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

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Homework Help Overview

The discussion revolves around the impact of a shift in mean on the calculation of a simple moving average for a time series. The original poster presents a scenario where the mean of the time series changes from m to m+b and seeks clarification on the expected value of the moving average under specific conditions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the expected value of the moving average during a transition period when the mean shifts. They express confusion regarding the conditions for the second part of the expected value formula and question the implications of the range provided.
  • Some participants seek clarification on the notation used, specifically the variable in the denominator, and suggest corrections to the formula presented.

Discussion Status

The discussion is ongoing, with participants actively questioning the details of the formula and exploring potential errors. There is no explicit consensus yet, as different interpretations of the formula are being examined.

Contextual Notes

Participants are navigating through the implications of the moving average calculation under changing conditions, with specific attention to the notation and the range of values considered in the formula.

neznam
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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
 
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What's the lowercase n in the denominator?
 
Sorry it is not lower case n --just the same upper case N
 
m+b-(t1+N-1)b/N when t1<=T<=t1+N-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.
 

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