Category Archives: M-competition

Business Forecasting – Practical Problems and Solutions

Forecasts in business are unavoidable, since decisions must be made for annual budgets and shorter term operational plans, and investments must be made.

And regardless of approach, practical problems arise.

For example, should output from formal algorithms be massaged, so final numbers include judgmental revisions? What about error metrics? Is the mean absolute percent error (MAPE) best, because everybody is familiar with percents? What are plus’es and minus’es of various forecast error metrics? And, organizationally, where should forecasting teams sit – marketing, production, finance, or maybe in a free-standing unit?

The editors of Business Forecasting – Practical Problems and Solutions integrate dozens of selections to focus on these and other practical forecasting questions.

Here are some highlights.

In my experience, many corporate managers, even VP’s and executives, understand surprisingly little about fitting models to data.

So guidelines for reporting results are important.

In “Dos and Don’ts of Forecast Accuracy Measurement: A Tutorial,” Len Tashman advises “distinguish in-sample from out-of-sample accuracy,” calling it “the most basic issue.”

The acid test is how well the forecast model does “out-of-sample.” Holdout samples and cross-validation simulate how the forecast model will perform going forward. “If your average error in-sample is found to be 10%, it is very probable that forecast errors will average substantially more than 10%.” That’s because model parameters are calibrated to the sample over which they are estimated. There is a whole discussion of “over-fitting,” R2, and model complexity hinging on similar issues. Don’t fool yourself. Try to find ways to test your forecast model on out-of-sample data.

The discussion of fitting models when there is “extreme seasonality” broke new ground for me. In retail forecasting, there might be a toy or product that sells only at Christmastime. Demand is highly intermittent. As Udo Sglavo reveals, one solution is “time compression.” Collapse the time series data into two periods – the holiday season and the rest of the year. Then, the on-off characteristics of sales can be more adequately modeled. Clever.

John Mello’s “The Impact of Sales Forecast Game Playing on Supply Chains,” is probably destined to be a kind of classic, since it rolls up a lot of what we have all heard and observed about strategic behavior vis a vis forecasts.

Mello describes stratagems including

  • Enforcing – maintaining a higher forecast than actually anticipated, to keep forecasts in line with goals
  • Filtering – changing forecasts to reflect product on hand for sale
  • Hedging – overestimating sales to garner more product or production capability
  • Sandbagging – underestimating sales to set expectations lower than actually anticipated demand
  • Second-guessing – changing forecasts to reflect instinct or intuition
  • Spinning – manipulating forecasts to get favorable reactions from individuals or departments in the organization
  • Withholding – refusing to share current sales information

I’ve seen “sand-bagging” at work, when the salesforce is allowed to generate the forecasts, setting expectations for future sales lower than should, objectively, be the case. Purely by coincidence, of course, sales quotas are then easier to meet and bonuses easier to achieve.

I’ve always wondered why Gonik’s system, mentioned in an accompanying article by Michael Gilliland on the “Role of the Sales Force in Forecasting,” is not deployed more often. Gonik, in a classic article in the Harvard Business Review, ties sales bonuses jointly to the level of sales that are forecast by the field, and also to how well actual sales match the forecasts that were made. It literally provides incentives for field sales staff to come up with their best, objective estimate of sales in the coming period. (See Sales Forecasts and Incentives)

Finally, Larry Lapide’s “Where Should the Forecasting Function Reside?” asks a really good question.

The following graphic (apologies for the scan reproduction) summarizes some of his key points.


There is no fixed answer, Lapide provides a list of things to consider for each organization.

This book is a good accompaniment for Rob Hyndman and George Athanasopoulos’s online Forecasting: Principles and Practice.

Scalability of the Pvar Stock Market Forecasting Approach

Ok, I am documenting and extending a method of forecasting stock market prices based on what I call Pvar models. Here Pvar stands for “proximity variable” – or, more specifically, variables based on the spread or difference between the opening price of a stock, ETF, or index, and the high or low of the previous period. These periods can be days, groups of days, weeks, months, and so forth.

I share features of these models and some representative output on this blog.

And, of course, I continue to have wider interests in forecasting controversies, issues, methods, as well as the global economy.

But for now, I’ve got hold of something, and since I appreciate your visits and comments, let’s talk about “scalability.”

Forecast Error and Data Frequency

Years ago, when I first heard of the M-competition (probably later than for some), I was intrigued by reports of how forecast error blows up “three or four periods in the forecast horizon,” almost no matter what the data frequency. So, if you develop a forecast model with monthly data, forecast error starts to explode three or four months into the forecast horizon. If you use quarterly data, you can push the error boundary out three or four quarters, and so forth.

I have not seen mention of this result so much recently, so my memory may be playing tricks.

But the basic concept seems sound. There is irreducible noise in data and in modeling. So whatever data frequency you are analyzing, it makes sense that forecast errors will start to balloon more or less at the same point in the forecast horizon – in terms of intervals of the data frequency you are analyzing.

Well, this concept seems emergent in forecasts of stock market prices, when I apply the analysis based on these proximity variables.

Prediction of Highs and Lows of Microsoft (MSFT) Stock at Different Data Frequencies

What I have discovered is that in order to predict over longer forecast horizons, when it comes to stock prices, it is necessary to look back over longer historical periods.

Here are some examples of scalability in forecasts of the high and low of MSFT.

Forecasting 20 trading days ahead, you get this type of chart for recent 20-day-periods.


One of the important things to note is that these are out-of-sample forecasts, and that, generally, they encapsulate the actual closing prices for these 20 trading day periods.

Here is a comparable chart for 10 trading days.


Same data, forecasts also are out-of-sample, and, of course, there are more closing prices to chart, too.

Finally, here is a very busy chart with forecasts by trading day.


Now there are several key points to take away from these charts.

First, the predictions of MSFT high and low prices for these periods are developed by similar forecast models, at least with regard to the specification of explanatory variables. Also, the Pvar method works for specific stocks, as well as for stock market indexes and ETF’s that might track them.

However, and this is another key point, the definitions of these variables shift with the periods being considered.

So the high for MSFT by trading day is certainly different from the MSFT high over groups of 20 trading days, and so forth.

In any case, there is remarkable scalability with Pvar models, all of which suggests they capture some of the interplay between long and shorter term trading.

While I am handing out conjectures, here is another one.

I think it will be possible to conduct a “causal analysis” to show that the Pvar variables reflect or capture trader actions, and that these actions tend to drive the market.