My first exposure to statistical analysis was from the marvelous book Chaos Theory Tamed by Garnett P. Williams. This book explores chaotic systems, systems that are organized by clearly defined rules yet have seemingly-random behavior and are highly sensitive to initial conditions. In this book he explored many of the fundamental techniques I apply to analyzing time series models such as stationarity checks, analysis for seasonality, periodicity, and trend.
The idea behind chaos theory is looking for trends in information, finding clues that indicate there is a pattern behind the data rather than just random noise. And this technique applies to many other branches of statistical analysis. One of the main goals in modelling is determining if there is some predictability in variables or if they have no effect on one another. Finding these correlations is vital to developing proper models.
Chaotic behavior is often found in places like fluid dynamics and hypothesized to be in systems as complex as the stock market. It is an incredibly interesting phenomena that demonstrates many of the interesting features of statistical modelling.
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