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
------
.. function:: bstat = breitung(y, trend, constant, demean, lags)

   :param y: data, M > 5.
   :type y: TxM matrix

   :param trend: 0 = no trend, 1 = trend.
   :type trend: scalar

   :param constant: if nonzero constant included in model.
   :type constant: scalar

   :param demean: 0 to specify no demeaning or 1 to subtract cross-sectional means.
   :type demean: scalar

   :param lags: number of lags.
   :type lags: scalar

   :return bstat: test statistic
   :rtype bstat: matrix

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);
   print "The Breitung test statistic = ";; tstat;

The results printed are:

::

  The Breitung test statistic = -19.95876
  
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

.. seealso:: Functions :func:`ips`