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HELP Moving Average Proof

  • Thread starter neznam
  • Start date
  • #1
15
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Please any help will be greatly appreciated.

Suppose that a simple moving average of span N is used to forecast a time series that varies randomly around a constant mean, that is yt=m (m-mean and yt is y sub t). At the start of the period t1 the process shifts to a new mean level, say, m+b. Show that the exepected value of the moving average is
m when T<=t1-1
m+b-(t1+N-1)b/n when t1<=T<=t1+N-2
m+b when T>=N

I can prove 1st and the last part I am just really confused on the 2nd part--is that condition supposed to be t1<=T<=t1+N-1. Otherwise aren't we missing values if we have N-2??? I am sure I am missing something but I don't know what. PLEASE any suggestions will help.

Thanks
 

Answers and Replies

  • #2
EnumaElish
Science Advisor
Homework Helper
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What's the lowercase n in the denominator?
 
  • #3
15
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Sorry it is not lower case n --just the same upper case N
 
  • #4
15
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m+b-(t1+N-1)b/N when t1<=T<=t1+N-2
 
  • #5
K^2
Science Advisor
2,469
28
You sure it's not m+b-(t1+N-1-T)b/N? EnumaElish found a clear error in your formula, and this is one I'm getting by working out the problem.
 

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