Title

segmcoint dm -- Davidson & Monticini (2010) subsample cointegration tests

Syntax

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

deterministic(string) const (default) or trend
(mean- / mean-and-trend-deviation residuals)

lambda0(#) minimum subsample / rolling-window length, one of
0.5, 0.35, 0.2, 0.1; default 0.5

statistic(string) subsample statistic: pp (default) or df

grid(#) subsample-search step (obs); default = automatic

graph plot each min-statistic against its 5% critical value

graphname(name) graph name

noheader suppress header

The data must be tsset. Critical values are tabulated for 1-2
regressors only; statistics are still reported for more regressors, without
critical values.

Description

segmcoint dm implements Davidson & Monticini (2010).
An ordinary residual-based cointegration statistic (Dickey-Fuller df or
Phillips-Perron pp) is computed on subsamples of the data and the
minimum (most negative) value is taken. Three subsample designs are reported:

o QS, QS* - split-sample (halves), the latter also
including the full sample;

o QI - incremental forward and backward samples of minimum
length lambda0;

o QR, QR* - rolling windows of fixed length lambda0.

The approach requires no model under the alternative and does not need the number
or type of breaks; it formalises the practice of "data-snooping" subsamples by
providing valid critical values for the extremum.

Options

deterministic(string) chooses mean-deviation (const) or
mean-and-trend-deviation (trend) subsample residuals. none is not
available (subsample residuals are always demeaned).

lambda0(#) is the minimum subsample length for the incremental test
and the fixed window length for the rolling test. Only the tabulated values
0.5/0.35/0.2/0.1 are accepted. QR/QR* critical
values are tabulated only for 0.5; smaller lambda0 yields more power to find a
short cointegrated window but has no tabulated rolling critical value.

statistic(pp|df) selects the subsample statistic; both share the same
asymptotic critical values.

Interpreting the output

Five min-statistics are printed with 10/5/2.5/1% lower-tail critical values
(Table 1). Reject the null of no cointegration on any subsample when a
statistic is below the critical value. A rejection points to the existence of
a cointegrating relationship in some subperiod, worthy of further investigation.
Entries marked (no CV) have no tabulated critical value for the current
lambda0 / number of regressors.

Remarks and practical guidance

o Power depends on lambda0 relative to the break location: to detect a cointegrated
window of length at least lambda0*T, choose lambda0 no larger than that window.
A mid-sample noncointegration block defeats large-lambda0 windows because every
window straddles it (use QI with small lambda0 to reach a clean tail).

o The incremental QI test is a good all-round default; QI(0.35)
performed well in the authors' simulations.

Stored results

segmcoint dm stores in r():

Scalars

r(qs), r(qsstar) split-sample statistics

r(qi) incremental statistic

r(qr), r(qrstar) rolling statistics

r(T), r(K) sample size and number of regressors

Matrices

r(stat) 5x1 min-statistics (QS,QS*,QI,QR,QR*)

r(cv) 5x4 critical values (10/5/2.5/1%)

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

github.com/merwanroudane