The cumulative mean. In the naive method, we assumed that only the last piece of information is useful in predicting the future, but what if we think that all prior data is useful in our forecast? That is the idea behind the cumulative mean. We take all of the data that we have, average it, and that is going to represent our forecast.

0:24

Now let’s look at the math. The cumulative mean is, again, denoted by F sub t, which is what we’re trying to forecast. And that is made up of the sum of demand, and that sum is going from the very first period we have, I=1, all the way to T-1, which is the very latest time period we have available.

0:52

And we are going to divide that by how many periods we had summed together and that would be t-1, and that gives us an average over all periods. So what this means on time frame is, if we are right here at t, then we are going to average all the demand from the prior periods and make that our forecast right here, a time t. So, how good is the cumulative mean? Well, it may work well in some situations and it’s really the antithesis to the naive method. Where’s the naive method? Was it very responsive, but also picked up a lot of noise? This forecast is very stable and averages out all the noise, so it really filters it out.

1:49

If you have a situation where your overall demand is built only by the level and noise, no other patterns, then this is a good forecast to use.

2:03

And advantage is, as I said, it’s stable. But it also may not recognize all the pattern, and you need to be careful how to use it.

2:13

The big assumption in the cumulative mean is that all prior data is equally useful. That may not be very robust, but it is the assumption. And there are other methods that may take into account that flaw in the cumulative mean.

# 5. The Cumulative Mean

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