Driven IFS and Data Analysis

Effects of Lag Time

It is little surprise that the daily percentage change graphs reveal relations between changes in closing prices of successive days. How far into the past does this trend continue? Will we see relations in a lag of two days, three days, a week?
To study this in a uniform fashion allowing comparison across longer time scales, Thornton used mean centered bins with B1 and B3 one standard deviation below and above the mean.
Here are the lag plots.
Unlike the daily percentage change plots, even the one day lag mean-centered graphs are quite similar.
As the lag time increases, we observe the familiar backward Z. Why does this appear?

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