Correlation and the time interval over which the variables are measured - A non-parametric approach

Area of Science:

• Financial econometrics
• Statistical modeling

Background:

• Pearson correlation (ρ) is affected by differencing intervals (n) when variables are multiplicative.
• Increasing n causes ρ to converge to zero, leading to unreliable correlation estimates.

Purpose of the Study:

• To introduce Spearman correlation (r) as a reliable alternative to Pearson correlation for multiplicative variables.
• To demonstrate the stability and advantages of Spearman correlation over Pearson correlation with increasing differencing intervals.

Main Methods:

• Theoretical proof of Spearman correlation's convergence properties.
• Simulation studies to compare the variability of Pearson and Spearman correlation estimators.

Main Results:

• Spearman correlation (r) converges to a stable limit independent of the differencing interval (n).
• The relative variability of Pearson correlation (ρ) increases with n, while Spearman correlation (r) remains stable.
• Pearson correlation becomes arbitrary and unreliable as n increases for multiplicative variables.

Conclusions:

• Spearman correlation is recommended over Pearson correlation for analyzing multiplicative variables, especially with larger differencing intervals.
• Spearman correlation provides a more robust and reliable measure of association in financial econometrics.
• The choice of correlation method is critical for accurate analysis of time-series data with multiplicative properties.