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From: flake@scr.siemens.com (Gary William Flake)
Subject: Re: Generating Time Series Based on Mackey-Glass Equation
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References: <1995Jul14.161030.1@v9001.ntu.ac.sg>
Date: Fri, 14 Jul 1995 13:47:34 GMT
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In article <1995Jul14.161030.1@v9001.ntu.ac.sg>,
 <ea1814168@v9001.ntu.ac.sg> wrote:
> Just a question regarding a popular time-series : The Mackey-Glass Equation.
> 
> This equation had been used extensively to test and evaluate the performance of
> various temporal-based NN models esp. in prediction. The common method to
> generate this series is to model the continuos equation using a difference
> equation as follows:
> 
> 	x(t+1) = x(t) + delta*[ -0.1x(t) + [ax(t-T)/(1 + x(t-T)^10)] ]
> 		where delta, a, and T are some constants.
> 
> To model the above using a difference equation, we have to specify the initial
> values of x(t) (eg. if T=30, we need x(0) and x(30) to find x(31)). The initial 
> values of x(t) are often not stated in the literature. Can someone give me a
> hint as to what their values might be.
> 
> Thank you.
> 
> P. B. Tan (NTU S'pore)
> 

The standard way is to set the x(0) through x(T) to the same single
random number.  You should probably throw away the first 500 points or
so.  (More for large T.)  The most common mistake made in computing
the MG series is that people treat it as a difference equation.  It's
not.  It's a delay differential equation, and you really need to
perform proper numerical integration with something like a Runge-Kutta.

I hope this helps.

Regards,
Gary Flake
-- 
Gary W. Flake,  flake@scr.siemens.com,  Phone: 609-734-3676,  Fax: 609-734-6565
Siemens Corporate Research,  755 College Road East,  Princeton, NJ  08540,  USA
