Uniform convergence of sample second moments of families of time series arrays

Annals of Statistics

Volumn 29, Issue 3, 2001, Pages 815-838

  Findley, David F ^a   Pötscher, Benedikt M ^b   Wei, Ching Zong ^c  

^a U S CENSUS BUREAU   (United States)

^b UNIVERSITY OF VIENNA   (Austria)

^c INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Consistency; Infinite variance processes; Lacunary systems; Locally stationary series; Long memory processes; Regression residuals; Seasonally adjusted series; Uniform laws of large numbers

Indexed keywords

EID: 0035539855     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1009210691     Document Type: Article

References (27)

1. BLOOMFIELD, P. (1973). An exponential model for the spectrum of a scalar time series. Biometrika 60 217-226.
2. BURMAN, J. P. (1980). Seasonal adjustment by signal extraction. J. Roy. Statist. Soc. Ser. A 143 321-337.
3. CHEN, Z.-G. and NI, J.-Y. (1989). Subset regression time series and its modeling procedures. J. Multivariate Anal. 31 266-288.
4. CLINE, D. (1983). Infinite series of random variables with regularly varying tails. Technical Report 83-24, Institute of Applied Mathematics and Statistics, Univ. British Columbia.
5. DAHLHAUS, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist. 25 1-37.
6. DAVIS, R. A. and RESNICK, S. (1985). Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann. Probab. 13 179-195.
7. DUNFORD, N. and SCHWARTZ, J. T. (1957). Linear Operators, Part I. Wiley, New York.
8. FELLER, W. (1966). An Introduction to Probability Theory and Its Applications 2. Wiley, New York.
9. FINDLEY, D. F. (1983). On the use of multiple models for multi-period forecasting. Proc. Business and Economic Statistics Section 528-531. Amer. Statist. Assoc., Alexandria, VA.
10. FINDLEY, D. F. (1991). Convergence of finite multistep predictors from incorrect models and its role in model selection. Note Mat. 11 145-155.
11. FINDLEY, D. F., MONSELL, B. C., BELL, W. R., OTTO, M. C. and CHEN, B.-C. (1998). New capabilities and methods of the X-12-ARIMA seasonal adjustment program (with discussion). J. Bus. Econom. Statist. 16 127-177.
12. FlNDLEY, D. F., PöTSCHER, B. M. and WEI, C. Z. (2000). Modeling of time series arrays by multistep prediction or likelihood methods. J. Econometrics. To appear.
13. FINDLEY, D. F. and WEI, C.-Z. (1993). Moment bounds for deriving time series CLT's and model selection procedures. Statist. Sinica 3 453-480.
14. GLESER, L. J. (1966). Correction to "On the asymptotic theory of fixed-size sequential confidence bounds for linear regression parameters." Ann. Math. Statist. 37 1053-1054.
15. HANNAN, E. J. (1970). Multiple Time Series. Wiley, New York.
16. HANNAN, E. J. (1978). Rates of convergence for time series regression. Adv. Appl. Probab. 10 740-743.
17. LAI, T. L. and WEI, C.-Z. (1983). Lacunary systems and generalized linear processes. Stochastic Proces. Appl. 14 187-199.
18. PARZEN, E. (1962). Spectral analysis of asymptotically stationary time series. Bull. Inst. Internat. Statist. 39 87-103.
19. PHILLIPS, P. C. B. and SOLO, V. (1992). Asymptotics for linear processes. Ann. Statist. 20 971-1001.
20. PÖTSCHER, B. M. (1987). Convergence results for maximum likelihood type estimators in multivariable ARMA models. J. Multivariate Anal. 21 29-52.
21. PÖTSCHER, B. M. (1998). Solution to Problem 97.4.2: Asymptotic properties of the least-squares estimator of the variance in a linear model. Econometric Theory 14 527-533.
22. PÖTSCHER, B. M. and PRUCHA, I. R. (1997). Dynamic Nonlinear Econometric Models: Asymptotic Theory. Springer, Berlin.
23. SCHMIDT, W. H. (1976). Strong consistency of variance estimation and asymptotic theory for tests of the linear hypothesis in multivariate linear models. Statistics 7 701-705.
24. STOUT, W. F. (1974). Almost Sure Convergence. Academic Press, New York.
25. STULAJTER, F. (1991). Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors. Appl. Math. 36 149-155.
26. TIAO, G. C. and XU, D. (1993) Robustness of maximum likelihood estimates for multistep predictions: the exponential smoothing case. Biometrika 80 623-641.
27. ZYGMUND, A. (1968). Trigonometric Series, Vols. I and II. Cambridge Univ. Press.