statsmodels.tsa.stattools.zivot_andrews

statsmodels.tsa.stattools.zivot_andrews = <statsmodels.tsa.stattools.ZivotAndrewsUnitRoot object>

Zivot-Andrews structural-break unit-root test.

The Zivot-Andrews test tests for a unit root in a univariate process in the presence of serial correlation and a single structural break.

Parameters
xarray_like

The data series to test.

trimfloat

The percentage of series at begin/end to exclude from break-period calculation in range [0, 0.333] (default=0.15).

maxlagint

The maximum lag which is included in test, default is 12*(nobs/100)^{1/4} (Schwert, 1989).

regression{“c”,”t”,”ct”}

Constant and trend order to include in regression.

  • “c” : constant only (default).

  • “t” : trend only.

  • “ct” : constant and trend.

autolag{“AIC”, “BIC”, “t-stat”, None}

The method to select the lag length when using automatic selection.

  • if None, then maxlag lags are used,

  • if “AIC” (default) or “BIC”, then the number of lags is chosen to minimize the corresponding information criterion,

  • “t-stat” based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test.

Returns
zastatfloat

The test statistic.

pvaluefloat

The pvalue based on MC-derived critical values.

cvdictdict

The critical values for the test statistic at the 1%, 5%, and 10% levels.

baselagint

The number of lags used for period regressions.

bpidxint

The index of x corresponding to endogenously calculated break period with values in the range [0..nobs-1].

Notes

H0 = unit root with a single structural break

Algorithm follows Baum (2004/2015) approximation to original Zivot-Andrews method. Rather than performing an autolag regression at each candidate break period (as per the original paper), a single autolag regression is run up-front on the base model (constant + trend with no dummies) to determine the best lag length. This lag length is then used for all subsequent break-period regressions. This results in significant run time reduction but also slightly more pessimistic test statistics than the original Zivot-Andrews method, although no attempt has been made to characterize the size/power trade-off.

References

1

Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews unit root test in presence of structural break,” Statistical Software Components S437301, Boston College Department of Economics, revised 2015.

2

Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics, 7: 147-159.

3

Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Studies, 10: 251-270.