3. Autoregressive Moving Average Models

  1. Ngai Hang Chan

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch3

Time Series: Applications to Finance with R and S-Plus, Second Edition

Time Series: Applications to Finance with R and S-Plus, Second Edition

How to Cite

Chan, N. H. (2010) Autoregressive Moving Average Models, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch3

Author Information

  1. The Chinese University of Hong Kong, Department of Statistics, Shatin, Hong Kong

Publication History

  1. Published Online: 28 JAN 2011
  2. Published Print: 13 SEP 2010

ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

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Keywords:

  • autocorrelation functions (ACF);
  • autoregressive integrated moving average models (ARIMAs);
  • autoregressive model (AR);
  • autoregressive moving average model (ARMA);
  • moving average model (MA)

Summary

This chapter introduces several commonly used probabilistic models for time series analysis. It briefly discusses the three kinds of models: the moving average model (MA), the autoregressive model (AR), and the autoregressive moving average model (ARMA) which are used to describe stationary time series. In addition, since certain kinds of nonstationarity can be handled by means of differencing, the chapter also studies the class of autoregressive integrated moving average models (ARIMAs). There seems to be confusion regarding the notion of stationarity and causality for AR (ARMA in general) models. The chapter clarifies this ambiguity. The usefulness of ARMA models lies in their parsimonious representation. As in the AR and MA cases, properties of ARMA models can usually be characterized by their autocorrelation functions (ACF). Since we usually process a time series before analyzing it (e.g., detrending), it is natural to consider a generalization of ARMA models, the ARIMA model.

Controlled Vocabulary Terms

autocorrelation function; autoregressive integrated moving average process; autoregressive model; autoregressive moving average process; moving average model