Hostname: page-component-76dd75c94c-nbtfq Total loading time: 0 Render date: 2024-04-30T07:32:05.196Z Has data issue: false hasContentIssue false

The Limiting Distribution of the t Ratio Under a Unit Root

Published online by Cambridge University Press:  11 February 2009

Abstract

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Brief Report
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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