The following table contains quarterly nominal GDP in U.S. (billions of dollars). Let Yt denote the GDP at time t and let yt = In (Yt).
(Show your calculations in a spreadsheet, e.g., in Microsoft Excel.)
a. Plot the time series (Yt). Can the underlying stochastic process be weakly stationary of any order? Explain why or why not.
b. Calculate the growth rate of nominal GDP by computing the percentage changes of the series, that is, glt = 100 x (Yt – Yt–1)/Yt–1.
c. Plot the natural logarithm of the series (y,) and compare with part i., com¬menting on stationarity and smoothness.
d. Repeat part ii. by taking the first log-differences (in percentage), that is, g2t= 100 x (Yt – Yt–,1)/Yt–1.
e. Do you observe any significant differences between g1t and g2t computed in ii. and iv, respectively?
DateGDP
2001-01-01. . . . . . . . . . . . . . . . . . . . . .10021.5
2001-04-01. . . . . . . . . . . . . . . . . . . . . .10128.9
2001-07-01. . . . . . . . . . . . . . . . . . . . . .10135.1
2001-10-01. . . . . . . . . . . . . . . . . . . . . .10226.3
2002-01-01. . . . . . . . . . . . . . . . . . . . . .10338.2
2002-04-01. . . . . . . . . . . . . . . . . . . . . .10445.7
2002-07-01. . . . . . . . . . . . . . . . . . . . . .10546.5
2002-10-01. . . . . . . . . . . . . . . . . . . . . .10617.5
2003-01-01. . . . . . . . . . . . . . . . . . . . . .10744.6
2003-04-01. . . . . . . . . . . . . . . . . . . . . .10884.0
2003-07-01. . . . . . . . . . . . . . . . . . . . . .11116.7
2003-10-01. . . . . . . . . . . . . . . . . . . . . .11270.9
2004-01-01. . . . . . . . . . . . . . . . . . . . . .11472.6
2004-04-01. . . . . . . . . . . . . . . . . . . . . .11657.5
2004-07-01. . . . . . . . . . . . . . . . . . . . . .11814.9
2004-10-01. . . . . . . . . . . . . . . . . . . . . .11994.8