Nonparametric estimation in null recurrent time series

Annals of Statistics

Volumn 29, Issue 2, 2001, Pages 372-416

  Karlsen, Hans Arnfinn ^a   Tjøstheim, Dag ^a  

^a Department of Mathematics ^*  (Norway)

Author keywords

Nonparametric kernel estimators; Nonstationary time series models; Null recurrent Markov chain; Split chain

Indexed keywords

EID: 0035602369     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1009210546     Document Type: Article

References (39)

1. APARICIO, F. M. and ESCRIBANO, A. (1997). Searching for linear and nonlinear cointegration: a new approach. Working paper 97-65, Univ. Carlos III de Madrid, Statistics and Economics Series.
2. BERGSTRØM, H. (1981). Weak Convergence. Academic Press, New York.
3. BILLINGSLEY, P. (1968). Convergence of Probability. Wiley, New York.
4. BINGHAM, N. H., GOLDIE, C. M. AND TEUGELS, J. L. (1989). Regular Variation. Cambridge Univ. Press.
5. CHOW, Y. S. and TEICHER, H. (1988). Probability Theory, 2nd. ed. Springer, New York.
6. DARLING, D. A. and KAC, M. (1957). On occupation times for Markoff processes. Trans. Amer. Math. Soc. 84 444-458.
7. DICKEY, D. A. and FULLER, W. A. (1979). Distribution of the estimators for autoregressive time series with unit root. Econometrica 49 1057-1072.
8. FEIGIN, P. D. and TWEEDIE, R. L. (1985). Random coefficient autoregressive processes: a Markov chain analysis of stationarity and finiteness of moments. J. Time Ser. Anal. 6 1-14.
9. FELLER, W. R. (1971). An Introduction to Probability Theory and Its Application 2, 2nd. ed. Wiley, New York.
10. GRANGER, C. W. J. (1995). Modelling nonlinear relationships between extended-memory variables. Econometrica 63 265-279.
11. GRANGER, C. W. J. and HALLMAN, J. (1991). Long memory series with attractors. Oxford Bull. Econom. Statist. 53 11-26.
12. HJELLVIK, V., YAO, Q. and TJØSTHEIM, D. (1998). Linearity testing using local polynomial approximation. J. Statist. Plann. Inference 68 295-321.
13. HÖPFNER, R. (1990). Null recurrent birth and death processes: limits for certain martingales and local asymptotic mixed normality. Scand. J. Statist. 17 201-215.
14. HÖPFNER, R. (1994). Estimating a parameter in a birth-and-death process model. Statist. Decisions 12 149-160.
15. HÖPFNER, R., JACOD, J. and LADELLI, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86 105-129.
16. JACOD, J. and SHIRYAEV, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin.
17. JOHANSEN, S. (1995). Likelihood-based Inference in Cointegrated Vector Autoregressive Models. Oxford Univ. Press.
18. KALLIANPUR, G. and ROBBINS, H. (1954). The sequence of sums of independent random variables. Duke Math. J. 21 285-307.
19. KARLSEN, H. A., MYKLEBUST, T. and TJØSTHEIM, D. (2000). Nonparametric estimation in a nonlinear cointegration type model. Sonderforschungsbereich 373 33. Humboldt Univ., Berlin.
20. KARLSEN, H. A. and TJØSTHEIM, D. (1998). Nonparametric estimation in null recurrent time series. Sonderforschungsbereich 373 50. Humboldt Univ., Berlin.
21. KASAHARA, Y. (1982). A limit theorem for slowly increasing occupation times. Ann. Probab. 10 728-736.
22. KASAHARA, Y. (1984). Limit theorems for Levy processes and Poisson point processes and their applications to Brownian excursions. J. Math. Kyoto Univ. 24 521-538.
23. KASAHARA, Y. (1985). A limit theorem for sums of random number of i.i.d. random variables and its application to occupation times of Markov chains. J. Math. Soc. Japan 37 197-205.
24. MASRY, E. and TJØSTHEIM, D. (1995). Nonparametric estimation and identification of nonlinear ARCH time series. Econometric Theory 11 258-289.
25. MASRY, E. and TJØSTHEIM, D. (1997). Additive nonlinear ARX time series and projection estimators. Econometric Theory 13 214-252.
26. MEYN, S. P. and TWEEDIE, R. L. (1994). Markov Chains and Stochastic Stability. Springer, London.
27. MYKLEBUST, T., KARLSEN, H. A. and TJØSTHEIM, D. (2001). A Markov chain characterization of unit-root processes and the problem of nonlinear cointegration. Unpublished manuscript.
28. NUMMELIN, E. (1984). General Irreducible Markov Chains and Nonnegative Operators. Cambridge Univ. Press.
29. PHILLIPS, P. C. B. and PARK, J. (1998). Nonstationary density estimation and kernel autoregression. Cowles Foundation Discussion Paper 1181, Yale Univ.
30. POLLARD, D. (1984). Convergence of Stochastic Processes. Springer, New York.
31. ROBINSON, P. M. (1983). Nonparametric estimators for time series. J. Time Ser. Anal. 4 185-207.
32. ROBINSON, P. M. (1997). Large sample inference for nonparametric regression with dependent errors. Ann. Statist. 25 2054-2083.
33. STOCK, J. H. (1994). Unit roots, structural breaks and trends. In Handbook of Econometrics (R. F. Engle and D. L. McFadden, eds.) 4 2740-2843. North-Holland, Amsterdam.
34. TOUATI, P. A. (1990). Loi fonctionnelle du logarithme iteré pour les processus de Markov recurrents. Ann. Probab. 18 140-159.
35. TJØSTHEIM, D. and AUESTAD, B. (1994). Nonparametric identification of nonlinear time series; projections and selecting significant lags. J. Amer. Statist. Assoc. 89 1398-1419.
36. WATSON, M.W. (1994). Vector autoregression and cointegration. In Handbook of Econometrics (R. F. Engle and D. L. McFadden, eds.) 4 2843-2918. North-Holland, Amsterdam.
37. WHEEDEN, R. L. and ZYGMUND, A. (1977). Measure and Integral. Dekker, New York.
38. XIA, Y. (1998). Doctoral thesis, Univ. Hong Kong.
39. YAKOWITZ, S. (1993). Nearest neigbour regression estimation for null-recurrent Markov times series. Stochastic Process. Appl. 48 311-318.