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Forecasting. "It's tough to make predictions, especially about the future." (Yogi Berra) This is another area that can have lots of mathematics. Perhaps more important ideas are: Garbage in, garbage out. The longer the forecast, the less reliable it is.

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  • "It's tough to make predictions, especially about the future." (Yogi Berra)
  • This is another area that can have lots of mathematics. Perhaps more important ideas are:
  • Garbage in, garbage out.
  • The longer the forecast, the less reliable it is.
  • Instability in the past suggests instability in the future.
  • Think about an analogy rather than an equation.

(From the Wharton site).

Judgmental vs. statistical


one or more variables;

data based or theory based;

linear models, or more complex


one person vs. groups;

Delphi techniques,


markets, etc.

some things can t be predicted
Some things can’t be predicted

There is no point thinking about how to predict a roulette wheel, or the order of a shuffled deck. If there were, casinos wouldn’t exist.

What about the stock market?

“… by this period I thought that the only sure way of making money from the stock market was to write a book about it. I tried this with Granger and Morgenstern (1970), but this was not a financially successful strategy.” Clive Granger, Int. J. Forecasting, 1992, p. 3-13 “Forecasting stock market prices: lessons for forecasters”. (The paper does hold out some hope, in fairness).

what about earthquakes
What about earthquakes?

This is where they are; you can count them and guess how many more weak ones will show up.

earthquake damage
Earthquake damage

This is estimated by multiplying the probability of an earthquake times the expected damage.

Expected damage is done by looking at the number of buildings and the type of construction.

At one level, you would just use gross estimates;

For better planning, you would actually look at specific buildings.

FEMA (Federal Emergency Management Agency) has a system named HAZUS that attempts to predict damages.

profit forecasting
Profit forecasting

Similarly, business forecasts are “probability of success times expected profit if we do win”.

Thus, ideally one wants to know how many people will buy something at a range of prices.

This is very difficult: you can try test-marketing, or running ads and seeing how many replies come back, but it may interfere with the final sales plan. Works best with products like books: you can try publishing one at an oddball price and see what happens.

simplest tomorrow like today
Simplest: tomorrow like today

You might think this is obviously inadequate, but…

Mean percentage error forecasting by surveys of consumer intention compared with “same as last six months”:

Lee, Elango & Schnaars, Int. J. Forecasting 1997, pp 127-135 but see also Armstrong et al., same journal, 2000, pp. 383-397

gigo many bad predictions
GIGO: many bad predictions

Club of Rome (1972): Malthusian collapse about now.

Paul Ehrlich: widespread famine in 1975. Ehrlich, in 1980, bet economist Julian Simon that the prices of chrome, copper, nickel, tin and tungsten would rise by 1990; they all fell.

Edward Yardeni, Chief Global Economist and Investment Strategist of Deutsche Bank Securities, … December 16, 1999 on CNBC he stated: "Y2K will cause enough disruption to cause a fairly intense downturn in the economy in the first six months of 2000…"

"You ain't goin' nowhere... son. You ought to go back to driving a truck.“ (Grand Ole Opry manager, firing Elvis Presley)

simple math
Simple math

Average: the world stays the same. The last year’s average is next month’s expected value.

Moving average: weight more recent data in making the average.

Linear: the change each month (or year) is the same.

Cyclic: there is some kind of pattern, typically seasonal.

Combined model: add up some combination of the above.

Often you add in randomness.

sample linear fit
Sample linear fit

Semiconductor sales 1976-89 plotted against durable equipment investments (if companies are making investments, they will also buy computers).

why not plot against year
Why not plot against year?

Wouldn’t be a good linear fit because of decline in 1986, and it doesn’t look cyclical either.

excel will fit linear functions
Excel will fit linear functions

The data are new car sales in Maryland for the last few years.

more complex math
More complex math

Multiple regression: fitting data to many variables.

Neural nets: having a computer program which “learns” the data pattern.

Theories: having some model which lets you use more complex data.

In general, more complex models don’t help enough; it’s just not possible to produce really accurate forecasts, and at least the simple ones can be understood.

neural nets
Neural nets

Each node is a linear combination of the nodes pointing to it. Weights are adjusted so that when you feed in certain input values, the outputs will be as trained for.

why neural nets
Why neural nets?

You don’t have to have any theory: you just feed in the numbers and the network will give results.

They supposedly represent “artificial intelligence” and mimic biological learning systems. A great deal of hype has been devoted to them.

Software is readily available to take input and output data and try to create a neural net that will implement the transformation. The standard algorithm is called “back propagation”.

They derive from a suggestion of Minsky’s called “Perceptrons” but Minsky somehow missed the basic idea back in the 1960s.

why not neural nets
Why not neural nets?

You don’t get any insight: it’s not possible to look at the internal nodes and find a “meaning” to them.

They actually have fairly low representational power; there are better statistical methods out there.

They often don’t work well. E.g. “Forecasting sales data with neural nets” by Chatfield suggests that they often go very wrong.

Getting the right training data is difficult: it has to be quite voluminous and evenly distributed over the possible input values (otherwise the program learns the most likely output values rather than the relation of input to output).

expert systems
Expert systems

Another AI spinoff, and sort of the reverse of neural nets: collecting rules about an organization or process.

Typically these are “production rules” of the form

if xxxx then yyyy

The original idea was that you could “debrief” the expert people in a company and encapsulate their knowledge in a set of rules.

Expert systems were a big fad in the 1980s

In practice obtaining the right information proved difficult as was knowing which rule to prefer in complex situations. Nevertheless, there are expert systems for forecasting.

example mycin
Example: MYCIN

MYCIN was an early expert system for the diagnosis of blood diseases. A typical rule might be:

IF the stain of the organism is gram negative

AND the morphology of the organism is rod

AND the aerobicity of the organism is anaerobic

THEN there is strongly suggestive evidence (0.8) that the class of the organism is Enterobacter iaceae

Collecting this knowledge is and was always the biggest bottleneck for expert systems. Imagine, for example, asking an art expert “how do you recognize a Vermeer?”

inference engine
Inference engine

Along with the rules, you need a program which applies them. It can either work forward (knowing a, b, and c, what rules can use those facts to deduce something else); or backwards (if we would like to prove k, and the rules that imply k require us to know i and j, what rules would help prove h, i and j)?

Off-the-shelf products exist for this; whereas nobody can really tell you what rules you need for your industry.

The products aren’t that hard because it is almost impossible to have an expert system with more than a few thousand rules: a bigger list becomes unmanageable (you can’t see what’s going wrong). By computer standards, this is easy.

why use expert systems
Why use expert systems?

You do get some insight: the system will tell you what rules it used to get its answer.

Relatively routine tasks can be done automatically and accurately when the rules can be written down.

Compared with programming in a normal language, you don’t have to think as much about control flow.

Successful examples are things like filling out tax forms and configuring computer systems.

Expert systems can also apply rules to make forecasts. They can combine human rules and time-series calculations. They are also able to use probabilities to make “fuzzy” forecasts.

why not use expert systems
Why not use expert systems?

The lack of control flow may mean that the system does something stupid and you can’t see how to fix it.

Collecting the expertise is hard, and the major reason why projects fail.

The whole area has a bad reputation left over from the period of the 1980s known as “AI winter”.

There are not a lot of success stories to imitate.

Expert systems are extremely narrow in their abilities; it has proven impossible to take two small expert systems and combine them to make a single expert system which can solve two different kinds of problems.

theoretical modeling
Theoretical modeling

The “S-curve”: product introduction, growth, leveling off.

Everything goes through such phases. Most of the money is made in the growth period; the question is how much advantage you get from having been the introducer.

moore s law
Moore’s law

Special for semiconductors: power doubles in 18 months.

and the model predicted
And the model predicted..

Right about now food and industrial output collapse, followed by widespread famine and population decline; the vertical and horizontal scales of this chart are deliberately obscure.


Find a similar product and hope your sales track.

Chart below are shipments for January in each year.

el ni o red and la ni a blue
El Niño (red) and La Niña (blue)

Analogy: in this case, just to a past instance of El Nino.

events matter
Events matter

From the “Financial Forecast Center”, May 2001 (courtesy of the Internet Archive). The actual Dow Jones average on October 31, 2001 was 9075.

Even without unusual events: in Jan. 2004 predicted the euro in June would be worth $1.08, correct answer was $1.21.


You can survey either ordinary people or experts. Below is from Wired magazine, Dec. 1995.

surveying the unknown
Surveying the unknown

People are not good at questions like “would you buy a …” if they have never seen one and don’t know what it is. So asking about new products is often more about how you word the question than what might actually happen.

In any case, asking about intentions is always lower quality data than looking at actual results.

Even experts often blow it. The California Energy Commission forecast natural gas prices in 1995 as likely to grow 3.6% per year. In early 2001 they went up 20% in two days (ok, this wasn’t a blown forecast, it was enemy action).

don t forecast in groups
Don’t forecast in groups

Focus groups have their uses, but forecasting surveys should use individuals working separately. In a group, one or two louder or more aggressive individuals are likely to sway the overall opinion.

Should one try to weight different opinions by perceived amount of expertise? Probably not: ability at forecasting seems extremely variable.

delphi methodology
“Delphi” methodology

Assemble a group of people who might know something.

Give them a questionnaire asking for predictions.

Average the results. Circulate these to the group again.

See if people change their minds.

Many problems: interactions between trends, bias in the questionnaire, and the experts may not be good forecasters.

1996 california forecast oil prices
1996: California forecast oil prices

In case you didn’t notice, oil prices per barrel in 2000 were $27 and are currently $54.

This was a Delphi forecast which more or less said that things would stay the same.

  • Finding analogies is probably as good as you can do.
  • Too much math isn’t that helpful.
  • You can combine different forecasts, but it’s best to give them as a range.
  • Try to understand unusual events.
  • You can’t beat the market. Or the roulette wheel.