Unit Root Tests for Long Memory Series in the Presence of Structural Breaks in Variance

Yuanyuan LI, Hao JIN

Abstract


This paper extends the unit root tests to long memory observations in the existence of variance breaks. Given for the case of non-constant variance, the asymptotic properties of commonly used unit root tests are derived under the null hypothesis. It is shown that the non-constant variance can both inflate and deflate the rejection frequency, thus the statistic tests are not robust. The simulation results also indicate the extent of size distortion is heavily sensitive to the location and magnitude of change points, long memory index and sample size.


Keywords


Unit root tests; Long memory; Variance breaks; Asymptotic properties

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References


Alexander, A., & Lajos, H. (2011). Structural breaks in time series. Journal of Time Series Analysis. doi: 10.1111/j.1467-9892

Beran, J. (1994). Statistic for long-memory processes. New York: Chapman & Hall.

Cao, W. H., & Jin, H. (2016). Ratio testing for changes in the long memory indexes. International Business and Management, 12(3), 62-70.

Cavaliere, G., & Taylor, A. M. R. (2007). Testing for unit roots in time series models with non-stationary volatility. Journal of Econometrics, 140, 919-947.

Cavaliere, G.(2004). Unit root tests under time-varying variances. Econometric Reviews, 23(3), 259-292.

Clemente, J., Montanes, A., & Reyes, M. (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters, 59, 175-182.

Davidson, J., & de Jong, R. M. (2000). The functional central limit theorem and weak convergence to stochastic integrals, II: Fractionally integrated processes. Econometric Theory, 16, 643-666.

Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427-431.

Digeo, L. (1996). Long-memory errors in time series regressions with a unit root. Journal of Time Series Analysis, 20, 565-577.

Glaura, C. F., Valderio, A. R., & Paula, A. B. (2004). Unit root tests using semi-parametric estimators of the long-memory parameter. Journal of Statistical Computation and Simulation, 76(8), 727-735.

Guglielmo, M. C., & Luis, A. G. (2007). The stochastic unit root model and fractional integration: An extension to the seasonal case. Applied Stochastic Models in Business and Industry, 23, 439-453.

Hamori, S., & Tokihisa, A. (1997). Testing for a unit root in the presence of a variance shift. Economics Letters, 57, 245-253.

Harvey, D., Leybourne, S., & Taylor, Z. (2014). On infimum Dickey-Fuller unit root tests allowing for a trend break under the null. Computational Statistics and Data Analysis, 78, 235-242.

Kim, T. H., Leybourne, S., & Newbold, P. (2002). Unit root tests with a break in innovation variance. Journal of Econometrics, 109, 365-387.

Mandelbrot, B. B., & Vanness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. Siam Rev, 10, 422-37.

Oh, Y. J., & Kim, Y. S. (2015). Unit root tests in the presence of multi-variance break and level shifts that have power against the piecewise stationary alternative. Communications in Statistics-Simulation and Computation R, 44, 1465-1476.

Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75, 335-346.

Phillips, P. C. B. (1987) Time series regression with a unit root. Econometrica, 55, 277-301.

Robinson, P. M. (1999). Alternative forms of fractional Brownian motion. Journal of Statistical Planning and Inference, 80, 111-122.

Robinson, P. M. (2003). Time series with long memory. Oxford: Oxford University Press.

Sen, A. (2009). Unit root tests in the presence of an innovation variance break that has power against the mean break stationary alternative. Statistics and Probability Letters, 79, 354-360.

Smallwood, A. D. (2014). A Monte Carlo investigation of unit root tests and long memory in detecting mean reversion in I(0) regime switching, structural break, and nonlinear data. Department of Economics, 35(6), 986-1012.

Sowell, F. (1990). The fractional unit root distribution. Department of Econometrica, 58(2), 495-505.

Tsay, W., & Chung, C. (1999). The spurious regressionof fractionally integrated process. Journal of Econometrics, 96(1), 155-182.




DOI: http://dx.doi.org/10.3968/9314

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