# Why does computing correlation between index levels vs. percentage changes yield completely different results?

I am examining the relationship between the S&P 500 and the Industrial Production Index. Computing the correlation between these these variables yield vastly different results if expressed in percentage changes as opposed to using the index approach (i.e. choosing an index year and multiplying the percentage changes).

Percentage changes CORR (S&P500, IndustrialProduction) = -0.006460759

Index levels CORR (S&P500, IndustrialProduction) = 0.890445169

How does this make sense?

• stats.stackexchange.com/a/7378 explains it all
– Ivan
Oct 7 '18 at 17:33
• The index level correlation is not valid and should be disregarded. It is a so-called "spurious correlation" between two random walks. fsb.miamioh.edu/lij14/672_2014_s8.pdf Oct 7 '18 at 18:29
• So it would be wrong to regress the index levels against each other using Vector Autoregression?
– DBE7
Oct 7 '18 at 18:35
• @DBE7 That depends on whether the processes are cointegrated. If the two processes are both integrated of order 1 and cointegrated, then regressing one on the other can recover the cointegrating vector with super-consistent convergence. But if they're not cointegrated, you'll get a spurious result (if you mistakenly assume regular OLS assumptions). Oct 8 '18 at 21:30