Resul Expression of the Time Series Prediction with GP

[andrew.kirillov]

What is the relationship between constants and the time series functions?

The time series function, which is found by GP algorithm, will consist of past values (like x[t-1], x[t-2]) and constants which you've specified. As you've already seen before, one of the solutions for one of the time series you had was x[t-1] + 2, where "2" is a constant selected from the list you gave.

why do we have these specific numbers as constants?

You can actually choose any numbers you like. Just keep in mind that you specify limited amount of constant, so you better choose those, which can be used to easily create other possible constants. For example, suppose you have a time series like x[t-1]+6. As you can see from the code, "6" is not in the list of constants. But GP algorithm can create it quite easily using "2*3", which are available. Of course there are some functions available, like ln, sin, cos, exp, etc., which can be also used in GP expressions.

[dobdo99]

Andrew many thanks

I just thought it was a "magical property" of prime numbers! or is that just coincidence?
sorry for the real basic questions:
I'm an empirical guy, I Like to "do", "to prove" manually.

I'm trying to return the predicted next value in the sequence using:

variables = data []
string function = "$6 $0 +";
double ret = PolishExpression.Evaluate(function, variables);

Where do the constants come into this? or is there another function? or do I need to write my own?

Or...................... I think I have got it wrong again!

[vincenzodentamaro]

So Andrew let me know if I understood correctly...
With a window size equals to 5, all variables that starts from $5 and up are constants, where $5 is the first previously declared constant and so on..

Instead,
$0 = X(t - 1)
$1 = X(t - 2)
$2 = X(t - 3)
$3 = X(t - 4)
$4 = X(t - 5)

But X(t - 1) means x*(previous value - 1) ??
Am I wrong??

Thank you

[andrew.kirillov]

But X(t - 1) means x*(previous value - 1) ??
Am I wrong??

If you are doing prediction of X(t) value of a time series, then X(t-1) means previous value of the time series.

[vincenzodentamaro]

Ok thank you!!