Title

fflm2 -- Two-break LM unit-root test with RALS and RALS2 (factor)
augmentation

Syntax

fflm2 varname [if] [in] [, options]

The series must be tsset.

rals(#) 0 plain two-break LM (default), 1 RALS, 2
RALS with common/group factors

factors(varlist) common and group factors (required with rals(2))

pmax(#) maximum augmentation lag (default 8)

ic(#) lag selection: 1=AIC, 2=BIC, 3=t-stat (default)

trim(#) break-location trimming fraction (default 0.10)

Description

fflm2 implements the Lee-Strazicich (2003) minimum-LM unit-root test with
two endogenous structural breaks in level and trend. The two break dates are
selected by grid search (minimising the LM statistic). With rals(1) the LM
regression is augmented by the residual-augmented least-squares (RALS) moment
terms for non-normal errors, and with rals(2) by supplied common and group
factors().

Unlike ffrals and ffadf, the two-break LM null distribution is
tabulated, so fflm2 computes deterministic p-values by
interpolation: the plain test uses the Lee-Strazicich (2003) critical values
(indexed by the break fractions) and the RALS test uses the Meng-Lee-Tieslau
(2017) rho-squared-indexed critical values with Hansen interpolation. The plain
test therefore reproduces the source GAUSS routine byte-for-byte; the RALS
statistic matches to about two decimal places (the residual difference is the
numerical linear algebra of the augmented impulse-dummy design). fflm2 is
part of the ffrals library.

Options

rals(#), factors(varlist): as in ffrals.

pmax(#), ic(#): the maximum lag (default 8) and lag-selection
rule (3=t-stat, the default, as in the source routine).

trim(#): the trimming fraction for the break search (default 0.10).

Examples

Plain two-break LM test:

. fflm2 lgdp, rals(0)

RALS and factor-augmented versions:

. fflm2 lgdp, rals(1)

. fflm2 lgdp, rals(2) factors(fcommon fgroup)

Stored results

fflm2 is rclass and stores r(stat), r(p),
r(break1), r(break2), r(lag), r(rho2) (RALS),
r(cv1), r(cv5), r(cv10) and r(N). The test rejects for a
statistic below the critical value. The break columns report the estimated
break periods in the units of the time variable.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane

Faithful Stata port of the GAUSS LM2_trend_break/RALS_LM2
routines by S. Nazlioglu; the plain test validated byte-for-byte against the GAUSS
output (statistic, breaks, lag and critical values).