Mehmet Balcilar is Professor of Econometrics at Eastern Mediterranean University located in Famagusta, North Cyprus. For many years I have been doing research on time series and teaching time series courses.

Recently, my interest drifted towards long-memory and nonlinear time series models. This is also a reflection of a philosophical view and my understanding of the universe. Human history as well as what surrounds us are nonlinear and unpredictable.

The written human history is not unfortunately an accurate description of the our unprecedented past. Our history is a highly nonlinear process, full of numerous dead ends, and messy. Historians write summaries of this past and make it appear like a simple, straight line.

Nonlinearity and chaos are two linked terms. The word chaos is used in rather a vague sense by a lot of writers, but in mathematics chaos means an aperiodic deterministic behavior which is very sensitive to its initial conditions. Our history would have been quite a different one, if Napoleon did not lose at Waterloo or Archduke Franz Ferdinand had not been assassinated in 28 June 1914.

Chaos is the complexity of causality or the relationship between events. This means that any seemingly insignificant event in the universe has the potential to trigger a chain reaction that will change the whole system. A well known saying in connection with this issue is "A butterfly flapping its wings in one part of the world can cause a hurricane on the other side of the earth." This is also known as the butterfly effect. The banner of this page is a reflection of chaos arising from a nonlinear system.

Some nonlinear dynamic systems generate fractals which look chaotic. A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoit Mandelbrot in 1975 and was derived from the Latin fractus meaning broken or fractured. If you move over the mouse pointer on the bar the left of this text you will see a graphical representation of fractals. These graphical representations are generated using Fractal Studio for the Macintosh.



Professional CV
A Short Excursion on My Life
My old Reproducible Research Page
My Research
Teaching