A statement about a feature of sequences of measurements that has always been true until now.
Emergence of predictability describes the fact that always true patterns of measurements can often be found by “creative construction” and active search of features of sets of measurements.
We look at the cumulated returns after T days for the following decision rule: “Go long if the 10-day moving average of the S&P 500 is greater that the 30-day moving average; hold cash otherwise” (Golden Cross).
If we search over cumulated returns for sequences of decisions, we find that for length T=3650 the sum of the returns is always greater 0.
After the first observation of this feature of a set of 3650 measurements, this relation would have been predicted eight times correctly.
Emergent Empirically Deterministic Law
If the rule that made always true predictions concerning a relation of features was found via “creative construction” and “active search” by a learning system, we call that rule Emergent Empirically Deterministic Law.
Often verified laws
We are able to find laws that have very often been verified even in the domain of financial markets. For example, the correlation between the returns of S&P500 and Dow Jones is greater than zero in each sequence of at least 18 days. This has been the case for 1778 non-overlapping sequences since 1896.
We have good reason to believe that this law will stay true and will further be verified in the future.
There is no sequence with T<=3500 for the Japanese Nikkei Index which has a positive sum of returns. We can say with absolute certainty that the statement “The sum of returns of a sequence with T<=3500 is always positive” will never be true for the Nikkei. This statement will remain falsified forever.