The data file gold contains 200 daily observations on the returns to shares in a company specializing in gold bullion for the period December 13, 2005, to September 19, 2006.

a. Plot the returns data. What do you notice about the volatility of returns? Identify the periods of big changes and the periods of small changes.

b. Generate the histogram of returns. Is the distribution of returns normal? Is this the unconditional or conditional distribution?

c. Perform a LM test for the presence of first-order ARCH.

d. Estimate a GARCH \((1,1)\) model. Are the coefficients of the correct sign and magnitude?

e. How would you use the estimated \(\operatorname{GARCH}(1,1)\) model to improve your forecasts of returns?