Editorial - Universidad Autónoma del Estado de México

16 Paradigma económico Año 3 Núm. 1
To formally test the presence of a unit root, Zivot and Andrews
considered the following t statistic for testing a=1 in (2),
(3)
Notice that this statistic depends on the location of the break
fraction . In this framework, the goal of Zivot and Andrews is
to estimate the breakpoint that gives the heaviest weight to the
trend stationary alternative, that is, the date of the break is chosen
to give the least favourable result for the null hypothesis (1) using
the test statistic (3). In other words, is chosen to minimise the
t statistic for testing a=1. Let denote such minimising value;
then, by definition,
where is an specified subset of (0,1).
The number of extra regressors, k, required in the adf regressions
is allowed to vary for each tentative choice of . In turn, in
order to determine the truncation lag parameter, k, we follow the
same selection procedure proposed by Perron (1989). 12 Finally,
let us say that when we treat the selection of as a result of
the estimation procedure we can no longer use the critical values
of Perron (1989). Therefore, Zivot and Andrews (1992) derive
the asymptotic distributions of the test statistic in (4) and the
corresponding critical values to test the null in (1) against the
alternative in (2). 13
(4)
12. The procedure starts with an upper bound lag, say k max
. If the last included lag
is significant, choose k = k max
; if not, reduce k by 1 until the last lag becomes significant.
If no lags are significant, set k = 0; k max
is set equal to 8 by Perron (1989). A 10% value
of the asymptotic normal distribution, 1.60, is applied to evaluate the significance of the
last lag. Moreover, Ng and Perron (1995) use a simulation approach to prove that these
sequential tests are superior to the information-based methods, such as the information
criteria of Akaike and Schwarz, since the former shows less size distortions without
much loss of power. Zivot and Andrews (1992) and Lumsdaine and Papell (1997) used
the same approach.
13. For further methodological details see Zivot and Andrews (1992). Lucatero