Unit root test under innovation outlier contamination small sample case

• Autorzy: Lynda Atil , Hocine Fellag , Karima Nouali
• Języki publikacji: EN

Abstrakty

EN

The two sided unit root test of a first-order autoregressive model in the presence of an innovation outlier is considered. In this paper, we present three tests; two are usual and one is new. We give formulas computing the size and the power of the three tests when an innovation outlier (IO) occurs at a specified time, say k. Using a comparative study, we show that the new statistic performs better under contamination. A Small sample case is considered only.

Słowa kluczowe

EN

autoregressive process; Dickey-Fuller test; innovation outlier; power; size

Kategorie tematyczne

• 62M10: Time series, auto-correlation, regression, etc.

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 5-17

Daty

wydano

2006

otrzymano

2005-02-11

Twórcy

autor

Lynda Atil

• Department of Mathematics, Faculty of Sciences University of Tizi Ouzou Tizi-Ouzou 15000, Algeria

autor

Hocine Fellag

• Department of Mathematics, Faculty of Sciences University of Tizi Ouzou Tizi-Ouzou 15000, Algeria

autor

Karima Nouali

• Department of Mathematics, Faculty of Sciences University of Tizi Ouzou Tizi-Ouzou 15000, Algeria

Bibliografia

• [1] Cabuk and Springer, Distribution of the quotient of noncentral normal random variables, Communication in Statistics, Theory and Methods 19 (3) (1990), 1157-1168.
• [2]D.A. Dickey and W.A. Fuller, Distribution of estimators for autoregressive time series with unit root, J. Amer. Statist. Assoc., 74 (1979), 427-431.
• [3]F.X. Diebold, Empirical modeling of exchange rate dynamics, Springer Verlag 1988.
• [4] A.J. Fox, Outliers in Time Series, J. Roy. Stat. Soc., Ser. B, 34 (1972), 350-363.
• [5] P.H. Franses and N. Haldrup, The effects of additive outliers on tests for unit roots and cointegration, Journal of Business Econom. Statistics 12 (4) (1994), 471-478.
• [6] W.A. Fuller, Introduction to statistical time series, second edition, John Wiley, New York 1996.
• [7] J.P. Imhoff, Computing the distribution of quadratic forms in normal variables, Biometrika 48 (3,4) (1961), 419-426.
• [9] P. Perron, The great crash, the oil rice shock, and the unit root hypothesis, Econometrica 57 (6) (1989), 1361-1401.
• [10] P.C.B. Phillips, Time series with unit root, Econometrica 55 (1987), 277-301.
• [11] P.C.B. Phillips and P. Perron, Testing for a unit root in time series regression, Biometrika 75 (1988), 335-346.
• [12] D.W. Shin, S. Sarkar and J.H. Lee, Unit root tests for time series with outliers, Statistics and Probability Letters 30 (3) (1996), 189-197.
• [13] C.A. Sims and H. Uhlig, Understanding unit rooters: a helicopter tour, Econometrica 59 (6) (1991), 1591-1599.

Identyfikatory

DOI

10.7151/dmps.1072