I have a problem right now at work. For certain business segments, some sales target are established each year. These targets are established based on the managers feelings. It's like this:

Manager: "so we grew 10% last year"
Employee: "yes, economic conditions where good"
Manager: "ok I feel this year we can grow 8%"

I'm currently analysing if this forecast tends to be too low and if that is one of the reason why managers tend to grow a lot more than initial target.

But when I showed that we are getting marks 130% over target on average. Managers just says it was because those years economic conditions where much more favorable than what they expected when the target was set. Which is kind of true, but that doesn't necessarily mean over performance is strictly cause favorable economic conditions. How could prove if this is true, what model could I use to try to isolate the effect of economic growth on sales target? I already try to explain variability on target growth using time series (ARIMA model). And economic inputs tend to be significant and tend to have positive significant parameters but what does this tell me?

How can I explain variability in target result in one year based on economic variability? If I can say that only a small part of target variability is explained by variability on economic growth I could argue that target might be too low. But how do I implement this analysis. It sound like I'm looking for some kind of R squared but I'm not sure how to make it from time series data.


This forecast problem seems to stem from your perception of what forecasting might achieve.

If we were to estimate the next seasons Champions League winner, knowing only that Real won in 2016, we will probably perform poorly.

However, if we follow player moves, understand coaching changes and the performance of each constituent team in a smaller league or higher frequency games, we may be able to add this to our forecasting decision.

Possibly the use of data harvesting and surveys in your business may prevent the stab-in-dark performance marks. Maybe business school can help...

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My first thought is that it depends a lot on what resources are available. Without knowing more, it's impossible to provide any specific advice regarding model selection... unless, of course, you're willing to go model-less.

If I were given this problem, my first impulse would be to do a peer comparison of annual growth. Since a peer group should respond to similar macro-economic inputs in similar ways, the relative normalized difference should be indicative of whether any out-performance is due to firm-specific factors (e.g., good management; good strategy; good sales people; a superior product; etc..).

I presume isolating firm specific factors is indeed your goal.

If so, and if I had access to a relevant peer group's revenue data, I could simply difference the annualized logarithmic growth rates over some number of years to arrive at an excess growth rate. Logs are generally appropriate for non-negative top-line numbers. I.e.,:

$\mathbb{E}[\Delta g] = \sum_n^N (\ln(S_{a,n}) - \ln (S_{a,n-1})) - (\ln(S_{M,n}) - \ln (S_{M,n-1})) \frac{1}{N}$


$\Delta g$ is the excess logarthmic growth rate of company $a$'s revenues versus a peer group aggregate's ,$M$.

The peer group's revenues, $S_M$, are simply an aggregation of its constituents.

The resultant metric, $\Delta g$, could then be standardized in any numerous ways. For example, a vector of annual excess growth rates could be fitted to a line from whence r-squared might come into play. Also, the metric over its standardized error, $\frac{\mathbb{E}[\Delta g]}{\sqrt{\mathbb{E}[\Delta g]^2}}$, would provide a standardized score. Presuming normality, this score could be fed into a cumulative density function to give a p-value for how likely your firm's out-performance is due chance versus its peer group. The assumption here being that statistically significant out-performance is more likely to persist going forward, vis-a-vis, a "forecast".

I personally favor this sort of weak model approach over standard econometric approaches because the amount calibration and parameterization required is effectively zero. To paraphrase a common axiom, "it's better to have a weak model which is approximately right than a strong one which is exactly wrong".

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