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);

Library

tsmt