Best ETF and CEF Absolute Lagged Correlation To the S&P 500

I found these results particularly interesting, as nearly none of the ETFs I expected are present. The following were my most interesting observations:

1. Japan seems to rank consistently well, with DND and DFJ taking 1-period and 17-period.
2. The overall best absolute correlation in this lag-range is found in the 21-day lag with the S&P Global Consumer Discretionary fund.
3. Correlations around multiples of 5 seem to be stronger, representing weekly periodicity as expected.
4. The Double Dow Inverse DXD ranks best in the 6-period lag.
5. The most common type of fund is "high income," something I am somewhat at a loss to explain.

Comments

[Javaharv]

Mike, I am really sorry, but could you give a brief explanation of "lagged correlation", I am not quite certain what you are demonstrating although I think it could be an interesting observation.

[MichaelBommarito]

Hello Harvey,
Lagged correlation here is the correlation between two time series with one shifted so that its dates are lagged by a certain number of periods. For instance, the 1-day lag correlation would be the correlation between DND on day N and the S&P on day N+1.

[davboz]

I'm stupid. I need words! Do you mean that 25% of the time, the S&P500 correlates exactly to what the RXI did 21 days earlier? Do you mean that 21 days behind the RXI, the S&P500 acts the same with a 25% variance? I doubt that this is what you mean but what can it be? 25% is the BEST? Why bother. And what about the neg.%'s? Is it helpful to know that something is 'off' or at variance at a 14% rate? That still leaves 86% that isn't neccesarily exactly correlating.....
I WANT to see a pattern like whatever it is I get a hint of what I THINK you could possibly mean..........but ....just what IS that?!?
Expand. Please. I'm beggin' ya!