Consider the US quarterly index of manufacturing real output from 1987.I to 2017.II. The data can be obtained from FRED (code: OUTMS). Let xt =

ln(Ot) − ln(Ot−1), where Ot is the real output index (2009=100).

(a) Build a linearARmodel for xt. Perform model checking and write down the fitted model.

(b) Fit the NAAR model

using the gam package. What are the estimates of the coefficients? Perform model checking. Is the model adequate? Why?

(c) Perform analysis of variance to confirm that the NAAR model contributes significantly over the linear AR model of part (a).

(d) Obtain the residual plots of the two fitted models in parts

(a) and (b).
Comments on the fit of the models.

Transcribed Image Text:

X = Co+fi (x_1)+f(x2)+