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ARIMA Time Series Models

  • Szymon Borak
  • Wolfgang Karl Härdle
  • Brenda López-Cabrera
Chapter
Part of the Universitext book series (UTX)

Abstract

The autoregressive moving average (ARMA) model defined as
$$X_{t} = \nu + \alpha _{1}X_{t-1} + \ldots + \alpha _{p}X_{t-p} + \beta _{1}\epsilon _{t-1} + \ldots + \beta _{q}\epsilon _{t-q} + \epsilon _{t},$$
deals with linear time series. The time series should be a covariance stationary process. It consists of two parts, an autoregressive (AR) part of order p and a moving average (MA) part of order q. When an ARMA model is not stationary, the methods of analyzing stationary time series cannot be used directly. In order to handle those processes within the framework of the classical time series analysis, we must first form the differences to get a stationary process.

Keywords

Autocorrelation Function Unit Root Moving Average ARMA Model ARIMA Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Szymon Borak
    • 1
  • Wolfgang Karl Härdle
    • 1
  • Brenda López-Cabrera
    • 1
  1. 1.Humboldt-Universität zu Berlin Ladislaus von Bortkiewicz Chair of StatisticsC.A.S.E. Centre for Applied Statistics and Economics School of Business and EconomicsBerlinGermany

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