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Question 1a: Exploratory Data Analysis • Plot the Time Series and ACF plots

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Question 1a: Exploratory Data Analysis • Plot the Time Series and ACF plots. Comment on the main features, and identify what (if any) assumptions of stationarity are violated. Hint: Before plotting, can you infer anything from the nature of the data? • On its own, which type of model do you think will fit the data best: trend or seasonality fitting? Question 1b: Trend Estimation Fit the following trend estimation models: • Moving average • Parametric quadratic polynomial • Local Polynomial • Splines Overlay the fitted values on the original time series. Construct and plot the residuals with respect to time and ACF of residuals. Comment on the four models fit and on the appropriateness of the stationarity assumption of the residuals. Question 1c: Seasonality Estimation Seasonality Estimation: Fit the following seasonality estimation models. • Categorical Linear Regression (ANOVA) • COS-SIN Overlay the fitted values on the original time series. Construct and plot the residuals with respect to time and ACF plots. Comment on how the two models fit and on the appropriateness of the stationarity assumption of the residuals. Also compare the fits to those in part B and comment if your initial prediction was correct.