Econ 3342 Assignment on Time Series

1. In this exercise you compute different types of growth rates for real GDP. First, go to https://fred.stlouisfed.org/ and search for the quarterly GDP series gdpc1 (otherwise, just google gdpc1), this series si available since

1947. In the possible formats, download as an EXCEL file. Then import your data into Eviews (you don't

have to clean the data, just import it and Eviews does the rest).

In what follows, let y represent gdpc1 (which is quarterly real GDP). After importing gdpc1 into Eviews, then for all the time periods (all quarters in this sample starting in 1947 Ql) do the following

a. In Eviews, create the variables growthi and difflog as

growth1 = 4 *100 *(yt - Yt-1)/Yt-1 difflog=4*100*(In(Yt)- In(Yt-1))

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 *(yt - Yt-4)/yt-4

where growth measures the annual growth of GDP with respect to the same quarter the previous year.

nI Eviews, ni order to generate anew variable, select Quick, Generate Series.., then write the equation that defines your new variable (can also see the videos posted in the class webpage). Once you have created each series, create a graph of the time series of each variable (In Eviews: View, graph) and take a screenshot of each of them (for an example, se my screenshots at the end of this document, which include all but the last data points for GDP. Your homework should also include the latest data points not included in my screenshot).

b. Compare the statistics (Quick, Series Statistics, Histogram and Stats) as well as the correlogram

(Quick, Series Statistics, Correlogram) of growth1 and difflog (produce the screenshots of this activity). Do there appear to be any significant differences between these 2 variables (you don't have to perform some

statistical test on the series, just contrast the histogram, correlogram and statistics)?

c. Compare the correlograms for growth1 and growth (produce the screenshots of this activity). Which series appears to have higher linear dependence (as measured by the magnitude of the AC and PAC coeffi- cients?) Do you have intuition for that? Explain

.2 Go to https://fred.stlouisfed.org/ and search for the monthly unemployment rate series unrate. Down- load the data series as an EXCEL file. Then import your data into Eviews (see videos on how to import the

date or see previous homework).

a. In Eviews, generate a graph of the unemployment rate time series since 1948 until the most recent observation (Produce the screenshot).

In what folows, for the rest of the assignment do the analysis starting ni January of 1970. b. Present the screenshot of the histogram and statistics of the unemployment rate.

c. Obtain the screenshot of the correlogram for the unemployment rate. Select 12 lags in your correlogram.

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.

e. Use a regression to estimate directly the second order partial autocorrelation coe cient. The coe - cient is NOT going to be identical to the PAC shown in the correlogram from Eviews since Eviews uses a recursive algorithm in order to compute autocorrelations (translation: Eviews correlogram uses a shortcut in its routine). Take a screenshot of your regression, explain how you obtained the second order partial autocorrelation coe cient and in your explanation mention the numerical value that is requested in this exercise.