# zandrews¶

## Purpose¶

The Zivot and Andrews (1992) unit root test uses a t-test statistic for testing the null hypothesis of stationarity. The procedure tests the null hypothesis of zero innovation variance in the residual against the alternative of non-zero residual innovation variance.

## Format¶

{ t_test, break_pt } = zandrews(yt, max_lags, trim_end, break_type, which_output)
Parameters:
• yt (Tx1 vector) – time series data.

• max_lags (scalar) – specifies the maximum lag order to be used in calculating the test statistic. A good default is to calculate max_lags as $$T^{0.25}$$.

• trim_end (scalar) – fraction of data range to skip at either end. A good default is 0.15. Range is 0 to 0.25.

• break_type (scalar) – -1 for intercept break, 0 for trend break, or 1 for a break in both.

• which_output (scalar) – 0 for no output, 1 to print statistics or 2 to print statistics and display of graph of unit-root test statistics across different break points.

Returns:
• t_test (scalar) – reports Zivot-Andrews test statistic.

• break_pt (scalar) – observation where structural break is most likely to occur.

## Example¶

new;
cls;
library tsmt;

// AR(1) time series, yt, generated using
// the simarmamt data generating function (included in the TSMT library):
// Coefficient
b = 0.5;

// Number of AR lags
p = 1;

// Number of MA lags
q = 0;

// Constant
const = 0.9;

// Turn trend off
trend = 0;

// Number of observations
n = 500;

// Number of series
k = 1;

// Standard deviation
std = 1;

// Random seed
seed = 10191;

yt = simarmamt(b, p, q, const, trend, n, k, std, seed);

{ t_test, break_pt } = zandrews(yt[., 1], 4, 0.10, -1, 1);


tsmt