3. This exercise uses the file “LYNX.txt” from the Exercises folder.

(i) Assess whether a transformation is required for the Lynx data. If a transformation is appropriate, use it to complete all steps of the exercise.

(ii) Estimate the period of the lynx data and use nls() to refine this estimate.

(iii) Fit a model with fixed period to the data and graph this model versus the data.

How good does this model look (compute R2)?

(iv) Fit a model with about three complete periods per window, and a fixed period, but allowing B, C, and ???? to vary. Plot the resulting model versus the data.

How much better is this model (compute R2)? Make a graph like Figure 17.5 showing how much the mean, phase, and amplitude vary.

(v) Use model selection based on the one-step ahead model to find the best window size. How similar to or different from the sunspot data is this.