What you’ll learn Identify Box-Jenkins autoregressive integrated moving average model integration order through level and differentiated time series first order trend stationary deterministic test and Phillips-Perron unit root test. Recognize autoregressive integrated moving average model autoregressive and moving average orders through autocorrelation and partial autocorrelation functions. Estimate autoregressive integrated moving average models such as random walk with drift and differentiated first order autoregressive. Identify seasonal autoregressive integrated moving average model seasonal integration order through level and seasonally differentiated time series first order seasonal stationary deterministic test. Estimate seasonal autoregressive integrated moving average models such as seasonal random walk with drift and seasonally differentiated first order autoregressive. Select non-seasonal or seasonal autoregressive integrated moving average model with lowest Akaike, corrected Akaike and Schwarz Bayesian information loss criteria. Evaluate autoregressive integrated moving average models forecasting accuracy through mean absolute error, root mean squared error scale-dependent and mean absolute percentage error, mean absolute scaled error scale-independent metrics. Identify generalized autoregressive conditional heteroscedasticity modelling need through autoregressive integrated moving average model squared residuals or forecasting errors second order stationary Ljung-Box lagged autocorrelation test. Recognize non-Gaussian generalized autoregressive conditional heteroscedasticity modelling need through autoregressive integrated moving average and generalized autoregressive conditional heteroscedasticity model with highest forecasting accuracy standardized residuals or forecasting errors multiple order stationary Jarque-Bera normality test. Estimate autoregressive integrated moving average models with residuals or forecasting errors assumed as Gaussian or Student™s t distributed and with Bollerslev simple or Glosten-Jagannathan-Runkle threshold generalized autoregressive conditional heteroscedasticity effects such as random walk with drift and differentiated first order autoregressive. Assess autoregressive integrated moving average model with highest forecasting accuracy standardized residuals or forecasting errors strong white noise modelling requirement. “Course Overview Course Description  Course Overview  Advanced Forecasting Models  Advanced Forecasting Models Data  Course File  Course Overview Slides  “Auto Regressive Integrated Moving Average Models ARIMA Models Slides  ARIMA Models Overview  First Order Trend Stationary Time Series  ARIMA Models Specification  Random Walk with Drift ARIMA Model  Differentiated First Order Autoregressive ARIMA Model  First Order Seasonal Stationary Time Series  SARIMA Models Specification  Seasonal Random Walk with Drift SARIMA Model  Seasonally Differentiated First Order Autoregressive SARIMA Model  ARIMA Model Selection  ARIMA Models Forecasting Accuracy  “Generalized Auto Regressive Conditional Heteroscedasticity Models GARCH Models Slides  GARCH Models Overview  Second Order Stationary Time Series  GARCH Models Specification  ARIMA-GARCH Models Estimation  Random Walk with Drift ARIMA-GARCH Model  Differentiated First Order Autoregressive ARIMA-GARCH Model  ARIMA-GJR-GARCH Models Estimation  Random Walk with Drift ARIMA-GJR-GARCH Model  Differentiated First Order Autoregressive ARIMA-GJR-GARCH Model  ARIMA-GARCH Model Selection  ARIMA-GARCH Models Forecasting Accuracy  “Non-Gaussian Generalized Auto Regressive Conditional Heteroscedasticity Models Non-Gaussian GARCH Models Slides  Non-Gaussian GARCH Models Overview  Multiple Order Stationary Time Series  Non-Gaussian GARCH Models Specification  ARIMA-GARCH-t Models Estimation  Random Walk with Drift ARIMA-GARCH-t Model  Differentiated First Order Autoregressive ARIMA-GARCH-t Model  ARIMA-GJR-GARCH-t Models Estimation  Random Walk with Drift ARIMA-GJR-GARCH-t Model  Differentiated First Order Autoregressive ARIMA-GJR-GARCH-t Model  Non-Gaussian ARIMA-GARCH Model Selection  Non-Gaussian ARIMA-GARCH Models Forecasting Accuracy  Residuals White Noise