Nonparametric estimation and identification of nonlinear arch time series: Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality

Econometric Theory

Volumn 11, Issue 2, 1995, Pages 258-289

  Masry, Elias ^a   Tjøstheim, Dag ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84974185463     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S0266466600009166     Document Type: Article

References (32)

1. Bollerslev T. (1986) Generalized autoregressive conditional heteroscedasticity. Journal of Economics 31, 307–327.
2. Bradley R.C. (1983) Approximation theorems for strongly mixing random variables. Michigan Mathematical Journal 30, 69–81.
3. Brock W., LeBaron B. & Hsieh D. (1991) Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence. Cambridge, Massachusetts: MIT Press.
4. Carroll R. (1982) Adapting for heteroscedasticity in linear models. Annals of Statistics 10, 1224–1233.
5. Chan K.S. & Tong H. (1985) On the use of deterministic Lyapunov function for the ergodicity of stochastic difference equations. Advances in Applied Probability 17, 666–678.
6. Chen R. & Tsay R. (1992) On the ergodicity of TAR(l) processes. Annals of Applied Probability 1, 613–634.
7. Collomb G. & Hardle W. (1986) Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stochastic Processes and Their Applications 23, 77–89.
8. Engle R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008.
9. Engle R.F. & Gonzāles-Rivera G. (1991) Semiparametric ARCH models. Journal of Business and Economic Statistics 9, 345–359.
10. Engle R.F. & Ng V.K. (1991) Measuring and Testing the Impact of News on Volatility. Discussion paper, Department of Economics, University of California, San Diego.
11. Fan J. & Masry E. (1993) Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes. Journal of Multivariate Analysis 43, 237–271.
12. Granger C.W.J. & Teräsvirta T. (1993) Modelling Nonlinear Dynamic Relationships. Oxford: Oxford University Press.
13. Hall P. & Heyde C. (1980) Martingale Limit Theory and Its Application. New York: Academic Press.
14. Mack Y.P. & Silverman B.W. (1982) Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 61, 405–415.
15. Masry E. (1993) Regression estimation with errors-in-variables for stationary processes. Nonparametric Statistics 3, 13–36.
16. Pagan A. & Ullah A. (1988) The econometric analysis of models with risk terms. Journal of Applied Econometrics 3, 87–105.
17. Pham D.T. (1986) The mixing property of bilinear and generalized random coefficient autoregressive models. Stochastic Processes and Their Applications 23, 291–300.
18. Priestley M.B. (1988) Nonlinear and Non-Stationary Time Series Analysis. London: Academic Press.
19. Robinson P.M. (1983) Nonparametric estimators for time series. Journal of Time Series Analysis 4, 185–207.
20. Robinson P.M. (1988) Root-N-consistent semiparametric regression. Econometrica 56, 931–954.
21. Rosenblatt M. (1969) Conditional probability density and regression estimates. In Krishnaiah P.R. (ed.), Multivariate Analysis II, pp. 25–31. New York: Academic Press.
22. Roussas G.G. (1990) Nonparametric regression estimation under mixing conditions. Stochastic Processes and Their Applications 36, 107–116.
23. Stone C.J. (1982) Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10, 1040–1053.
24. Teräsvirta T., Tjøstheim D. & Granger C.W.J. (1994) Aspects of modelling nonlinear time series. In Engle R.F. & McFadden D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2917–2960. Amsterdam: North Holland.
25. Tjøstheim D. (1990) Non-linear time series and Markov chains. Advances in Applied Probability 22, 587–611.
26. Tjøstheim D. & Auestad B. (1994) Nonparametric identification of non-linear time series: Selecting significant lags. Journal of the American Statistical Association 89, 1410–1419.
27. Tong H. (1990) Non-Linear Time Series. A Dynamic System Approach. Oxford: Oxford University Press.
28. Tran L.T. (1990) Kernel Density Regression Estimation for Dependent Random Variables and Time Series. Manuscript.
29. Tweedie R.L. (1975) Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space. Stochastic Processes and Their Applications 3, 385–403.
30. Tweedie R.L. (1988) Invariant measures for Markov chains with no irreducibility assumptions. Journal of Applied Probability (A Celebration of Applied Probability) 25A, 275–285.
31. Volkonskii V.A. & Rozanov Yu. A. (1959) Some limit theorems for random functions. Theory of Probability and Application 4, 178–197.
32. Wheeden R.L. & Zygmund A. (1977) Measure and Integral. New York: Marcel Dekker.