How to predict a company's revenues without knowing anything about its business (Part 1 of 2)

Next Tuesday, HP announces its third quarter results. The following week, Dell releases its second quarter results. What revenues will the two companies announce? Pundits in Wall Street and beyond, many of whom spend a lot of time tracking these companies, will make their forecasts. First Call will produce a consensus of the estimates of the more respected analysts.

But here's a mechanical way to produce a forecast in which you need to know nothing about what the company does, its markets or its competitors. All you need to know are the company's revenue figures for the past six quarters. This is Time Series forecasting.

Introduction

Four-quarter moving averages tend to smooth out the irregularities in a company's quarterly performance. The graph below shows IBM's worldwide revenues in blue, and the four-quarter moving average of the revenues in red.




Note also that the moving average graph starts after the actual revenue graph—three quarters later, in fact. This is because the moving average is the average of the quarter in question and the previous three quarters.

Four-quarter moving averages look tantalisingly predictable. If we can predict the next quarter's value for the ''moving average'', then from that figure, we can derive a prediction for next quarter's ''revenue''. There is likely to be a degree of error, and if we repeat the process by predicting the following quarter by applying the formula to a set of numbers, one of which is a forecast—not an actual—we will compound the error and increase the inaccuracy. But most of the time, people only ask us to predict next quarter's revenues, and if we could do that with sufficient accuracy, we could make ourselves rich.

The Maths

If T_n is the Four-Quarter Moving Total in quarter n, then

where R_n is the revenue in quarter n.

And if A_n is the Four-Quarter Moving Average in quarter n, then simply

First-order Predictor

Assuming the next quarter's moving average is simply the continuation of the straight line from the previous quarter to the current quarter, then:

where P_n+1 is the predicted value of A_n+1.

So, rearranging the equation and substituting:

Assessing the Accuracy of the First-Order Predictor

When tested out on 660 quarterly revenue figures of IT vendors, going back to 2003, the average error generated by this formula was 6.8%.

Well, it's not the end of the world, but 6.8% is bigger than the annual growth many of these firms are achieving!

Tomorrow I'll describe a second-order predictor, whose accuracy is only a little better, and I'll demonstrate the accuracy of the formula that the Solver function within Microsoft Excel produces, when required to produce coefficients for a linear formula.