Assessing the Significance of Lagged Return Correlations

Summary

The document asks how to assess correlations between one stock’s returns and another stock’s returns shifted across different lags. It distinguishes this cross-series question from the usual use of the Ljung–Box test for autocorrelation within one series. The answer offers a rough screening rule: compare the absolute sample correlation with two divided by the square root of the sample count.

The response also warns that nonstationary series can generate apparently significant but spurious correlations. It does not derive the rule, specify assumptions such as independent observations, or address the repeated testing involved in examining many lags. Thus, the threshold is presented as a simple heuristic rather than a complete inference procedure; time dependence, multiple comparisons, and data properties can affect whether a finding is convincing.

Key ideas

• The question concerns significance testing for correlations between return series at different lags.
• The answer gives an approximate threshold based on the sample size.
• The threshold is presented as a simple rule rather than a fully derived test.
• Nonstationary data can produce spurious correlations.
• Testing many lags raises issues the document does not resolve.

Tags

# Testing Significance of Correlation


# 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.

## Answer by dkhokhlov (score 4)

https://quant.stackexchange.com/a/7690

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

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