Lesson 3: Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values

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Assignments:

  • Reading Assignment
    • Sections 3.1 and 3.2 (pages 83-96) are worth a skim, but don't get too bogged down in the theory.
    • Section 3.7 (pages 141-144).
    • Section 3.8 (pages 144-153) is a core section about building models. 
    • Sections 3.3-3.6 are quite mathematical and can be skipped or lightly skimmed unless you have a deep interest in theory.  Pages 106-108 are of interest.
    • Pages 52-53 in Chapter 2 might also be helpful.
  • Read through the Lesson 3 online notes that follow.
  • Complete Lesson 3 Assignment.

Overview:

This week we'll learn some techniques for identifying and estimating non-seasonl ARIMA models.  We'll also look at the basics of using an ARIMA model to make forecasts.  We'll look at seasonal ARIMA models next week.  Lesson 3.1 gives the basic ideas for determining a model and analyzing residuals after a model has been estimated.  Lesson 3.2 gives a test for residual autocorrelations.  Lesson 3.3 gives some basics for forecasting using ARIMA models.  We'll look at other forecasting models later in the course.

This all relates to Chapter 3 in the book, although the authors give quite a theoretical treatment of the topic(s).

Learning Objectives:

After successfully completing this lesson, you should be able to:

  • Identify and interpret a non-seasonal ARIMA model
  • Distinguish ARIMA terms from simultaneously exploring an ACF and PACF
  • Test that all residual autocorrelations are zero
  • Convert ARIMA models to infinite order MA models
  • Forecast with ARIMA models
  • Create and interpret prediction intervals for forecasts