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Lesson 3: Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values | STAT 510
The Pennsylvania State University - Eberly College of Science
STAT 510 Applied Time Series Analysis
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Lesson 3: Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values
This week we'll learn some techniques for identifying and estimating non-seasonal 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).
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
Next3.1 Non-seasonal ARIMA Models »
Lesson 1: Time Series Basics
1.1 Overview of Time Series Characteristics
1.2 Sample ACF and Properties of AR(1) Model
1.3 R Code for Two Examples in Lessons 1.1 and 1.2
Lesson 2: MA Models, Partial Autocorrelation, Notational Conventions
2.1 Moving Average Models (MA models)
2.2 Partial Autocorrelation Function (PACF)
Lesson 3: Identifying and Estimating ARIMA models; Using ARIMA models to forecast future values
3.1 Non-seasonal ARIMA Models
3.3 Forecasting with ARIMA Models
Lesson 4: Seasonal Models
4.1 Seasonal ARIMA models
4.2 Identifying Seasonal Models and R Code
Lesson 5: Smoothing and Decomposition Methods and More Practice with ARIMA models
5.2 Smoothing Time Series
Lesson 6: The Periodogram
Lesson 8: Regression with ARIMA errors, Cross correlation functions, and Relationships between 2 Time Series
8.1 Linear Regression Models with Autoregressive Errors
8.2 Cross Correlation Functions and Lagged Regressions
Lesson 9: Prewhitening; Intervention Analysis
9.1 Pre-whitening as an Aid to Interpreting the CCF
Lesson 10: Longitudinal Analysis/ Repeated Measures
10.1 Repeated Measures and Longitudinal Data
Lesson 11: Vector Autoregressive Models/ ARCH Models
11.2 Vector Autoregressive models VAR(p) models
Lesson 12: Spectral Analysis
12.1 Estimating the Spectral Density
Lesson 13: Fractional Differencing and Threshold Models
13.1 Long Memory Models and Fractional Differences
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