Consider the monthly mean duration of unemployment in the USA. The data were seasonally adjusted from January 1948 to August 2017. They are available from FRED and are also in the file Unempduration.csv. The mean duration shows an upward trend so let xt be the first difference of the original data.

(a) Build a linearARmodel for xt. Write down the fitted model and perform model checking.

(b) Perform the threshold tests of Chapter 1 to confirm that xt exhibits threshold nonlinearity.

(c) Use p = 5 and d ∈ {1,…, 5}, where d denotes the delay, to select the threshold variable xt−d. You may use the p value of the threshold test to select d.

(d) Build a two-regime TAR(5) model for xt. Perform model checking and write down the fitted model.

(e) Compare the linear AR model and the TAR model.