Periodic VAR Processes and Intervention Models

  • Helmut Lütkepohl


In the previous chapter we have considered nonstationary VAR models with time invariant parameters. Nonstationarity, that is, time varying first and/or second moments of a process, can also be modeled in the framework of time varying parameter processes. Suppose, for instance, that the time series show a seasonal pattern. In that case a VAR(p) process with different intercept terms for each season may be a reasonable model:
$$ y_t = v + A_1 y_{t - 1} + \cdots + A_p y_{t - p} + u_t $$
Here v i is a (K × 1) intercept vector associated with the i-th season, that is, in (12.1.1) the time index t is assumed to be associated with the i-th season of the year. It is easy to see that such a process has a potentially different mean for each season of the year.


Intervention Model Exogenous Variable Likelihood Ratio Statistic Nonstationary Process Asymptotic Normal Distribution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Helmut Lütkepohl
    • 1
  1. 1.Institute of Statistics and EconometricsUniversity of KielKielGermany

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