Problem 1.3 1. Open and run the script file dsp.asc to create the numeric vector DSP. The entries of this vector represent the daily closing values of the S&P 500 index between the beginning of January 1960 and September 18, 2001. Compute the vector of log-returns and call it DSPLR.

2. Open and run the script file intrasp.asc to create the numeric vector MSP. The entries of this vector represent minute by minute quotes of the S&P 500 on September 10, 1998.

Compute the corresponding log-return vector and call it MSPLR.

3. Produce a Q-Q plot of the empirical distributions of the two log-return vectors, and comment.

In particular, say if what you see is consistent with the claim that the properties of the daily series are shared by the minute by minute series. Such an invariance property is called self-similarity. It is often encountered when dealing with fractal objects.

4. Fit a GPD to the DSPLR and MSPLR data, and compare the distributions one more time by comparing the shape parameters.