Decisions, Uncertainty, and All That
Fractals and Time Series Analysis
Volume 3, Issue 1
Robert J. Korsan
Over the past thirty years the branch of applied microeconomics known
as modern finance theory has developed and coalesced into the Capital Asset
Pricing Model. CAPM is founded upon the efficient market hypothesis,
which is represented mathematically as the assertion that financial time
series, especially series of log-returns, should be well approximated by
a random walk with increments drawn from a Gaussian or normal distribution.
Some of the most exciting work in mathematics today in fractals and chaos
theory shows that there are cracks in the foundation of CAPM. This column
will trace some of the research and provide Mathematica tools to
explore time series of log-returns. You can choose your favorite series,
analyze, and judge for yourself.