統計学輪講（第１８回）

日時    2005年 9月 20日(火)  15時〜16時40分
場所    経済学部新棟３階第３教室
講演者  荒井 洋一(経済)
演題    Point optimal tests for cointegration with unknown variance- 
        covariance matrix (joint with Eiji Kurozumi)
概要：
  This paper investigates point optimal invariant (POI) tests for 
the null hypothesis of cointegration assuming the unknown variance 
covariance matrix of the error term. Since the variance-covariance 
matrix is unknown, we consider the POI test among a class of tests 
that are invariant to scale change as well as location shift in the 
dependent variable. As a special case of the POI test, we also derive 
the locally best invariant and unbiased (LBIU) test. We find that our 
LBIU and POI tests have different characteristics from the locally best 
invariant test in Shin (1994) and the POI test in Jansson (2005), both 
of which consider only location invariance. We show that the difference 
comes from the distributional difference between the maximal invariants. 
We also propose to modify our tests to accommodate general assumptions 
on the error term. Monte Carlo simulations are conducted to investigate 
the finite sample properties of the tests, and it is shown that our 
modified tests perform better than Jansson's and Shin's tests in finite 
samples.

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Tokyo University