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I was wondering if anyone can provide some mathematical insights to forecasting the "SUM" in this link as a time series. It is an oscillatory, range bound and poisson distribution. How can Monte Carlo or other methods be applied?

http://sg.myfreepost.com/sgTOTO_analysispower.php?draws=60&fn0=notselected&fn1=notselected&fn2=Sum

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2 Answers 2

You cannot meaningfully forecast this: it is a random lottery draw. The best you can do is work out the probability of a particular sum.

As far as I can tell it is the sum of $7$ numbers sampled without replacement from $1$ to $45$. The minimum value is $28$ and the largest $294$. Ignoring the order in which the balls come out there are ${45 \choose 7}=45379620 $ possibilities (or $\frac{45!}{38!}=228713284800$ if you do take order into account).

As for the number of ways of getting a particular sum $s$, this is the number of partitions of $s$ into $7$ distinct parts each no more than $45$. You can use generating functions or recurrences to find this, but I already have a java applet to do this. For instance for the most likely outcome $s=161$ which turned up on 21 May 2012, choose

  • "Partitions with distinct terms of:" 161
  • "Exact number of terms:" 7
  • "Each term no more than:" 45

then click on "calculate partitions" to get the answer $554256$ and so a probability of $\frac{554256}{45379620} \approx 0.0122$.

The equivalent for a sum of $81$ as in 6 February was $\frac{23573}{45379620} \approx 0.0005$.

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Isn't Monte Carlo method used for forecasting brownian type bell curve distribution? –  shelagh May 23 '12 at 6:52
    
@shelagh: This is not a Brownian process. There is a bell-shaped curve though it is not exactly normal. A simulation will give you approximate estimates of the probabilities while the calculations above are exact. Your choice. –  Henry May 23 '12 at 6:54
    
Where can I find MC simulation in excel for this case? –  shelagh May 23 '12 at 6:57
    
If it is not really normal bell curve, then exact calculations may not be meaningful. –  shelagh May 23 '12 at 7:16
    
@shelagh: It is bell shaped but not precisely a normal distribution (in particular it is discrete and has a limited range). But since you can calculate the exact probabilities, that does not matter. –  Henry May 23 '12 at 7:37
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Regarding Monte Carlo Simulation in Excel, you might want to check this out: http://investexcel.net/670/geometric-brownian-motion-excel/

Not sure if it is directly applicable to your case, maybe others here can share their MC SIM resources(Excel or otherwise), I am curious too.

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Thanks but I am looking for something with forecasting (next value) feature not just MC simulation. –  shelagh May 24 '12 at 19:10
    
Well, maybe not next exact value, but rather a changing next period best 80 numbers moving range instead of always having 161+-40 as a fixed best range. And, I am not referring to moving average line or range. –  shelagh May 24 '12 at 19:30
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