Vector Autoregressive Moving Average Processes

  • Helmut Lütkepohl


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.


Forecast Error Move Average Vector Autoregressive White Noise Process Optimal Forecast 
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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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