We investigate Shanghai Stock Exchange Index data (SSE) as an example (monthly closing price from 1991-2015). Let Shanghai Stock Exchange Index be 𝑖 , 𝑖 = 1, 2, 3 … . To find the differences (Y) of the original data (X), we take the following form.
𝑖 𝑖−1
) − ln( 𝑖−1 )
) = ln( 𝑖
𝑖
= ln (
Where X i
is approximately measured in percentage change. One observation is
lost due to differencing.
Figure 1. Shanghai Stock Exchange Index
for i = 2, 3 …, let 𝑖
=
In order to calculate the relationship between X i
and X i-1
𝑖+1 , and then the following formula (S1) can be used to calculate the sample correlation coefficient between X and Y:
𝑆
=
𝑆
√𝑆
− ̅ ) 2 𝑆
− ̅ ) 2
ℎ 𝑆
= ∑( 𝑖
− ̅ )( 𝑖
− ̅ ) , 𝑆
= ∑( 𝑖
= ∑( 𝑖
Using the Excel we get that the correlation coefficient = −0.0440 .
2
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