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Can a moving average value result be higher than the highest constituent value on which the moving average is based?

I realize that somewhere here there maybe an answer, but I have been unable to find one specific to this question. I do not believe that a "moving average value result" based on a set of values over the moving time period specified (such as the previous 4 weeks sales) can be higher than the individual highest constituent sales total that is one of the values considered in the moving average calculation. Am I right here?

Thank you.

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    $\begingroup$ You are indeed correct under certain assumptions. The answer depends on (a) how the moving average is started and (b) the coefficients in the average. What can you tell us about them? Could you give us the specifics of the moving average algorithm you are actually using? $\endgroup$ – whuber Jan 10 '14 at 15:35
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    $\begingroup$ Daily Net Margin: 11, 12, 13, 14, 15, 16, 17 First day of 5-day Simple Moving Average: (11+12+13+14+15) / 5 = 13 Second day of 5-day Simple Moving Average: (12+13+14+15+16)/5 = 14 Third day of 5-day Simple Moving Average: (13+14+15+16+17)/5 = 15 $\endgroup$ – user37134 Jan 10 '14 at 16:31
  • $\begingroup$ Thank you all for your input. I forgot to mention that I was calculating what I thought to be a simple moving average. But, also, I believe that calculating, say, for instance, a moving block of the previous 4 weeks average is still a simple moving average, and advance by each week passing, but is calculated over the new set of 4 weeks. $\endgroup$ – user37134 Jan 10 '14 at 16:33
  • $\begingroup$ The question comes up as a result of the following calculation claimed to be a moving average: Assumptions: 4 weeks = 28 days; Total GM for January based on daily values -- Calculation employed: (TotalGM For January)/28*31(days in January) = moving average last 4 weeks. This is claimed to be a moving average. Does this calculation make sense? Thank you. $\endgroup$ – user37134 Jan 10 '14 at 16:41
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yes . for example the model y(t)=constant + y(t-1) can provide a forecast that may be greater than any observed value. Additionally ARIMA models can often suggest increasing values with an ultimate change point or assymptote.

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    $\begingroup$ I suspect your understanding of "moving average" (as a time series model) may differ from the OP's understanding (which might be the more ordinary sense of a moving-window weighted average). $\endgroup$ – whuber Jan 10 '14 at 15:36

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