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
------
.. function:: {t_test, break_pt} = zandrews(yt, max_lags, trim_end, break_type, which_output)
:param yt: time series data.
:type yt: Tx1 vector
:param max_lags: specifies the maximum lag order to be used in calculating the test statistic. A good default is to calculate max_lags as :math:`T^{0.25}`.
:type max_lags: scalar
:param trim_end: fraction of data range to skip at either end. A good default is 0.15. Range is 0 to 0.25.
:type trim_end: scalar
:param break_type: -1 for intercept break, 0 for trend break, or 1 for a break in both.
:type break_type: scalar
:param which_output: 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.
:type which_output: scalar
:return t_test: reports Zivot-Andrews test statistic.
:rtype t_test: scalar
:return break_pt: observation where structural break is most likely to occur.
:rtype break_pt: scalar
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);
Library
-------
tsmt