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Unformatted text preview: alculation, the S&P500 index was detrended. The
plot of the index from 1972 through 1996 is shown in Fig. 1 below.
Fig. 1: S&P 500 index from 1972 through 1996
600 S&P 500 index 500
0 200 400 600
Data number 1000 1200 The trend is clearly exponential, which is logical since inflation cumulatively reduces the
value of the dollar. To detrend this data, the logarithm of this data was taken and this
logarithm of the index was detrended using detrend() in MATLAB, using a line
detrending, rather than simply removing the mean. Similarly, the long and short term
interest rates were detrended by simply removing the mean. Fig. 2 and 3 show the crosscorrelation between the long term interest rate delayed 53 weeks and the detrended index
(Fig. 3 is a zoomed in version of Fig. 2). It can be seen that there is a strong negative
correlation between the long term rate delayed 7 weeks through 25 weeks. Although, the
correlation with the lesser delay is stronger, here...
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- Spring '12