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THE ORDER OF THE ERROR TERM FOR MOMENTS OF

THE LOG LIKELIHOOD RATIO UNIT ROOT TEST

IN AN AUTOREGRESSIVE PROCESS

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ROLF LARSSON

*Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden*
(Received October 25, 1996; revised March 24, 1997)

**Abstract.**
This paper investigates the asymptotics
of the log likelihood ratio test for a unit root in an
autoregressive (AR) process of general order. The main result
is that the expectation and variance (in fact, all moments) of
the test statistic may, to the order of *T*^{ -1}, where *T* is
the number of observations, be approximated by the expectation
and variance of the corresponding test in an AR(1) process.
This result has obvious implications for the asymptotics of
unit root tests for panels. An explicit formula for the
approximation error of a test in an AR(2) process is also
given.

*Key words and phrases*:
Approximation error, unit
root test.

**Source**
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