claim: Skeptics have long pointed to ice gain in the Southern Hemisphere as evidence climate change wasn’t occurring, but scientists warned that it was caused by natural variations and circulations in the atmosphere.
evidence: Assuming returns are reinvested, if the returns over n {\displaystyle n} successive time sub-periods are R 1 , R 2 , R 3 , ⋯ , R n {\displaystyle R_{1},R_{2},R_{3},\cdots ,R_{n}} , then the cumulative return or overall return over the overall time period is the result of compounding the returns together: ( 1 + R 1 ) ( 1 + R 2 ) ⋯ ( 1 + R n ) − 1 {\displaystyle (1+R_{1})(1+R_{2})\cdots (1+R_{n})-1} If the returns are logarithmic returns however, the logarithmic return over the overall time period is: ∑ i = 1 n R l o g , i = R l o g , 1 + R l o g , 2 + R l o g , 3 + ⋯ + R l o g , n {\displaystyle \sum _{i=1}^{n}R_{\mathrm {log} ,i}=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}+R_{\mathrm {log} ,3}+\cdots +R_{\mathrm {log} ,n}} This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e.