Summary of 9.4: Dynamic regression (ARIMAX) models in R

00:00:00 - 00:05:00

In the YouTube video "9.4: Dynamic regression (ARIMAX) models in R," the speaker demonstrates how to use ARIMA X models for time series forecasting in R, specifically for the Personal Consumption and Income data sets. After confirming both series are stationary using the KPSS test, they fit an ARIMA X model with an AR process and two MA processes to capture time series dynamics, using the R function "arima" and the "xreg" argument to include income as a covariate. The speaker checks the residuals, which are mostly white noise but exhibit some heteroskedasticity, and decides to use the model for forecasting. Since future income values are not available, eight future income values are generated by repeating the mean income value. The speaker then uses the fitted model and future income values to generate forecasts for consumption using the "forecast" function. The ARIMA X model allows for multiple explanatory variables, such as consumption and production, resulting in a zero-order AR process and three MA processes for the time series dynamics, as well as intercept and slope coefficients for income and production. The model is represented by two equations: the first equation uses the regression model to forecast the yt variable based on multiple xt variables, and the second equation captures time series dynamics.

• 00:00:00 In this section of the video, the speaker demonstrates how to use dynamic regression models, specifically ARIMAX models, in R for time series forecasting. They begin by ensuring the Personal Consumption and Income data sets are stationary using the KPSS test. After confirming both series are level stationary, they fit an ARIMA X model using the R function "arima" and the "xreg" argument to include the income variable as a covariate. The model includes an AR process and two MA processes to capture time series dynamics. The speaker then checks the residuals of the model and finds they are mostly white noise but exhibit some heteroskedasticity. Despite this, they decide to use the model for forecasting. Since future income values are not available, the speaker generates eight future income values by repeating the mean income value.
• 00:05:00 In this section of the YouTube video titled "9.4: Dynamic regression (ARIMAX) models in R," the speaker explains how to use ARIMA X models for forecasting future values based on past data. They generate future income values and use them in the forecast function along with the fitted model that has income as an explanatory variable for consumption. The speaker also mentions that it's possible to regress a dependent variable on multiple explanatory variables by passing multiple variables in the autorimma function. In this case, they use consumption and production as explanatory variables, resulting in a zero-order AR process and three MA processes for the time series dynamics, as well as intercept and two slope coefficients for income and production. The ARIMA X model is represented by two equations: the first equation uses the regression model to forecast the yt variable based on multiple xt variables, and the second equation captures time series dynamics.