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Vector Autoregressive Moving Average Processes

  • Helmut Lütkepohl

Abstract

In this chapter, we extend our standard finite order VAR model,
$$y_t = \nu + A_1 y_{t - 1} + \ldots + A_p y_{t - p} + \varepsilon _t , $$
by allowing the error terms, here εt, to be autocorrelated rather than white noise. The autocorrelation structure is assumed to be of a relatively simple type so that εt has a finite order moving average (MA) representation,
$$\varepsilon _t = u_t + M_1 u_{t - 1} + \ldots + M_q u_{t - q} ,$$
where, as usual, u t is zero mean white noise with nonsingular covariance matrix Σu. A finite order VAR process with finite order MA error term is called a VARMA (vector autoregressive moving average) process.

Keywords

Forecast Error Move Average Vector Autoregressive White Noise Process Optimal Forecast 
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 2005

Authors and Affiliations

  • Helmut Lütkepohl
    • 1
  1. 1.Department of EconomicsEuropean University InstituteFirenzeItaly

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