Exercise 2.5. Stock returns are often modeled in Finance as coming from an underlying Normal distribution. Generate 3000 standard Normal deviates.

(a) Show a time series plot of this series.

(b) Compare that against your time series plot of returns. Does this argue for or against using a Normal distribution as a model for stock returns?

(c) Show a histogram with a 150 breaks for this series.

(d) Comparing the shape of your histogram of returns and this new histogram, in what ways does a Normal distribution seem like a good model and in what ways is it not?

A simple measure of variability (or risk) in stocks is the daily range, which is the daily high of Closing Price minus the daily low of Closing Price.

(a) In R, compute the daily range and explore its nature using the techniques you have practiced, above. Do not be alarmed that the histogram will be right-skewed. (b) Take the logarithm of the range (R function log) and explore what happens with that, using the techniques and concepts in this lecture note. Does taking the log seem to make time series more manageable? How so?