Multiple Time Series Modeling Using the SAS VARMAX Procedure

Chapter 6: Models for Univariate Time Series

Introduction

Autocorrelations

Autoregressive Models

Moving Average Models

ARIMA Models

Infinite-Order Representations

Multiplicative Seasonal ARIMA Models

Information Criteria

Use of SAS to Estimate Univariate ARIMA Models

Conclusion

Introduction

This chapter briefly introduces the theory of Autoregressive Integrated Moving Average (ARIMA) models for univariate time series. First, the series has to be differenced if necessary to meet the assumption of stationarity. (For more information, see Chapter 5.) The “I” in ARIMA is for integrated because a series that is transformed into stationarity by differencing is called integrated. Then an Autoregressive Moving Average (ARMA) model is fitted to the stationary ...