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
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