@APBreakTest performs Andrews-Ploberger(1994) and Andrews-Quandt structural break tests for a linear regression, with p-values using Hansen's approximations. These are used to test for a single structural break at an unknown point within the sample. A series of LM statistics are generated for breaks at each of the points in the middle range of the data set. The Andrews-Quandt test uses as the test statistic the maximum of the LM statistics, while Andrews-Ploberger uses the geometric mean. These both have highly non-standard distributions. Asymptotic p-values are computed as described in Hansen(1997).

The related procedure @APGradientTest can be applied to the series of gradients from a non-linear estimation such as one done with GARCH or MAXIMIZE.

@APBREAKTEST( options ) depvar start end

# list of regressors (in regression format)

Parameters

depvar |
dependent variable |

start, end |
range for regression. By default, the maximum range permitted by all variables involved in the regression. |

Options

PI=fraction of entries on ends of sample not examined as break points [.15]

This is written assuming PI is .15. A different "pi" value than .15 would require a different table of entries to compute the approximate p-values.

SMPL=standard SMPL option [not used]

ROBUST/[NOROBUST]

If ROBUST, heteroscedasticity-consistent LM tests are used

GRAPH/[NOGRAPH]

If GRAPH, the procedure produces a time-series graph of the breakpoint test statistics.

[PRINT]/NOPRINT

TITLE="title for output" ["Andrews-Ploberger Break Tests"]

Variables Defined

All are for the test on the full coefficient vector

%%BREAKPOINT |
Entry with largest break test (INTEGER) |

%%AQTEST |
Andrews-Quandt test statistic (REAL) |

%%APTEST |
Andrews-Ploberger test statistic (REAL) |

%%AQSIGNIF |
Approximate significance value for AQ test (REAL) |

%%APSIGNIF |
Approximate significance value for AP test (INTEGER) |

Example

@APBREAKTEST is used in the ONEBREAK.RPF example file.

ONEBREAK.RPF