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Re: Need evaluation of example method for forecasting
random-numbers.
Posted:
Jan 24, 2005 8:19 AM
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socraticquest wrote:
> I've been experimenting with a method for forecasting random numbers.
> I've provided an example of this method. Are similar methods in use?
> What downloads are available?
I guess you're trying to forecast random numbers that have some bias or are
correlated in some way. For example maybe you are trying to forecast
tomorrow's temperature.
> Take a random sequence of twenty numbers ranging from 1 to 20. The
> objective is to predict a twenty-first number.
>
> In trials, resulting predictions are often plus or minus one-away from
> the twenty-first occurring number.
I take this to mean you are allowing an error tolerance of plus or minus
one.
> Random number sequence:
> 20,13,16,2,11,13,12,6,3,13,12,13,11,17,3,2,14,17,13,16
>
> Next, take numbers 1 to 20 and list in descending numerical order 20,
> 19,18,17,16 etc.
>
> The reason for listing the numbers in descending order is that the
> majority of numbers are over the median number (10) in the 1 to 20
> range in the above number sequence. If the majority of numbers were at
> or under the median number of (10), then a listing of numbers in
> ascending order would be used.
>
> The objectives of using ascending or descending numbers is to get an
> analysis which may best reflect the 'randomness' of the number
> sequence for subsequent forecasting.
>
> Next, the descending order of numbers (N) are listed after each of the
> twenty random numbers. The objective here is to use each random number
> (RN) as a "seed of sorts." The routine has (RN) becoming (N). This
> subsequent (N) contains an (RN) value that is tallied. For reference,
> the tallied (RN) can be listed as (TRN)
>
> Listed as / (RN or TRN)-(N) /: 20-20 / 13-19 / 16-18 / 2-17 / 11-16 /
> 13-15 / 12-14 / 6-13 / 3-12 / 13-11 / 12-10 / 13-9 / 11-8 / 17-7 / 3-6
> / 2-5 / 14-4 / 17-3 / 13-2 / 16-1
>
> Example: (RN) 20 equals (N) 20 that is (TRN) 20. Number 20 is tallied.
> // (RN) 13 equals (N) 13 that is (TRN) 6. Number 6 is tallied. // (RN)
> 16 equals (N) 11 that is (TRN) 13. Number 13 is tallied //. This
> process is repeated until (RN) 16 equals (N) 11 that is (TRN) 13.
> Number 13 is tallied.
>
> Here are the tallies: Listed as (TRN)-(final tallies) (Numbers in
> sequence that received zero tallies are not noted) 2-2, 3-2, 6-1,
> 11-2, 12-2, 13-5, 14-1, 16-2, 17-2, 20-1. The projected twenty-first
> number (based on frequency) is 13 plus or minus one. The actual
> occurring number was 12.
I have a hard time understanding your description. But I think your
prediction for the 21st number is just the median of the first 20.
If that's what you are doing, you won't be correct very often. For example,
you'll never predict anything near the endpoints of the distribution, so
you'll never be correct if the actual number is 1 or 20 in your example.
Using the observed samples as an estimate of the underlying distribution,
you could improve upon your method (in terms of the chance of a correct
prediction) by picking the mode rather than the median. Actually you should
pick N such that the combined observations of N-1, N, and N+1 is the
highest.
Bob H
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