Use Excel to plot your data and generate required spreadsheets.
1. Visit www.bea.gov and download the data on quarterly U.S. real GDP.
a. Provide a plot the time series data on U.S. GDP.
b. What is the exact definition of the variable that you plotted in part a. of the question? What is the unit of measurement of the variable?
c. Do you think that the underlying stochastic process is first order weakly stationary? Second order weakly stationary? Explain.
d. Provide a plot the natural log of the series. In the natural log of the real U.S. GDP weakly stationary of any order? Explain.
e. Now provide a plot the first difference of the log series. Call it g2. Is the new series weakly stationary of any order?
f. Now provide a spreadsheet similar to Table 3.1 in your text book (reproduced in the Power Point lecture note.) using data only for the years 2010 - 2014. Do you see any significant differences between the growth rates calculated using the exact formula of growth rate and its approximation by the difference-in-log formula?
2. Use the spreadsheet that you developed in Problem 1(f).
a. Compute and report the sample mean and variance of g2.
b. Compute and report the sample autocorrelation function of g2 for k=1, 2, 3 and 4.
c. Are these autocorrelations statistically significant? How do you know?
3. Visit https://finance.yahoo.com/q/hp?s=%5EGSPC+Historical+Prices. Download monthly data on S&P 500 Index from for the years 1988 through 2006.
a. Provide a plot the time series.
b. What is the exact definition of the variable that you plotted in part a. of this question? What is the unit of measurement of the variable?
c. Do you think that the underlying stochastic process is first order weakly stationary? Second order weakly stationary? Explain.
d. Provide a plot the first difference the series. In the first difference of the S&P 500 Index weakly stationary of any order? Explain.
e. Provide a plot the natural log of the series. In the natural log of the real U.S. GDP weakly stationary of any order? Explain.
f. Now provide a plot of the first difference of the natural log of the series. How would you interpret the first difference of the natural log of S&P 500? Is this new series weakly stationary of any order? Explain.
g. In a spreadsheet, compute and report the sample ACF for the series that you created in part f. of this problem for k=1,2, & 3. Are these autocorrelations statistically significant? How do you know?