Finding Repetitive Patterns in Economic Data

Date: 28 Jan 1995 14:14:55 -0500
From: Joe Fleming
Subject: Finding Repetitive Patterns in Economic Data

Subject: Locating specific curve patterns in plottable data

In classical music there are repeated themes and/or 
sub-themes. If one looks at the music notations on paper, 
"patterns" are seen.

In historical economic information there may be repeated 
"waves." If one looks at government financial data, 
"patterns" are seen.

What branch/subset of mathematics do I need to learn so 
that I can write computer software that will identify 
and/or search pairs of data for specific patterns?

Can you recommend a good source for the information I need 
to study?

If the data pair is time and a value, is there a way to pick a 
pattern in one set of time periods and then ask a computer 
to locate the same pattern in other time periods?

I have vague memories of an nth order equation defining 
the relation between a dependend and independent variable 
as an approximation to the absolute definition of the 
relation between two variables.  Perhaps using n+1 
equations in n unknowns to solve for the coefficients of the 
powers of the independent variable?

I also have vague memories that perhaps Fourier 
Transformations can be used to combine together the sines and 
cosines of a set of angles to model a curve.

(I am not a K-12 student.  I am a 57-year-old retired computer 
programmer so I will understand if you think I should not be 
sending this note to you.  Thank you for whatever efforts you 
may choose to make in response to this note!)

I am quite fascinated that "Electronic Assisted Learning" 
exists.

Joe Fleming

Date: 31 Jan 1995 00:43:15 GMT
From: Dr. Math
Subject: Re: Finding Repetitive Patterns in Economic Data

Hey Joe,

Here is what I can give you that somebody sent in to help us answer 
your question, which was a little beyond our capacity:

     The subject is the analysis of "time series." In mathematics,
     it's most often considered part of statistics, but there are many
     in fields other than mathematics (though of course they can all be
     seen as mathematical). Economics is one of the big ones, and I'm
     sure Dr. Math can turn up a few books about time series analysis
     of economic data specifically.

     One of the hot trends on Wall Street now is to do time series
     analysis with neural networks.

       	 Jay

I hope that helps.  I looked in our library and found a pretty basic
textbook explaining time series analysis.  It is _The Analysis of Time
Series:  Theory and Practice_, by Chistopher Chatfield.

Ethan, Dr. On call