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:
“Knew her own mind. But the mind radically commonplace, only its inherited force, & cumulative sense of power, making it remarkable.”
—Virginia Woolf (1882–1941)
“The two most far-reaching critical theories at the beginning of the latest phase of industrial society were those of Marx and Freud. Marx showed the moving powers and the conflicts in the social-historical process. Freud aimed at the critical uncovering of the inner conflicts. Both worked for the liberation of man, even though Marx’s concept was more comprehensive and less time-bound than Freud’s.”
—Erich Fromm (1900–1980)
“The average educated man in America has about as much knowledge of what a political idea is as he has of the principles of counterpoint. Each is a thing used in politics or music which those fellows who practise politics or music manipulate somehow. Show him one and he will deny that it is politics at all. It must be corrupt or he will not recognize it. He has only seen dried figs. He has only thought dried thoughts. A live thought or a real idea is against the rules of his mind.”
—John Jay Chapman (1862–1933)