The name is absent

Maddala and Kim (1998) argues, that because of the size distortions and poor power problems
associated with the Augmented Dickey-Fuller unit root tests, it is preferable to use the DF-
GLS unit root test, derived by Elliott, Rothenberg and Stock (1996).

Elliott, Rothenberg and Stock develop the asymptotic power envelope for point optimal
autoregressive unit root tests, and propose several tests whose power functions are tangent to
the power envelope and never too far below (Maddala and Kim, 1998). The proposed DF-
GLS test works by testing the a0=0 null hypothesis in regression (3):

∆ydt = a0y^dt-1 + a1∆y^dt-1 +...+ ap∆^dt-p + et                                                           (3)

where y^dt is the locally detrended yt series that depends on whether a model with a drift or
linear trend is considered. In case of a model with a linear trend, the following formula is
used to obtain the detrended series y^dt:

ydt = yt — β о — β t •                                                                                 (4)

β^{^}0 and β^{^}t are obtained by regressing y on z , where:

У = [y 1,(^{1 - a}L)y2^,∙∙∙^,(^{1 - a}L)Ут ]                                                                ⁽⁵⁾

z = [z ₁,(1 - aL)z₂,∙∙∙,(1 - aL)z_T ] .                                                               (6)

Elliott, Rothenberg and Stock argue that fixing c = -7 in the drift model, and c = -13∙5in the
linear trend model, used in (7) and (8), the test IS within 0∙01 of the power envelope:
zt = (1,t)^'                                                                                                            (7)

— c                                                                                                       . .

^a = ^{1 +} t ■                                                                        ⁽⁸⁾
4.2. Testing for unit roots in the presence of structural breaks

Perron (1989) has carried out tests of the unit root hypothesis against the alternative
hypothesis of trend stationarity with a break in the trend∙ The two breakpoints included were
1929 (the Great Crash), and 1973 (the Oil Shock)∙ Perron analysed the Nelson and Plosser
(1982) macroeconomic data and quarterly post-war GNP series∙ His results rejected the unit
root null hypothesis for most time series∙ Three models were considered:

yt = ɑɪ + β1t + (o⅛ - α1)DUt + et, t=1,2,.∙T

yt = α1 + β1t + (β2 - β1)DTt + et, t=1,2,.∙T

yt = α1 + β1t + (α2 - α1)DUt + (β2 - β1)DTt + et, t=1,2,..T

f t if t > TB
where, DT_t = <

0 else

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