I went through and removed most of the Forex markets from my analysis. (The trading profit/loss on SGX/JPY converted to historical USD isn't very intuitive.) Before giving an updated table, I want to talk about time period.
I find correlation and cointegration to be highly interesting. They both provide some fairly easy tools to get a quick understanding of the relationships between the markets. On the other hand, I have read some academic work by someone I respect that said that correlation in the markets is a characteristic of the particular sample and not of the underlying markets. I have certainly seen many bogus pairs which had some coincident correlation, but I have also seen plenty where upon research, a real reason could be uncovered. My first line of defense is to consistency in different time periods.
For example, consistency in nested time frames:
Code:
Correlation
Time Span Linear Rank
0.125 Year 98.5_% 97.4_%
0.25 Year 98.3_% 96.6_%
0.5 Year 98.3_% 97.1_%
1 Year 98.6_% 97.7_%
2 Year 97.9_% 97.3_%
2.5 Year 95.0_% 97.3_%
5 Year 95.7_% 97.9_%
7.5 Year 96.3_% 98.5_%
10 Year 97.0_% 98.9_%
12.5 Year 97.6_% 99.1_%
15 Year 97.8_% 99.2_%
and consistency using different metrics in disjoint time frames:
Code:
Year Price Correlation Log Correlation Return Correlation
Linear Rank Linear Rank Linear Rank
Pearson Spearman Pearson Spearman Pearson Spearman
2010 100.0_% 99.9_% 100.0_% 99.9_% 98.5_% 97.6_%
2009 99.9_% 99.9_% 99.9_% 99.9_% 97.9_% 97.2_%
2008 99.5_% 99.1_% 99.5_% 99.1_% 93.0_% 96.8_%
2007 100.0_% 99.9_% 100.0_% 99.9_% 99.6_% 99.5_%
Bone's comment that 10 years is too long, made me wonder, what is a good initial time frame for searching. Is there a time frame for which a strong reading implies that the other time frames are also likely to have strong readings. To get an idea, I looked at 10 nested time frames (40 years down to 1/8 of a year), and measured the conditional expectation that if a market pair had a positive linear correlation of daily return at 90% or higher, then the same pair would also have a 90% of higher correlation in the second time period.
Code:
Year40 Year30 Year20 Year10 Year5 Year2 Year1 Year0.5 Year0.25 Year0.125
Year40 100% 100% 100% 60% 60% 60% 60% 100% 100% 60%
Year30 100% 100% 100% 60% 60% 60% 60% 100% 100% 60%
Year20 26% 26% 100% 74% 79% 68% 79% 89% 84% 37%
Year10 7% 7% 30% 100% 78% 89% 57% 93% 57% 63%
Year5 3% 3% 17% 42% 100% 90% 84% 88% 62% 40%
Year2 1% 1% 3% 9% 16% 100% 78% 72% 47% 41%
Year1 1% 1% 3% 5% 14% 71% 100% 71% 51% 33%
Year0.5 1% 1% 3% 8% 14% 65% 71% 100% 58% 43%
Year0.25 1% 1% 5% 8% 16% 67% 80% 91% 100% 55%
Year0.125 1% 1% 2% 9% 11% 64% 57% 74% 60% 100%
I know that this is not a well controlled test, but that is the nature of working with real data.
The lower-left values should be small since there is an explosion of markets in recent years. It is unlikely, by chance, that a pair with 1/8 year of history consists of two markets both of which have existed for 40 years.
The fact that the first two rows are duplicate and that the first two columns are duplicate reflects the small sample size of markets which have been existent and highly correlated for such long time frames.
The 100%'s along the diagonal is just a truism.
One would expect that the first cells above the diagonal to be large since knowing that for the last 20 years a pair was highly correlated does imply that for each of the first and second 10 years in the sample, the pair was fairly highly correlated. I have some ideas about how to compute a null-hypothesis, but let's proceed anyhow.
With these basic biases pointed out, the columns for 1/8th of a year has quite small values 30-50%. Even the off-diagonal 55% is quite small. (Knowing that a pair was highly correlated for the last 1/4 of a year suggests only a 55% chance that it will be highly correlated the the last 1/8th of a year.) This suggests to me at the 1/8th of a year time frame is not very predictable from longer time frames, and I would even go further to say that it is probably not very characteristics of the market pair itself but rather just on the current circumstances. A similar pattern is demonstrated in the bottom of the 1/4 of a year column.
Another feature of the numbers in this table is that for both 1/2 and 1/4 of a year, the conditional probabilities increase as one goes up from the diagonal. Thus knowing that a pair has been correlated for 20 years is a stronger implication that it will be correlated in the last 1/2 year then only saying that it has been correlated for 10 years. This tells me that there is something legitimate in correlation. That having a longer period correlation is a function of the market and the underlying economics.
Back to the original question of whether there were any time frames for which high correlation would suggest high correlation in other time frames, the rows from 5 years and up satisfies this property.
As the underlying economics change over long spans and as there aren't many markets with 30-40 years of history, I can't recommend using these. The 5-20 time frames have similar conditional probabilities within the assumed sampling error. Myself, I usually use the 10 year time frame due to the inconvenience in sifting through recently introduced markets.
