Assignment #2 Instructions: please type your group project into MS Word or some other word processor and turn it on the due date, before the class starts. 1. Go to https://fred.stlouisfed.org/ and search for the quarterly GDP series gdpc1, this series is available since 1947. In the possible formats, download as an EXCEL le. Then import your data into Eviews (you dont have to clean the data, just import it and Eviews does the rest). Let yt be real GDP in 2012 prices (the variable for which you have the time series) a. In this exercise you compare growth rates with their log approximations. In eviews, create the variables growth1 and di og as growth1 = 4 100 ytyt1 yt1 di og = 4 100 [ln (yt) ln (yt1)] The reason we multiply by 4 the above growth rates is that we are interested in following the conventions regarding GDP, where the growth rate reported by the FED is annualized (while our data is quarterly). Also compute a third variable, growth4, given by growth4=100 ytyt4 yt4 where growth4 measures the annual growth of GDP with respect to the same quarter the previous year. In Eviews, in order to generate a new variable, select Quick, Generate Series..., then write the equation that denes your new variable. Once you have imported each series, present a graph of the time series of each variable (View, graph). b. Compare the statistics (Quick, Series Statistics, Histogram and Stats) as well as the correlogram (Quick, Series Statistics, Correlogram) of growth1 and di og. Do there appear to be any signicant dierences between these 2 variables? c. Compare the correlograms for growth1 and growth4. Which series appears to have higher linear dependence (as measured by the magnitude of the AC and PAC coe cients?) Do you have intuition for that? Explain 2. Go to https://fred.stlouisfed.org/ and search for the monthly unemployment rate series unrate. Download the data series as an EXCEL le. Then import your data into Eviews (follow the instructions of the previous homework). In what follows, do the analysis starting in January of 1970. a. In Eviews, generate a graph of the unemployment rate since 1970 until the most recent observation. b. Present the histogram and statistics of the unemployment rate c. Obtain the correlogram for the unemployment rate. Select 16 lags d. Given your output for (c), interpret what the 4th row in the Q-stat column means. Mention what is the null hypothesis, the alternative, and whether there is evidence to reject the null hypothesis Now you estimate autocorrelations with regression. Warning: The correlogram presented in Eviews uses a recursive algorithm in order to compute autocorrelations, hence what you nd in your manual exercises is not identical to the output presented in the correlogram in Eviews. Thus use regression for the autocorrelations (see posted slides). e. Let yt unemployment rate at time t. Estimate the following model equations and present the Eviews outputs of each regression 1) yt = 0 + 1 yt 2) yt = 0 + 1 yt2 + ut 3) yt = 0 + 1 yt3 + ut 4) yt = 0 + 1 yt4 + ut The coe cients b 1 in these models represent the autocorrelations coe cients. f. Now estimate the following regressions (and show your output for each of them), which are used to estimate the partial autocorrelation coe cients (see page 70 in textbook) 5) yt = 0 + 1 yt1 + 2 yt2 + ut 6) yt = 0 + 1 yt1 + 2 yt2 + 3 yt3 + ut 7) yt = 0 + 1 yt1 + 2 yt2 + 3 yt3 + 4 yt4 + ut g. Now collect the autocorrelation coe cients from regressions (1), (2), (3) and (4), as well as the partial autocorrelation coe cients from regressions (5), (6) and (7). Fill in the following table with the information collected (numbers without proof of regressions receive no credit). These numbers do not have to match the output in Eviews when you ask for a correlogram (formulas used in Eviews are slightly dierent) lag AC PAC 1 2 3 4 h. Compare your estimated AC and PAC coe cients to the correlogram in Eviews. Explain dierences and similarities. i. Use the correlations that you collected from your regressions in order to manually construct the LjungBox Q3 statistic (see formula in slides for chapter 3). Note: Eviews output on Q3 cannot accepted, you need to show what is each magnitude in your statistic, as well as determining the appropriate critical value in the chi-square tables if = :01. Hint: chi-square tables shown in pages 466 - 467