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13 - Linear Time Series Models

from PART FOUR - Stationary Time Series

Published online by Cambridge University Press:  05 January 2013

Vance Martin
Affiliation:
University of Melbourne
Stan Hurn
Affiliation:
Queensland University of Technology
David Harris
Affiliation:
Monash University, Victoria
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Summary

The maximum likelihood framework presented in Part ONE is now applied to estimating and testing a general class of dynamic models known as stationary time series models. Both univariate and multivariate models are discussed. The dynamics enter the model in one of two ways. The first is through lags of the variables, referred to as the autoregressive part, and the second is through lags of the disturbance term, referred to as the moving average part. In the case where the dynamics of a single variable are being modelled, these models are referred to as autoregressive moving average (ARMA) models. In the multivariate case, where the dynamics of multiple variables are modelled, these models are referred to as vector autoregressive moving average (VARMA) models. Jointly, these models are called stationary time series models where stationarity refers to the types of dynamics allowed for. The case of nonstationary dynamics is discussed in Part FIVE.

The specification of dynamics through the inclusion of lagged variables and lagged disturbances is not new. It was discussed in Part TWO in the context of the linear regression model in Chapter 5 and more directly in Chapter 7 where autoregressive and moving-average dynamics were specified in the context of the autocorrelated regression model. In fact, a one-to-one relationship exists between the VARMA class of models investigated in this chapter and the structural class of regression models of Part TWO, where the VARMA model is interpreted as the reduced form of a structural model.

Type
Chapter
Information
Econometric Modelling with Time Series
Specification, Estimation and Testing
, pp. 467 - 511
Publisher: Cambridge University Press
Print publication year: 2012

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  • Linear Time Series Models
  • Vance Martin, University of Melbourne, Stan Hurn, Queensland University of Technology, David Harris, Monash University, Victoria
  • Book: Econometric Modelling with Time Series
  • Online publication: 05 January 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043205.015
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  • Linear Time Series Models
  • Vance Martin, University of Melbourne, Stan Hurn, Queensland University of Technology, David Harris, Monash University, Victoria
  • Book: Econometric Modelling with Time Series
  • Online publication: 05 January 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043205.015
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Linear Time Series Models
  • Vance Martin, University of Melbourne, Stan Hurn, Queensland University of Technology, David Harris, Monash University, Victoria
  • Book: Econometric Modelling with Time Series
  • Online publication: 05 January 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139043205.015
Available formats
×