Prediction: a quick way to look like an idiot.

What is a prediction? A prediction is a statement about what will happen or might happen in the future. This is the standard definition that you will find in a dictionary. Other, softer definitions, run like this: a statement about what you think will happen in the future. According to these two definitions – both are from prestigious dictionaries – one could say that these are predictions:

‘Tomorrow the Sun will rise’.

‘I think that tomorrow the Sun might rise’.

The first sentence is a statement of the obvious, the second one is ridiculous. By the way, Wittgenstein said: ‘the fact that the Sun will rise tomorrow is only a hypothesis’. In any event, setting philosophy aside,  the above “predictions” are pretty much useless.

Consider this. I have just dropped an object from a height of 100 meters and I predict that it will hit the ground after 4.51 seconds. Is that a prediction? No, that is just physics 101.

According to Paul A. Samuelson, ‘Wall Street indices predicted nine out of the last five recessions’. But let us see what prediction is and what it should be.

Predicting A versus B is useless unless you also specify what will happen if A takes place and what will happen if instead B does. Let us see what this implies.

Let us define better A and B. A and B are scenarios. A scenario may be described by a vector of variables, {x}, with N components. In a given scenario the components have certain values. But that is only part of the story. The entries of {x} are, generally correlated. This means that each of them will ‘react’ to changes in the others. So, predicting :

‘A will happen’

means that you should, in addition, specify also:

the values of all the entries in {x}, and

the structure of correlations between the components of {x}

An example. Suppose that we’re trying to predict if Donald or Hillary wins the US election. Thousands of analysts started to analyze tweets and facebook posts, counting the ones that were pro or against this or that candidate. A pretty straightforward exercise. You just need to identify a few keywords and count the number of times they occur. This is plain and simple arithmetic.

However, saying that Donald will lose and Hillary will win, or vice-versa, is irrelevant unless you also specify what the resulting scenario will be.

Suppose that the scenario may be described a vector of a few macroeconomic variables, say these:

{x}={Price of Oil, Unemployment, Dollar/Euro, Dollar/Yen, Price of Gold, Interest Rates, Exports, Debt, NASDAQ, Dow Jones}

Setting aside the fact that some of the above variables don’t change overnight when an election takes place (while others do), the situation may be described formally as:

Scenario A (Hillary wins):

{x_A} = {Price of Oil, Unemployment, Dollar/Euro, Dollar/Yen, Price of Gold, Interest Rates, Exports, Debt, NASDAQ, Dow Jones}_A

and

Scenario B (Donald wins):

{x_B} = {Price of Oil, Unemployment, Dollar/Euro, Dollar/Yen, Price of Gold, Interest Rates, Exports, Debt, NASDAQ, Dow Jones}_B

So, if you’re attempting a serious prediction, you should specify, in addition to ‘A wins over B’, or vice-versa, the values of the components of {x}. Moreover, you should also specify the way these components will correlate, i.e. [C], which represents a matrix. A neat way to express the entire correlation structure in a scenario involving a number of variables is via a map. Something like this:

Scenario A (Hillary wins)

Scenario B (Donald wins)

Clearly, if many people are trying to predict if A wins instead of B, a certain percentage will inevitably get it “right”. If you’re not specifying the values of {x}, not to mention the corresponding correlation structure, all you’re doing is playing a more or less extravagant and irrelevant guessing game.

It doesn’t take rocket science to count “good” and “bad” tweets and say that one is making predictions. In the case of Trump’s elections there was supposed to be panic on the markets. Quite the opposite is happening. It appears that there are two types of forecasts: the lucky ones and the wrong ones.

The following conditions need to be satisfied simultaneously if one wishes to claim that the outcome of an experiment has been predicted correctly:

1. Trivial condition: you guess the right answer, i.e. A rather than B.
2. Weak condition: you get the values of {x} right
3. Strong condition: you get the correlation structure [C] right

Clearly, specifying the values of {x} and [C] ahead of time is quite impossible, especially for situations involving very many variables. We don’t have the science for that. We probably never will. So, what can one do? You will need to read our future blogs to find out.