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ARMA and ARIMA Models

  1. Ulrich Helfenstein

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a12003

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Helfenstein, U. 2005. ARMA and ARIMA Models. Encyclopedia of Biostatistics. 1.

Author Information

  1. Zurich University, Zurich, Switzerland

Publication History

  1. Published Online: 15 JUL 2005

Abstract

Notifications of diseases, entries in a hospital, and so on are frequently collected in regular intervals. Consecutive observations of such “time series data” are likely to be dependent. In environmental medicine, where series such as daily concentrations of pollutants are analyzed, it is evident that dependence of consecutive measurements may be important. A flexible class of models allowing representing of the stochastic dependence of consecutive data are ARIMA models (autoregressive integrated moving average models). They may be particularly useful for forecasting. Forecasts of epidemiological time series are needed since it is of interest to know what frequencies of diseases might be expected in the future, in order to better plan the distribution of resources. It may also be of interest to assess relations between two ARIMA time series, a “response” series such as “daily number of patients coming to a clinic” and “explanatory” series such as daily concentrations of a pollutant, daily mean temperature, and so on. Such situations may be adequately represented by the so-called “transfer function model”. Analogous questions arise when studying time series data recorded in an individual subject. This article reviews basic concepts of the topic. The methods are illustrated by medical applications.

Keywords:

  • ARMA models;
  • ARIMA models;
  • time series data;
  • transfer function models