Compute and plot the first twenty autocorrelations of the series and comment on the persistence of unemployment rate.

Questions

1. Compute and plot the first twenty autocorrelations of the series and comment on the persistence of unemployment rate.
2. Compute the quarterly change in the unemployment rate, and call it . Plot the value of for 1958:Q2 to 2013:Q4. Why is there one less observation in the series than the series? Does the series look stationary (substantiate your answer)?
3. Compute and plot the first eight autocorrelations of the series. How does this compare to the autocorrelation of unemployment in Question 2? What can you say about the persistence in the series.
4. Fit AR(1), AR(2) and AR(3) models to the using the lm() -command; that is, run an OLS regression of on , … using the lm() -command. Report the estimated regression results for all three models and discuss the estimated coefficients. Hint I: Consult slides from live lecture
5. Hint II: Compute robust standard errors.
6. Using the best model from Question 5, make a 1-step ahead forecast of the unemployment rate in 2014:Q1. Report your forecast. Hint I: Consult slides from live lecture
7. Hint II: You are asked to forecast ! 1 1 # R-script for EC2208 problem set 7 2 # Author: 3 # Date: 4 # Load relevant libraries 5 library(AER) # load Applied Econometrics with R library 6 library(quantmod) # Load quantmod library for time series analysis 7 library(readxl) # Load readxl to load spreadsheet data 8 library(stats) # Load stats to compute acf functions 9 # Read US quarterly macro series into dataframe usmac 10 usmac <- read_excel("./PS6/us_macro_quarterly.xlsx") 11 # Fix format of date 12 usmac$...1 <- as.yearqtr(usmac$...1, format = "%Y:0%q") 13 # Relabel column names in dataframe 14 colnames(usmac) <- c("Date", "GDPC96", "JAPAN_IP", "PCECTPI", "GS10", "GS1", "TB3MS", "UNRATE", "EXUSUK", "CPIAUCS L") 15 UNRATE UNRATE unempt unempt unempt Δunempt Δunempt Δunempt unempt Δunempt Δunempt Δunempt Δunempt Δunempt Δunempt−1 unemp2014:Q