Consider the annual sunspot series referred to as Series E in this text. The series is also available for a slightly longer time period as series ‘‘sunspot.year’’ in the R datasets package.

(a) Plot the time series and fit an AR(3) model to the series.

(b) Use the procedure described by McLeod and Li (1983) to test for nonlinearity in the series.

(c) Repeat part

(b) using the Keenan and Tsay tests for nonlinearity.

(d) Describe how you might fit a nonlinear time series model to this series.