Trend and seasonality analysis 1a. Plot the Time Series and…
Trend and seasonality analysis 1a. Plot the Time Series and the ACF plot for the time series on beer production. Comment on the stationarity of the time series based on these plots. Which (if any) stationarity assumptions are violated? How would you suggest to model this time series? 1b. Fit a moving average trend, splines trend estimation and a local polynomial trend on the time series. Overlay the fitted values derived from each trend estimation model on the corresponding data and calculate the Mean Absolute Percentage Error MAPE for the fitted values from each model. Comment on the effectiveness of each model to estimate the trend for the series, particularly with respect to MAPE. Comment on the trend with respect to the beer production. 1c. Fit an ANOVA and a cos-sin seasonality model on the time series. Overlay the residuals of the fitted values derived from each seasonal estimation model and comment on the fit. Calculate the MAPE for the fitted values from each model. Do the residuals show that the seasonal models are sufficient to capture seasonality? Comment and compare on the significance of each model estimation of the season coefficients for the series versus beer production. 1d. Fit a nonparametric trend-seasonality model to the time series. Overlay the fitted values and calculate MAPE for the model. How does the fit of this model compare with the trend estimation models that you created in Question 1b and the seasonal models created in Question 1c? Does the combination of trend and seasonality improve the fit? Compare the MAPE of the trend-only, seasonality-only and trend-seasonality models. 1e. Plot the residuals and their ACF and PACF for the model that you created in Question 1d. Evaluate stationarity for the model residuals based on these plots. Provide your explanation on whether the stationarity assumptions hold.