In a cumulative moving average, the data arrive in an ordered datum stream and the statistician would like to get the average of all of the data up until the current datum point. For example, an investor may want the average price of all of the stock transactions for a particular stock up until the current time. As each new transaction occurs, the average price at the time of the transaction can be calculated for all of the transactions up to that point using the cumulative average, typically an unweighted average of the sequence of i values x1, ..., xi up to the current time:
The brute-force method to calculate this would be to store all of the data and calculate the sum and divide by the number of datum points every time a new datum point arrived. However, it is possible to simply update cumulative average as a new value xi+1 becomes available, using the formula:
where can be taken to be equal to 0.
Thus the current cumulative average for a new datum point is equal to the previous cumulative average plus the difference between the latest datum point and the previous average divided by the number of points received so far. When all of the datum points arrive (i = N), the cumulative average will equal the final average.
The derivation of the cumulative average formula is straightforward. Using
and similarly for i + 1, it is seen that
Solving this equation for CAi+1 results in:
Read more about this topic: Moving Average (technical Analysis)
Famous quotes containing the words cumulative, moving and/or average:
“But while ignorance can make you insensitive, familiarity can also numb. Entering the second half-century of an information age, our cumulative knowledge has changed the level of what appalls, what stuns, what shocks.”
—Anna Quindlen (b. 1952)
“and the deaf soul
struggles, strains forward, to lip-read what it needs:
and something is said, quickly,
in words of cloud-shadows moving and
the unmoving turn of the road, something
not quite caught ...”
—Denise Levertov (b. 1923)
“The average Kentuckian may appear a bit confused in his knowledge of history, but he is firmly certain about current politics. Kentucky cannot claim first place in political importance, but it tops the list in its keen enjoyment of politics for its own sake. It takes the average Kentuckian only a matter of moments to dispose of the weather and personal helath, but he never tires of a political discussion.”
—For the State of Kentucky, U.S. public relief program (1935-1943)