Hello John,

Thanks a lot for your reply….Actually here is the only forum where I was able to get more or less clear feedback on my question so pleas do not disappear…)) I am trying to find if there is a relation between the variance of the sub-period correlations an dthe correlation of the whole period becaue I need to find a method for establishing the significance of the correlation. I got this sub-period idea from the book on money management – “Money Management Strategies for Futures Traders”:

A good way of judging whether a correlation is genuine or otherwise is

to rework the correlations over smaller subsample periods. For example,

the period 1983-1988 may be broken down into subperiods, such as

1983-84, 1985-86, and 1987-88, and correlations obtained for each of

these subperiods, to check for consistency of the results. Appendix C

presents correlations over each of the three subperiods.

If the numbers are fairly consistent over each of the subperiods, we

can conclude that the correlations are genuine. Alternatively, if the numbers

differ substantially over time, we have reason to doubt the results.

This process is likely to filter away any chance relationships, because

there is little likelihood of a chance relationship persisting with a high

correlation score across time.

Table 4.7 illustrates this by first reporting all positive correlations

in excess of t-O.80 for the entire 1983-88 period and then reporting

the corresponding numbers for the 1983-84, 1985-86, and 1987-88

subperiods.

Table 4.7 reveals the tenuous nature of some of the correlations. For

example, the correlation between soybean oil and Kansas wheat is 0.876

between 1987 and 1988, whereas it is only 0.410 between 1983 and

1984. Similarly, the correlation between corn and crude oil ranges from

a low of -0.423 in 1987-88 to a high of 0.735 between 1983 and

1984. Perhaps more revealing is the correlation between the S&P 500

and the Japanese yen, ranging from a low of -0.644 to a high of 0.949!

Obviously it would not make sense to attach too much significance to

high positive or negative correlation numbers in any one period, unless

the strength of the correlations persists across time.

If the high correlations do not persist over time, these commodities

ought not to be thought of as being interrelated for purposes of diversification.

Therefore, a trader should not have any qualms about buying

(or selling) corn and crude oil simultaneously. Only those commodities

that display a consistently high degree of positive correlation should be

treated as being alike and ought not to be bought (or sold) simultaneously

I included the picture of the table that the author was referring to. Hope you can comment on using this method of establishing the significance of the correlation. Finding the variance of the subperiod correlations is just my way of “mathematizing” the authors words that “Obviously it would not make sense to attach too much significance to high positive or negative correlation numbers in any one period, unless the strength of the correlations persists across time”

Hoping for any kind of feedback)

Dima