7. Additional Issues in ARIMA Models

  1. Søren Bisgaard and
  2. Murat Kulahci

Published Online: 31 MAY 2011

DOI: 10.1002/9781118056943.ch7

Time Series Analysis and Forecasting by Example

Time Series Analysis and Forecasting by Example

How to Cite

Bisgaard, S. and Kulahci, M. (2011) Additional Issues in ARIMA Models, in Time Series Analysis and Forecasting by Example, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118056943.ch7

Author Information

  1. Technical University of Denmark

Publication History

  1. Published Online: 31 MAY 2011
  2. Published Print: 5 JUL 2011

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470540640

Online ISBN: 9781118056943



  • ARIMA model;
  • deterministic trend models;
  • forecasting;
  • linear difference equations;
  • stochastic models;
  • time series data analysis;
  • unit root nonstationary processes


ARIMA models have been used extensively in practice for the analysis of time series data and forecasting. This chapter discusses linear difference equations, which provide the theoretical foundation for the ARIMA models. It also shows that there is a very close relationship between the deterministic trend models and the ARIMA models when it comes to the forecasts made on the basis of these models. There are ways to work around the rigidity of the deterministic trends, for example, by simply allowing the trend and seasonal components to follow stochastic models. ARIMA models offer flexible, reasonable, sound, and easy-to-understand alternatives for many situations encountered in practice. First order nonstationary processes are sometimes called unit root nonstationary processes. The random walk is a simple example of a nonstationary unit root process.

Controlled Vocabulary Terms

ARIMA model; forecasting; stochastic processes; trend analysis