Question 2: U.S. Quarterly GDP This question requires the use of the data for quarterly nominal U.S. GDP in billions of US dollars provided in the Excel file \"Data Set for Assignment 1\". Let Y; denote the GDP at time t and let y; = In(Y;). a) b) c) d) e) g) Plot the time series {Y;}. Can the underlying stochastic process be weakly stationary of any order? Explain why or why not. Calculate the growth rate of nominal GDP by computing the percentage changes of the series {Y;}; thatis, g;, = 100 X Y\"; t-1 Plot the time series {g,;} and compare with part a), commenting on stationarity and smoothness. Plot the natural logarithm of the series {Y;} and compare with part a), commenting on stationarity and smoothness. Take the first log-differences (in percentage); that is g, = 100 X (y; 1)- Do you observe any significant differences between g, and g,;? Compute the sample moments, mean /i and variance , of g,;. Compute the autocorrelation function of g,; thatis p, fork=1, 2, 3, 4, 5. Interpret the autocorrelations by plotting g,, against the lagged values of g,,_,. Give an economic interpretation. Compute the partial autocorrelation function of g,, fork=1, 2, 3, 4, 5. What observations can you make together with the ACF in part (f)? Hint: You can use the \"Data Sheet\" in the excel file \"L3 Simulation of Stochastic Processes and Price Dynamics\" to determine the ACF and PACF values