Testing Significance of Correlation

Lets say I have the returns of two stocks(stock1 and stock2). Now without running a regression, I lag one of the variables, calculate the correlation between the two stocks and repeat this process as I keep stock1's returns fixed as I continually lag stock2's returns forward. What are some valid statistics that one could use to determine if the correlation (corr(stock1 return, stock2 return(-n)) at any given lag is statistically significant? Ljung-Box is pretty much used for looked at autocorrelation for a variable and its past lags, not for another variable.

-
The correlation tests you ran with differents lags are themselves 'significance' tests (???). The higher the Pearson (Spearman, ...) correlation the more 'significant'. Besides, you might wish to ensure correlations you found are stable over time. –  edouard Apr 7 '13 at 12:36

Simple rule: correlation coefficient R of N samples is statistically significant if: $|R| > 2 / \sqrt{N}$ http://capone.mtsu.edu/dwalsh/436/CORRSIG.pdf But watch out for spurious correlations. It is possible to find statistically significant correlation for non stationary data series even though there is no correlation. http://www.investopedia.com/terms/s/spurious_correlation.asp