I need to estimate cumulative earnings over the next Y years and I'd like to find a solution that is theoretically sound and relatively simple. Can anyone recommend an approach?
I have 30 years of historical monthly earnings.
If you want a generic mechanical approach, try to build a time-series model. A log-linear trend model or building an auto-regressive model such as ARMA (on a stationary) series would probably work. As a start point I would plot the data to see what features you notice (seasonality? exponential growth? mean-reversion? trend? one-off shocks?)
Note that securities analysts forecasts are better than these time-series models. Also these time-series models would have limited ability to extrapolate beyond a couple k-step ahead periods. So if you need cumulative out-of-sample earnings in years and your training data is in months, you will have low confidence in your prediction.
There is a rich academic history of using such models used to forecast quarterly earnings although that doesn't mean it's a great trading strategy.
Most of these models would be very industry specific, but there is never going to be a default way to estimate earnings. Banks are very descriptive of these earnings models. I would start with an industry report and go from there.
This is a serious task to do for one company. Much more so than I think you realize.
The most common model is...."Next year's earnings will be this year's earnings plus some percentage (an exponential trend)". Why?
Look closely at the process that generates an earnings number.
Earnings = Sales - Costs
Let's start off by assuming that you can estimate
Sales with 100% accuracy. And, let's assume that you can estimate
Costs within +/- 5% (not likely, but let's use this anyway). If
Costs are typically 90% of
Sales (a 10% profit margin), then the +/- 5% error in
Costs gives you an
Earnings Estimate that is 5% to 15% of
Sales. That's an
Earnings spread based on
Earnings of -50% to +50% (for a +/-5% error in
Costs). As you can imagine, a higher uncertainty in
Costs plus the uncertainty in
Sales can drive that
Earnings Estimate spread to some really big numbers.
So, it turns out that you'll be lucky if you can estimate an
Earnings exponential trend.
One other thing to keep in mind. The smaller the company, the more ridiculous the
Earnings Estimates. And, estimating the
Earnings of the S&P500 beyond an exponential trend, the easiest of all estimates, is by no means easy.
If you want to try some schemes on various companies, here's some data:
Here's some S&P500 data:
From your question, to get cumulative
Earnings over some time period, you simply add up the
Earnings for that time period.
I agree with @Quant Guy's answer. His approach should definitely be the first thing you try, and you should also heed his warning regarding the low confidence when forecasting out many years.
I would only add that if you have data for more companies available, even if your goal is to only estimate the earnings for one company, you can improve your estimate further with a vector auto-regression (VAR). Better yet, you can estimate relationships between this firm and its industry average earnings and add a term for convergence of this firm's growth rate to the industry average. ARMA estimates will also probably be better on aggregates such as industries/sectors.