. That pushed up VHS's market share even more, and the small initial difference grew rapidly. XIVChaos is the term used to describe the apparently complex behaviour of what we consider to be simple, well-behaved systems. Chaotic behavior, when baked at causal, looks erratic and almost random-almost like the behavior, of a system strongly influenced by outside, random noise or the complicated behaviour of a system with many, many degrees of freedom, each "doing its own thing", The type of behavior, however, that in the last 10 years has come to be called chaotic arises in very simple systems, which are almost free of noise. In fact, these systems are essentially deterministic, that is, precise knowledge of the conditions of the system at one time allow us, at least in principle, to predict exactly the future behavior of that system. The problem of understanding chaos is to reconcile these apparently conflicting notions randomness and determinism. The key element in this understanding is the notion of nonlinearity. We can develop an intuitive idea of nonlinearity by characterizing the behavior of a system in terms of stimulus and response: If we give the system a "kick" and observe a certain response to that kick, then we can ask what happens if we kick the system twice as hard. If the response is twices large, then the system's behavior is said to be linear. If the response is not twice as large then we say the system's behavior is nonlinear. The study of chaos has provided new conceptual and theoretical tools enabling us to categorize and understand complex behavior that had confounded previous theories. Chaotic behavior seems to be universal - it shows up in mechanical oscillators, electrical circuits, lasers, nonlinear optical systems, chemical reactions, nerve cells, heated fluids, and many other systems. Even more importantly, this chaotic behavior shows dramatic qualitative and quantitative universal features. These universal features are independent of the details of the particular system. This universality means that what we learn about chaotic behavior by studying, for example, a simple electrical circuit or simple mathematical models, can be applied immediately to understand the chaotic behavior of lasers and beating heart cells. In the past few years, a large literature has appeared on nonlinearity in finance and economics. At a theoretical level, it has been shown that even very simple economic models often involve a rich variety of dynamic processes, including in some cases the possibility of nonlinear or complex chaotic behaviour for some range of parameter values. More recently, the published empirical literature has concentrated on testing economic and financial time series for the presence of nonlinear dependencies using various measures indicative of complex dynamics. This study has addressed three major questions. Is there any long-term memory in Istanbul Stock Exchange (IMKB) individual stock returns? Is there a nonlinear structure in the process generating returns on the IMKB individual stock returns? And, if so, is there any evidence that the process may be chaotic? XVAbout %48.2 of individual stock returns are persistent time series and they follow a biased random walk. These stocks exhibit and they follow a based random walk. These stocks exhibits trend-reinforcing behavior, not mean-reverting behaviour. Higher values of Hurst exponent mean less risk, because there is less noise in the data. Most of the individual stock returns in IMKB have fractal dimensions between 2 and 4. This is good news, because it means that we should be able to model the dynamics of these stocks with three or four variables. We can model each of the stock returns in IMKB with low-dimensional nonlinear dynamic models. All of the individual stock returns have positive largest Lyapunov exponent. This implies that deterministic chaos maybe explanation of the exact nature of nonlinearities in IMKB. XVI