Standard & Poor's (S&P 500) introduced its first stock index in 1923. The S&P 500 index in its present form began on March 4, 1957. The open prices of S&P 500 on 24 th and 27 th of July 2015 were 2102.24 and 2078.19 respectively where a sharp drop on Index could be clearly seen.
SSE VS S&P
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SSE Adjusted
S&P Adjusted
Figure 1 Adjusted close share prices of SSE and S&P 500 which have been rebased, 2001:12-2015:4, monthly observations.
From visually expectations, it is clear that there is no obvious relationship between these two shares during this period of time so we might expect the cointegration statistic measured is low.
2. Methodology
a. Integration: basic introduction
i. Stationarity and Non-stationarity
Why do we need to test for stationarity?
Spurious regressions. If two variables are trending over time, a regression of one on the other could have high 𝑅 2 even if the two are totally unrelated. If the variables in the regression model are not stationary, then it can be proved that the standard assumptions for asymptotic analysis will not be valid. In other words, the usual ‘t-ratios’ will not follow a t-distribution,
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