Abstract
This paper presents response surface estimates of finite sample critical values of the Efficient Wald test for Fractional Unit Roots of Lobato and Velasco (Econometrica 75:575–590, 2007) in the presence of deterministic components. Lag-adjusted critical values of the augmented versions of the tests illustrate that as in the context of traditional unit root and stationarity tests, incorporating adjustments for serial correlation affects the finite sample distributions of the test statistics.
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References
Cheung YW, Lai KS (1995) Lag order and critical values of the augmented Dickey-Fuller test. J Bus Econ Stat 13: 277–280
Cheung YW, Lai KS (1995) Lag order and critical values of a modified Dickey-Fuller test. Ox Bull Econ Stat 57: 411–419
Cook S (2001) Finite sample critical values of the augmented Dickey-Fuller statistic: a note on lag order. Econ Iss 6: 31–38
Cragg JG (1983) More efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 51: 751–763
Dolado JJ, Gonzalo J, Mayoral M (2002) A fractional Dickey-Fuller test for unit roots. Econometrica 70: 1963–2006
Dolado JJ, Gonzalo J, Mayoral M (2005) Structural breaks vs long memory: what is what. Universidad Carlos III, Madrid. mimeo
Dolado JJ, Gonzalo J, Mayoral M (2006) Testing I(1) against I(d) alternatives in the presence of deterministic components. Universidad Carlos III, Madrid. mimeo
Dolado JJ, Gonzalo J, Mayoral M (2006) Testing I(1) against I(d) alternatives with Wald tests in the presence of deterministic components. Universidad Carlos III, Madrid. mimeo
Lobato I, Velasco C (2007) Efficient Wald tests for fractional unit roots. Econometrica 75: 575–590
Lobato I, Velasco C (2008) Power comparison among tests for fractional unit roots. Econ Lett 99: 152–154
MacKinnon JG (1991) Critical values for cointegration tests. In: Engle RF, Granger CWJ(eds) Long-run economic relationships: readings in cointegration. Oxford University Press, Oxford, pp 267–276
MacKinnon JG (1994) Approximate asymptotic distribution functions for unit-root and cointegation tests. J Bus Econ Stat 12: 167–176
MacKinnon JG (1996) Numerical distribution functions for unit root and cointegration tests. J Appl Econ 11: 601–618
MacKinnon JG, Haug A, Michelis L (1999) Numerical distribution functions of likelihood ratio tests for cointegration. J Appl Econ 14: 563–577
MacKinnon JG (2000) Computing numerical distribution functions in econometrics. In: Pollard D, Mewhort D, Weaver D(eds) High performance computing systems and applications. Kluwer, Amsterdam, pp 455–470
Ng S, Perron P (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69: 1519–1554
Ng S, Perron P (2005) A note on the selection of time series models. Ox Bull Econ Stat 67: 115–134
Presno MJ, Lopez AJ (2003) Response surface estimates of stationarity tests with a structural break. Econ Lett 78: 395–399
Robinson PM (1991) Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. J Econometrics 47: 67–84
Robinson PM (1994) Efficient tests of nonstationarity hypotheses. J Am Stat Assoc 89: 1420–1437
Said SE, Dickey DA (1984) Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71: 599–608
Sephton PS (1995) Response surface estimates of the KPSS stationarity test. Econ Lett 47:255–261
Sephton PS (2008) Critical values of the augmented fractional Dickey Fuller Test. Empir Econ. Available via http://www.springerlink.com/content/t3p2883431rhmv50/fulltext.pdf
Shimotsu K (2006) Simple (but Effective) tests of long memory versus structural breaks. mimeo
Shimotsu K, Phillips PCB (2005) Exact local Whittle estimation of fractional integration. Ann Stat 33: 1890–1933
Velasco C (1999) Gaussian semiparametric estimation of non-stationary time series. J T S An 20: 87–127
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Sephton, P.S. Critical values for the augmented efficient Wald test for fractional unit roots. Empir Econ 37, 615–626 (2009). https://doi.org/10.1007/s00181-008-0249-3
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DOI: https://doi.org/10.1007/s00181-008-0249-3