Approximate distributions for the various serial correlograms

Bernoulli

Volumn 4, Issue 4, 1998, Pages 497-518

  Butler, Ronald W ^a   Paolella, Marc S ^b  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

saddlepoint approximation; serial correlation; serial correlogram

Indexed keywords

EID: 0013442150     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318663     Document Type: Article

References (28)

1. Anderson, T.W. (1971) The Statistical Analysis of Time Series. New York: Wiley.
2. Barndorff-Nielsen, O.E. (1978) Information and Exponential Families in Statistical Theory. New York: Wiley.
3. Barndorff-Nielsen, O.E. and Cox, D.R. (1979) Edgeworth and saddlepoint approximations with statistical applications (with discussion). J. Roy. Statist. Soc. B, 41, 279-312.
4. Barndorff-Nielsen, O.E. and Cox, D.R. (1989) Asymptotic Techniques for Use in Statistics. London: Chapman & Hall.
5. Booth, J.G. and Butler, R.W. (1990) Randomization distributions and saddlepoint approximations in generalized linear models. Biometrika, 77, 787-796.
6. Butler, R.W. and Paolella, M.S. (1996) Approximate distributions for the various serial correlograms. Technical Report 96/11. Department of Statistics, Colorado State Universisty, Fort Collins, CO.
7. Daniels, H.E. (1956) The approximate distribution of serial correlation coefficients. Biometrika, 43, 169-185.
8. Diggle, P.J. (1990) Time Series, A Biostatistical Introduction. Oxford: Oxford University Press.
9. Drezner, Z. (1978) Computation of the bivariate normal integral. Math. Comput., 32, 277-279.
10. Durbin, J. (1980a) Approximations for densities of sufficient statistics. Biometrika, 67, 311-333.
11. Durbin, J. (1980b) The approximate distribution of serial correlation coefficients calculated from residuals on Fourier series. Biometrika, 67, 335-350.
12. Durbin, J. and Watson, G.S. (1950) Testing for serial correlation in least squares regression I. Biometrika, 37, 409-428.
13. Durbin, J. and Watson, G.S. (1951) Testing for serial correlation in least squares regression II. Biometrika, 38, 159-178.
14. Geary, R.C. (1944) Extension of a theorem by Harald CrameÂr on the frequency distribution of the quotient of two variables. J. Roy. Statist. Soc., 17, 56-57.
15. Henshaw, R.C. (1966) Testing single equation least squares regression models for autocorrelated disturbances. Econometrica, 34, 646-660.
16. Hull, J.C. (1993) Options, Futures, and Other Derivative Securities. London: Prentice-Hall.
17. Imhof, J.P. (1961) Computing the distribution of quadratic forms in normal variables. Biometrika, 48, 417-426.
18. Jensen, J.L. (1988) Uniform saddlepoint approximations. Adv. Appl. Probab., 20, 622-634.
19. Lieberman, O. (1994) Saddlepoint approximation for the least squares estimator in first-order autoregression. Biometrika, 81, 807-811.
20. Lugannani, R. and Rice, S.O. (1980) Saddlepoint approximations for the distribution of sum of independent random variables. Adv. Appl. Probab., 12, 475-490.
21. McGregor, J.R. (1960) An approximate test for serial correlation in polynomial regression. Biometrika, 47, 111-119.
22. Phillips, P.C.B. (1978) Edgeworth and saddlepoint approximations in the first-order non-circular autoregression. Biometrika, 65, 91-98.
23. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1989) Numerical Recipes in Pascal: The Art of Scientific Computing. Cambridge: Cambridge University Press.
24. Priestley, M.B. (1981) Spectral Analysis and Time Series. New York: Academic Press.
25. Skovgaard, I.M. (1987) Saddlepoint expansions for conditional distributions. J. Appl. Probab., 24, 275-287.
26. Temme, N.M. (1982) The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions. SIAM J. Math. Anal., 13, 239-253.
27. Vinod, H.D. (1973) Generalization of the Durbin-Watson statistic for higher order autoregressive processes. Commun. Statist. A, 2, 115-144.
28. Wang, S. (1992) Tail probability approximations in the first-order non-circular autoregression. Biometrika, 79, 431-434.