Starting with an example, assume yesterday's close was above the simple 10D moving average: will today's close be below the 10D moving average?

Two things change from yesterday to today - today's close will be added to the series, and the close 10 days ago which was part of the moving average will be dropped (as it becomes 11 days ago).

C1 = today's close
C2 = yesterday's close
C10 = close 10 days ago
MAt = 10DMA as of today

MAt = sum(C10:C1)/10  (sum of C10 through C1)

The statement that "today's close < MAt " can be written

 C1 < sum(C10:C1)/10

10C1 < sum(C10:C1)

10C1 < C1 + sum(C10:C2)     ( Using: sum(C10:C1) = C1 + sum(C10:C2) )

9C1 <  sum(C10:C2)

C1 <  sum(C10:C2)/9

The right hand side is the 9 day moving average as of yesterday.

Thus today's close is below the ten day moving average if and only if today's close is below yesterday's 9 day moving average.


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