Correlations over 6yrs higher than any individual 1yr correlation over the same period I just need a simple yes/no answer (hopefully yes) to confirm I haven't done something stupid here - I'm doing some data analysis and looking at the correlation of 2 variables X and Y over the past 6 years. My correlation over these 6 years comes out in MS Excel as 96% (that is, the usual definition of correlation as detailed here http://office.microsoft.com/en-us/excel-help/correl-HP005209023.aspx): however, my correlations for each of these 6 years are 73%, 84%, 95%, 42%, 84% and 82% supposedly. 
Is this possible, that the 6yr correlation is so much higher than any of the individual ones? I was surprised at how much higher the 6-year correlation was than any of the yearly ones. From drawing a picture this seems plausible, but I couldn't find any simple mathematical justification for the fact without things in the formula getting extremely messy, and there are a few hundred data points per year so it's not really feasible to check my data by hand. 
 A: There's no reason this couldn't happen, that I can see. 
Further, one year (if I am reading your question correctly) has a correlation of 95% and your overall is 96%, which isn't so different.
One way this could happen is if year has an effect on both x and y; in this case, you could have individual correlations of 0 and an overall one that is very high:
set.seed(1021827)
year <- rep(2000:2005, each = 100)
x <- year*3 + rnorm(600)
y <- year*3 + rnorm(600)
cor(x,y)
cor(x[year == 2000],y[year == 2000])
cor(x[year == 2001],y[year == 2001])
cor(x[year == 2002],y[year == 2002])
cor(x[year == 2003],y[year == 2003])
cor(x[year == 2004],y[year == 2004])
cor(x[year == 2005],y[year == 2005])

In this case the relationship between x and y is confounded by time. But that isn't necessary given the values you gave. 
A: Yes, this is possible.  Indeed, it's not just possible but a fairly common situation.  For example I was looking recently at time series data (1987-2011) for world oil and natural gas prices (adjusted for general price inflation), and found that the correlation over the whole time period was higher than that over either half of the period. The reason is that both prices are on an upward trend, but the correlation coefficients for the shorter periods are more influenced by differences in fluctuations about the trend.
