In this case each observation would have its own

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could be considered consistent with the estimated equation. In this case each observation would have its own period-specific dummy. Such tests are sometimes called post-sample predictive tests. Consider the following model ( t =1 991, 1992, …,2000) : 0 1 1 2 2 2001 2001 2002 2002 2003 2003 t t t t Y X X e I e I e I u where the observation-specific dummies of 2001 I , 2002 I and 2003 I are defined as: 2001 1 for 2001 0 otherwise I , 2002 1 for 2002 0 otherwise I , 2003 1 for 2003 0 otherwise I Here, the coefficients of observation-specific dummies denoted by 2001 e , 2002 e and 2003 e are the expected value of forecast errors (prediction errors) of the corresponding years (The proof is beyond the scope of this lecture). In order to test for structural change in 2001, 2002 and 2003; we can test 2001 e , 2002 e and 2003 e individually (t test) and jointly (F test) different from zero.
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Christopher Reinemann
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