Regression asymptotics using martingale convergence methods

Econometric Theory

Volumn 24, Issue 4, 2008, Pages 888-947

  Ibragimov, Rustam ^a   Phillips, Peter C B ^a,b,c  

^a YALE UNIVERSITY   (United States)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 45249089885     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S0266466608080365     Document Type: Article

References (54)

1. Akonom, J. & C. Gouriéroux (1987) A functional limit theorem for fractional processes. Technical report 8801, CEPREMAP.
2. Anderson, T.W. (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676-687.
3. Avram, F. (1988) Weak convergence of the variations, iterated integrals and Doléans-Dade exponentials of sequences of semimartingales. Annals of Probability 16, 246-250.
4. Billingsley, P. (1968) Convergence of Probability Measures. Wiley.
5. Borodin, A.N. & I.A. Ibragimov (1995) Limit theorems for functionals of random walks. Proceedings of the Steklov Institute of Mathematics 195, no. 2.
6. Burkholder, D.L. (1973) Distribution function inequalities for martingales. Annals of Probability 1, 19-42.
7. Chan, N.H. & C.Z. Wei (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050-1063.
8. Chan, N.H. & C.Z. Wei (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367-401.
9. Coffman, E.G., A.A. Puhalskii, & M.I. Reiman (1998) Polling systems in heavy traffic: A Bessel process limit. Mathematics of Operations Research 23, 257-304.
10. Coquet, F. & J. Mémin (1994) Vitesse de convergence en loi pour des solutions d'équations différentielles stochastiques vers une diffusion. (Rate of convergence in law of the solutions of stochastic differential equations to a diffusion.) In J. Azema, P.-A. Meyer, & M. Yor (eds.), Séminaire de Probabilités, XXVIII, Lecture Notes in Mathematics 1583, pp. 279-292. Springer.
11. Csörgocombining double acute accent, M. & L. Horvàth (1993) Weighted Approximations in Probability and Statistics. Wiley.
12. Dedecker, J. & F. Merlevède (2002) Necessary and sufficient conditions for the conditional central limit theorem. Annals of Probability 30, 1044-1081.
13. Dedecker, J. & E. Rio (2000) On the functional central limit theorem for stationary processes. Annales de l'Institut H. Poincaré. Probabilités et Statistiques 36, 1-34.
14. de Jong, R.M. (2002) Nonlinear Estimators with Integrated Regressors but without Exogeneity. Working paper, Michigan State University.
15. p-bounds for sums of multilinear forms. Annals of Probability 31, 630-675.
16. Dharmadhikari, S.W., V. Fabian, & K. Jogdeo (1968) Bounds on the moments of martingales. Annals of Mathematical Statistics 39, 1719-1723.
17. Doukhan, P. (2003) Models, inequalities, and limit theorems for stationary sequences. In P. Doukhan, G. Oppenheim, & M.S. Taqqu (eds.), Theory and Applications of Long-Range Dependence, pp. 43-100. Birkhäuser.
18. Doukhan, P., G. Oppenheim, & M.S. Taqqu, eds. (2003) Theory and Applications of Long-Range Dependence. Birkhäuser.
19. Durrett, R. (1996) Stochastic Calculus. A Practical Introduction. CRC Press.
20. Dynkin, E.B. & A. Mandelbaum (1983) Symmetric statistics, Poisson point processes, and multiple Wiener integrals. Annals of Statistics 11, 739-745.
21. Giraitis, L. & P.C.B. Phillips (2006) Uniform limit theory for stationary autoregression. Journal of Time Series Analysis 27, 51-60.
22. Hall, P. & C.C. Heyde (1980) Martingale Limit Theory and Its Application. Academic Press.
23. He, S.-W., J.-G. Wang, & J.-A. Yan (1992) Semimartingale Theory and Stochastic Calculus. CRC Press.
24. Hu, L. & P.C.B. Phillips (2004) Dynamics of the federal funds target rate: A nonstationary discrete choice approach. Journal of Applied Econometrics 19, 851-867.
25. Ibragimov, R. (1997) Estimates for moments of symmetric statistics. Ph.D. (Kandidat Nauk) dissertation, Institute of Mathematics of Uzbek Academy of Sciences, Tashkent; http://www.economics.harvard.edu/faculty/ibragimov/files/ IbragimovPh.D.Dissertation.pdf.
26. Ibragimov, R. & P.C.B. Phillips (2004) Regression Asymptotics Using Martingale Convergence Methods. Cowles Foundation Discussion paper 1473; http://cowles.econ.yale.edu/P/cd/0d14b/d1473.pdf.
27. Ibragimov, R. & S. Sharakhmetov (2002) Bounds on moments of symmetric statistics. Studia Scientiarum Mathematicarum Hungarica 39, 251-275.
28. Ikeda, N. & S. Watanabe (1989) Stochastic Differential Equations and Diffusion Processes. North-Holland.
29. Jacod, J. & A.N. Shiryaev (2003) Limit Theorems for Stochastic Processes, 2nd ed., Springer-Verlag.
30. 1.) Probability Theory and Related Fields 81, 111-137.
31. Jeganathan, P. (2003) Second Order Limits of Functionals of Sums of Linear Processes That Converge to Fractional Stable Motions. Working paper, Indian Statistical Institute.
32. Jeganathan, P. (2004) Convergence of functionals of sums of r.v.s to local times of fractional stable motions. Annals of Probability 32, 1771-1795.
33. Kurtz, T.G. & P. Protter (1991) Weak limit theorems for stochastic integrals and stochastic differential equations. Annals of Probability 19, 1035-1070.
34. Liptser, R.Sh. & A.N. Shiryaev (1989) Theory of Martingales. Kluwer.
35. Mandelbaum, A. & M.S. Taqqu (1984) Invariance principle for symmetric statistics. Annals of Statistics 12, 483-496.
36. Mémin, J. (2003) Stability of Doob-Meyer decomposition under extended convergence. Acta Mathematicae Applicatae Sinica. English Series 19, 177-190.
37. Mémin, J. & L. Słomiński (1991) Condition UT et stabilité en loi des solutions d'équations différentielles stochastiques. Séminaire de Probabilités, XXV, Lecture Notes in Mathematics 1485, pp. 162-177. Springer.
38. Nze, P.A. & P. Doukhan (2004) Weak dependence: Models and applications to econometrics. Econometric Theory 20, 995-1045.
39. Park, J.Y. & P.C.B. Phillips (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269-298.
40. Park, J.Y. & P.C.B. Phillips (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117-161.
41. Phillips, P.C.B. (1987a). Time-series regression with a unit root. Econometrica 55, 277-301.
42. Phillips, P.C.B. (1987b). Towards a unified asymptotic theory for autoregression. Biometrika 74, 535-547.
43. Phillips, P.C.B. (1999) Discrete Fourier Transforms of Fractional Processes. Cowles Foundation Discussion paper 1243, Yale University; http://cowles.econ.yale.edu/P/cd/d12a/d1243.pdf.
44. Phillips, P.C.B. (2007) Unit root log periodogram regression. Journal of Econometrics 138, 104-124.
45. Phillips, P.C.B. & T. Magdalinos (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics 136, 115-130.
46. Phillips, P.C.B. & P. Perron (1988) Testing for a unit root in time series regression Biometrika 75, 335-346.
47. Phillips, P.C.B. & W. Ploberger (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 64, 381-413.
48. Phillips, P.C.B. & V. Solo (1992) Asymptotics for linear processes. Annals of Statistics 20, 971-1001.
49. Pötscher, B.M. (2004) Nonlinear functions and convergence to Brownian motion: Beyond the continuous mapping theorem. Econometric Theory 20, 1-22.
50. Prigent, J.-L. (2003) Weak Convergence of Financial Markets, Springer Finance. Springer-Verlag.
51. Saikkonen, P. & I. Choi (2004) Cointegrating smooth transition regressions. Econometric Theory 20, 301-340.
52. Shorack, G.R. & J.A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley.
53. Stroock, D.W. & S.R.S. Varadhan (1979) Multidimensional Diffusion Processes. Springer-Verlag.
54. White, J.S. (1958) The limiting distribution of the serial correlation coefficient in the explosive case. Annals of Mathematical Statistics 29, 1188-1197.