2. From the Exercises folder scan the file “Furnas 31 78.txt” (aka DataMarket–Time seriesdata library–hydrology–Monthly riverflow in cms, Furnas–vazoes medias mensais, 1931–1978)

(i) Plot the data. Does it appear periodic? Is a transformation required?

(ii) Develop a table ofmodel selection information and useAIC to pick the optimal periodic model.

(iii) Using the same information, develop sequential likelihood ratio tests. What is picked as the best model?

(iv) Use data splitting (explain how and why you chose the split in the data) to fit a model to a training set and validate the model on the rest of the data. What is R2 for the training set? The validation set?

(v) Plot and produce the acf() plot for the residuals from the saturated model and the model picked as best by AIC. How comparable are the residuals?