breitung#

Purpose#

Panel series unit root testing. The z-statistic constructed from the mean t-statistic has an asymptotic standardized normal distribution and tests the null hypothesis that all series are I(1) against the alternative that all series are I(0)

Format#

bstat = breitung(y, trend, constant, demean, lags)#

Parameters:

y (TxM matrix) – data, M > 5.
trend (scalar) – 0 = no trend, 1 = trend.
constant (scalar) – if nonzero constant included in model.
demean (scalar) – 0 to specify no demeaning or 1 to subtract cross-sectional means.
lags (scalar) – number of lags.

Returns:

bstat (matrix) – test statistic

Example#

new;
library tsmt;

// Load data
fname = getGAUSSHome("pkgs/tsmt/examples/index.dat");
y00 = loadd(fname);

// Assign y
y0 = y00[., 2:9];

// Percent Change in Y
y = 100*ln(y0[2:rows(y0), .]./y0[1:rows(y0)-1, .]);

// Indicator to run test with trend variable
trend = 1;

// Indicator to run test with constant
const = 1;

// Turn off data demeaning
demean = 0;

// Set number of lags to 3
lags = 3;

// Compute test statistics
tstat = breitung(y, trend, const, demean, lags);

The results printed are:

Test:                                Breitung and Das (2005)
Test Variable:                                             Y
Timespan:                                            Unknown
Ho:                                                Unit Root
Model:                                    Constant and Trend
N. Obs:                                                  367
N. Groups:                                                 8
Panel Type:                                         Balanced
============================================================
Z-stat                                               -19.959

Critical Values:
                            1%             5%            10%
                        -2.326         -1.645         -1.282
============================================================

Reject the null hypothesis of unit root at the 1% level.

Remarks#

The Breitung panel series unit root test utilizes the sample mean of the t-statistics across all individual series within a panel of time series variables. However, the procedure pre-adjusts data to address biased estimation.

It is assumed that the autoregressive parameter is constant across all panels. This allows the use of the standard t-statistic but requires that the panels be strongly balanced.

The procedure performs an individual ADF test on each series n then forms the sample mean of the t-statistic. The z-statistic constructed from the mean t-statistic has an asymptotic standardized normal distribution and tests the null hypothesis that all series are I(1) against the alternative that all series are I(0).

Library#

tsmt

Source#

breitung.src