Unit root tests with a break in innovation variance. (English) Zbl 1043.62107

Summary: It is shown that an abrupt change in the innovation variance of an integrated process can generate spurious rejections of the unit root null hypothesis in routine applications of Dickey-Fuller tests. We develop and investigate modified test statistics, based on unit root tests of P. Perron [see Econmetrica 57, 1361–1401 (1989; Zbl 0683.62066)] for a time series with a changing level, or changing intercept and slope, which are applicable when there is a change in innovation variance of an unknown magnitude at an unknown location.


62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


Zbl 0683.62066
Full Text: DOI


[1] Andrews, D. W. K.: Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821-856 (1993) · Zbl 0795.62012
[2] Bai, J.: Least squares estimation of a shift in linear processes. Journal of time series analysis 15, 453-472 (1993) · Zbl 0808.62079
[3] Bai, J.: Least absolute deviation estimation of a shift. Econometric theory 11, 403-436 (1995)
[4] Bai, J.; Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66, 47-79 (1998) · Zbl 1056.62523
[5] Bai, J.; Lumsdaine, R.; Stock, J.: Testing for and dating common breaks in multivariate time series. Review of economic studies 65, 395-432 (1998) · Zbl 0910.90074
[6] Bhattacharya, P. K.: Maximum likelihood estimation of a change-point in the distribution of independent random variables: general multiparameter case. Journal of multivariate analysis 23, 183-208 (1987) · Zbl 0659.62033
[7] Fu, Y.; Curnow, R. N.: Maximum likelihood estimation of multiple change points. Biometrika 77, 563-573 (1990) · Zbl 0724.62025
[8] Hamori, S.; Tokihisa, A.: Testing for a unit root in the presence of a variance shift. Economics letters 57, 245-253 (1997) · Zbl 0903.90022
[9] Hsu, S.: Tests for variance shift at an unknown time point. Applied statistics 26, 279-284 (1977)
[10] Inclán, C.: Detection of multiple changes of variance using posterior odds. Journal of business and economic statistics 11, 289-300 (1993)
[11] Leybourne, S. J.; Mills, T. C.; Newbold, P.: Spurious rejections by Dickey–fuller tests in the presence of a break under the null. Journal of econometrics 87, 191-203 (1998) · Zbl 0944.62083
[12] Nunes, Lc.; Kuan, C. M.; Newbold, P.: Spurious break. Econometric theory 11, 736-749 (1995)
[13] Perron, P.: The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361-1401 (1989) · Zbl 0683.62066
[14] Perron, P.: Testing for a unit root in a time series with a changing mean. Journal of business and economic statistics 8, 153-162 (1990)
[15] Perron, P., Vogelsang, T.J., 1992. Testing for a unit root in a time series with a changing mean: corrections and extensions. Journal of Business and Economic Statistics 10, 467–470.
[16] Picard, D.: Testing and estimating change-points in time series. Advances in applied probability 176, 841-867 (1985) · Zbl 0585.62151
[17] White, H.: Estimation, inference and specification analysis. (1996) · Zbl 0860.62100
[18] Wichern, D. W.; Miller, R.; Hsu, D.: Changes of variance in first-order autoregressive time series models-with an application. Applied statistics 25, 248-256 (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.