# 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;

fname = getGAUSSHome() \$+ "pkgs/tsmt/examples/index.dat";

// 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).

tsmt

## Source#

breitung.src

Functions `ips()`