By Edgar E. Peters
A number one pioneer within the box deals functional purposes of this leading edge technology. Peters describes complicated suggestions in an easy-to-follow demeanour for the non-mathematician. He makes use of fractals, rescaled variety research and nonlinear dynamical types to provide an explanation for habit and comprehend expense hobbies. those are particular instruments hired by means of chaos scientists to map and degree actual and now, financial phenomena.
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Extra resources for Fractal Market Analysis: Applying Chaos Theory to Investment and Economics
2 Dow jones Induslrials, Regression Resul ts, Te rm Structure of Volatility: 1888- 1990 Regression out put; Cons tan t Standard error of Y (estimated) R squared Numbe( of ob5ervatioos Degrees 01 freedom X coefficient(s) Standard error of coefficieot t N .. 996032 0. 097666 8 1 h ilul"1! ln 3D H ypnlh~s inves tors incur more fi sk than is implied by the no rmal distribut ion for inves tment ho rizons of less than four years. Howeve r. investors incur inc reasingly less risk fo r inves tme nt horizons g rea te r th an four yea rs.
However. we can see- less convincingly. to be sure- a term str ucture of bond volatility that is simil ar to the one we saw for stoc ks. s. Currencies For cu rrenc ies. we face sim ilar da ta problems. Until the Bretton Woods ag ree me nt of 1972, exchange rates did nol fl oat ; they were fixed by the respect ive governments. From 1973 onward, howeve r, we have plent y of inform ation on many different. acti vely traded exchange rates. 5, we saw that the yen/dollar exchange rate had the now familia r fa t·tailed distribution.
Olher capilal markels show similar characteristics. These fal-Iailed di st ribUlions are often evidence of a 20 15 en '10 5 Normat- ·5 .. 5 197 1- 1990. year US. T·Bond y:elds. frequency distribulion of returns: 1979-1992 . long. memory system generated by a nonlinear stochast ic process. This non· linear process can be caused by time·varying variance (ARCH), or a long. memory process called Pareto-Levy. In due course, we will discuss both. At this point , we can simply say that fat-tailed dist ribut ions are oft en symp· tomatic of a non linear Slochastic process.