How Does a Shift in Mean Affect the Moving Average Calculation?

[neznam]

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

 

[EnumaElish]

What's the lowercase n in the denominator?

 

[neznam]

Sorry it is not lower case n --just the same upper case N

 

[neznam]

m+b-(t1+N-1)b/N when t1<=T<=t1+N-2

 

[K^2]

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.