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The Limiting Distribution of the t Ratio Under a Unit Root

Published online by Cambridge University Press:  11 February 2009

Abstract

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Brief Report
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Abadir, K.M. (1992) A distribution generating equation for unit-root statistics. Oxford Bulletin of Economics and Statistics 54, 305323.10.1111/j.1468-0084.1992.tb00004.xCrossRefGoogle Scholar
Abadir, K.M. (1993a) Expansions for some confluent hypergeometric functions. Journal of Physics A 26, 40594066 (corrigendum for printing error, 1993, p. 7663).10.1088/0305-4470/26/16/021CrossRefGoogle Scholar
Abadir, K.M. (1993b) On the asymptotic power of unit root tests. Econometric Theory 9, 189221.10.1017/S0266466600007507CrossRefGoogle Scholar
Abadir, K.M. (1993c) The limiting distribution of the autocorrelation coefficient under a unit root. Annals of Statistics 21, 10581070.10.1214/aos/1176349164CrossRefGoogle Scholar
Abramowitz, M. & Stegun, I. A. (eds.) (1965) Handbook of Mathematical Functions. New York: Dover Publications.Google Scholar
Anderson, T.W. (1959) On asymptotic distributions of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676687.10.1214/aoms/1177706198CrossRefGoogle Scholar
Bleistein, N. & Handelsman, R.A. (1975) Asymptotic Expansions of Integrals. New York: Dover Publications.Google Scholar
De Bruijn, N.G. (1981) Asymptotic Methods in Analysis. New York: Dover Publications.Google Scholar
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, 427431.Google Scholar
Dickey, D.A. & Fuller, W.A. (1981) Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 10571072.10.2307/1912517CrossRefGoogle Scholar
Erdélyi, A. (ed.) (1953) Higher Transcendental Functions, vols. 1 and 2. New York: McGraw-Hill.Google Scholar
Erdélyi, A. (1956) Asymptotic Expansions. New York: Dover Publications.Google Scholar
Evans, G.B.A. & Savin, N.E. (1981) Testing for unit roots: 1. Econometrica 49, 753779.10.2307/1911521CrossRefGoogle Scholar
Evans, G.B.A. & Savin, N.E. (1984) Testing for unit roots: 2. Econometrica 52, 12411269.10.2307/1910998CrossRefGoogle Scholar
Fuller, W.A. (1976) Introduction to Statistical Time Series. New York: John Wiley & Sons.Google Scholar
Gurland, I. (1948) Inversion formulae for the distribution of ratios. Annals of Mathematical Statistics 19, 228237.10.1214/aoms/1177730247CrossRefGoogle Scholar
Nankervis, J.D. & Savin, N.E. (1985) Testing the autoregressive parameter with the t statistic. Journal of Econometrics 27, 143161.10.1016/0304-4076(85)90084-3CrossRefGoogle Scholar
Nankervis, J.D. & Savin, N.E. (1988) The Student's t approximation in a stationary first order autoregressive model. Econometrica 56, 119145.10.2307/1911844CrossRefGoogle Scholar
Oberhettinger, F. & Badii, L. (1973) Tables of Laplace Transforms. Berlin: Springer-Verlag.10.1007/978-3-642-65645-3CrossRefGoogle Scholar
Phillips, P.C.B. (1987a) Time series regression with a unit root. Econometrica 55, 277301.10.2307/1913237CrossRefGoogle Scholar
Phillips, P.C.B. (1987b) Towards a unified asymptotic theory for autoregression. Biometrika 74, 535547.10.1093/biomet/74.3.535CrossRefGoogle Scholar
Phillips, P.C.B. & Perron, P. (1988) Testing for a unit root in time series regression. Biometrika 75, 335346.10.1093/biomet/75.2.335CrossRefGoogle Scholar
Solo, V. (1984) The order of differencing in ARIMA models. Journal of the American Statistical Association 79, 916921.10.1080/01621459.1984.10477111CrossRefGoogle Scholar
Spiegel, M.R. (1965) Laplace Transforms. New York: McGraw-Hill.Google Scholar
Spiegel, M.R. (1981) Complex Variables. New York: McGraw-Hill.Google Scholar
White, J.S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Annals of Mathematical Statistics 29, 11881197.10.1214/aoms/1177706450CrossRefGoogle Scholar
White, J.S. (1959) The limiting distribution of the serial correlation coefficient in the explosive case II. Annals of Mathematical Statistics 30, 831834.10.1214/aoms/1177706213CrossRefGoogle Scholar
Whittaker, E.T. & Watson, G.N. (1927) A Course of Modern Analysis. Cambridge: Cambridge University Press.Google Scholar