Title

segmcoint kim -- Kim (2003) weighted-LS tests for segmented cointegration

Syntax

segmcoint kim depvar indepvars [if] [in]
[, options]

deterministic(string) none, const (default), trend
= Kim Case I / II / III

trimbar(#) upper bound on the length of the noncointegration interval,
as a fraction of T (Lemma 1 conservative bound); default 0.3

minlen(#) minimum noncointegration length as a fraction of T; default 0.05

bwidth(#) Bartlett bandwidth for the long-run variance; default = automatic

adflags(#) number of lagged differences in the ADF variant; default 0

grid(#) search-grid step (obs); default = automatic thinning for large T

graph plot each statistic against its 5% critical value

graphname(name) graph name

noheader suppress header

The data must be tsset. n = 1 + number of regressors must be <= 6
(the range of the tabulated critical values).

Description

segmcoint kim implements the procedure of
Kim (2003). For a trial noncointegration interval N_T the
cointegrating vector is estimated by weighted least squares that zeroes the weight
on N_T (the only weighting that yields a consistent estimator under the
alternative), Phillips-Perron-Ouliaris (Zrho*, Zt*) and augmented
Dickey-Fuller (ADFrho*, ADFt*) statistics are formed on the resulting
cointegration-set residuals, and the infimum over all admissible N_T is taken.
The smallest value constitutes the evidence against the null. The command also
reports the estimated location of the noncointegration interval.

Options

deterministic(string) selects the deterministic kernel of the
cointegrating regression, matching the tabulated critical-value cases.

trimbar(#) is the upper bound l-bar on the relative length of the
noncointegration interval used when searching and when selecting critical values.
Kim tabulates l-bar = 0.3; a smaller bound gives a more conservative test
(Lemma 1).

minlen(#) sets the shortest interval considered.

bwidth(#) fixes the Bartlett/Newey-West bandwidth of the long-run
variance estimator; the default uses floor(4 (Tc/100)^(2/9)).

adflags(#) adds lagged differences to the ADF variant (eq 3.5).

grid(#) thins the segmentation search for speed; the statistics are
continuous in the segmentation fractions so a coarse grid changes results only
slightly in large samples.

Interpreting the output

Four statistics are printed with their 1/2.5/5/10% lower-tail critical values
(Kim Tables 1-2, l-bar = 0.3). Reject the null of no cointegration when a
statistic is below the critical value; stars mark the level. Zt* is
generally the most powerful. The last block reports the estimated noncointegration
interval N_T as sample fractions, from both the inf-Zt* segmentation and the
extremum (Lambda-max) estimator of eq (3.16)-(3.17).

Remarks and practical guidance

o Power depends strongly on n and the AR root of the stationary error: Kim's
Table 4 shows high power for Zt* at n=3 but modest power at n=2 when the root
is near unity.

o Because the critical values are computed for l-bar = 0.3, the test is
conservative when the true noncointegration interval is shorter (Lemma 1).

o For multiple noncointegration intervals Kim suggests detecting one at a time
(Bai 1997); this command handles a single interval.

Stored results

segmcoint kim stores in r():

Scalars

r(zt) inf Zt* statistic

r(zrho) inf Zrho* statistic

r(adft) inf ADFt* statistic

r(adfrho) inf ADFrho* statistic

r(tau0), r(tau1) estimated noncointegration interval fractions

r(n), r(T) n and sample size

Matrices

r(stat) 4x3: statistic, tau0, tau1 for each of Zrho,Zt,ADFrho,ADFt

r(cv_rho), r(cv_t) critical-value rows (1/2.5/5/10%)

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane