Modeling of time series arrays by multistep prediction or likelihood methods

Journal of Econometrics

Volumn 118, Issue 1-2, 2004, Pages 151-187

  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 ACADEMIA SINICA   (Taiwan)

Author keywords

Baxter's inequality; Consistency; Infinite variance process; Long memory process; Misspecification; Nonstationary models; Regression residuals; Spectral density; Uniform laws of large numbers

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; MATHEMATICAL MODELS; METHOD OF MOMENTS; OPTIMIZATION; PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS; SPECTRUM ANALYSIS; STATISTICAL TESTS;

ECONOMETRICS; GAUSSIAN DISTRIBUTIONS; MULTISTEP PREDICTION ERRORS;

TIME SERIES ANALYSIS;

EID: 0346724431     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(03)00139-8     Document Type: Article

References (48)

1. Bhansali, R.J., 1999. Parameter estimation and model selection for multistep prediction of a time series: a review. In: Subir Ghosh (Ed.), Asymptotics, Nonparametrics and Time Series. Marcel Decker, New York.
2. Bell W.R. Signal extraction for nonstationary time series. The Annals of Statistics. 13:1984;646-664.
3. Bloomfield P. An exponential model for the spectrum of a scalar time series. Biometrika. 60:1973;217-226.
4. Box, G.E.P., Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control, Revised Edition. Holden-Day, San Francisco.
5. Brillinger D.R. Time Series: Data Analysis and Theory. 1975;Holt, Rinehart and Winston, New York.
6. Brockwell P.J., Davis R.A. Time Series: Theory and Methods. 2nd Edition:1991;Springer, New York.
7. Cheng R., Pourahmadi M. Baxter's inequality and convergence of finite predictors of multivariate stochastic processes. Probability Theory and Related Fields. 95:1993;115-124.
8. Dahlhaus R. Fitting time series models to nonstationary processes. The Annals of Statistics. 25:1997;1-37.
9. Dahlhaus R., Pötscher B.M. Convergence results for maximum likelihood type estimators in multivariable ARMA models II. Journal of Multivariate Analysis. 30:1989;241-244.
10. Dahlhaus R., Wefelmeyer W. Asymptotically optimal estimation in misspecified time series models. The Annals of Statistics. 24:1996;952-974.
11. Davis R.A., Resnick S. Limit theory for moving averages of random variables with regularly varying tail probabilities. The Annals of Probability. 13:1985;179-195.
12. Deistler M., Dunsmuir W., Hannan E.J. Vector linear time series models. corrections and extensions Advances in Applied Probability. 10:1978;360-372.
13. Dunford N., Schwartz J.T. Linear Operators, Part I. 1957;Wiley-Interscience, New York.
14. Dunsmuir W., Hannan E.J. Vector linear time series models. Advances in Applied Probability. 8:1976;339-364.
15. Durbin J., Quenneville B. Benchmarking by state space models. International Statistical Review. 65:1997;23-48.
16. Findley, D.F., 1983. On the use of multiple models for multi-period forecasting. Proceedings of the Business Economics and Statistics Section of the American Statistical Association, pp. 528-531.
17. Findley, D.F., 1990a. Making difficult model comparisons. Statistical Research Division Research Report RR-90/11, Bureau of the Census, Washington, DC. http://www.census.gov/srd/papers/pdf/rr-90-11.pdf.
18. Findley, D.F., 1990b. Making difficult model selections graphically. Proceedings of the Section on Survey Methods Research of the American Statistical Association, pp. 622-627.
19. Findley, D.F., 1991a. Model selection for multistep forecasting. Proceedings of the Business Economics and Statistics Section of the American Statistical Association, pp. 243-247.
20. Findley, D.F., 1991b. Convergence of finite multistep predictors from incorrect models and its role in model selection. Note di Matematica XI 145-155.
21. Findley D.F., Monsell B.C., Bell W.R., Otto M.C., Chen B.-C. New capabilities and methods of the X-12-ARIMA seasonal adjustment program. Journal of Business and Economic Statistics. 16:1998;127-177. (with Discussion).
22. Findley D.F., Pötscher B.M., Wei C.Z. Uniform convergence of sample second moments of families of time series arrays. The Annals of Statistics. 29:2001;815-838.
23. Grenander U., Szegö G. Toeplitz Forms and Their Applications. 1958;University of California Press, Berkeley.
24. Hannan E.J. Multiple Time Series. 1970;Wiley, New York.
25. Hannan E.J. The asymptotic theory of linear time-series models. Journal of Applied Probability. 10:1973;130-145.
26. Hannan E.J., Deistler M. The Statistical Theory of Linear Systems. 1988;Wiley, New York.
27. Hannan E.J., Dunsmuir W., Deistler M. Estimation of vector ARMAX models. Journal of Multivariate Analysis. 10:1980;275-295.
28. Haywood J., Tunnicliffe-Wilson G. Fitting time series models by minimising multistep-ahead errors. a frequency domain approach Journal of the Royal Statistical Society B. 59:1997;237-254.
29. Kabaila P.V. Estimation based on one step ahead prediction versus estimation based on multi-step ahead prediction. Stochastics. 6:1981;43-55.
30. Kabaila P.V. Parameter value of ARMA models minimizing the one-step-ahead prediction-error when the true system is not in the model set. Journal of Applied Probability. 20:1983;405-408.
31. Kabaila P.V., Goodwin G.C. On the estimation of the parameter of an optimal interpolator when the class of interpolators is restricted. SIAM Journal of Control and Optimization. 18:1980;121-144.
32. Kohn R., Ansley C.F. Estimation, prediction and interpolation of ARIMA models with missing data. Journal of the American Statistical Association. 81:1986;751-761.
33. Ljung L. Convergence analysis of parametric identification methods. IEEE Transactions on Automatic Control. AC-23:1978;770-783.
34. Parzen E. Spectral analysis of asymptotically stationary time series. Bulletin Institut International Statistique. 39:1962;87-103.
35. Ploberger W. Slight misspecifications for linear systems. Feichtinger G., Kall P. Operations Research in Progress. 1982;413-424 Reidel, Dordrecht.
36. Ploberger, W., 1982b. On the prediction error estimation of linear rational models I. Research Report No.13, Department of Econometrics and Operation Research, University of Technology, Vienna.
37. Pötscher B.M. Convergence results for maximum likelihood type estimators in multivariable ARMA models. Journal of Multivariate Analysis. 21:1987;29-52.
38. Pötscher B.M. Noninvertibility and pseudo-maximum likelihood estimation of misspecified ARMA models. Econometric Theory. 7:1991;435-449. Corrections: Econometric Theory 10, 811.
39. Pötscher B.M., Prucha I.R. Dynamic Nonlinear Econometric Models: Asymptotic Theory. 1997;Springer, Berlin.
40. Rudin W. Functional Analysis. 1973;McGraw Hill, New York.
41. Stoica P., Nehorai A. On multistep prediction error methods for time series models. Journal of Forecasting. 8:1989;357-368.
42. Stoica P., Söderström T. Uniqueness of estimated. r -step prediction models of ARMA processes Systems and Control Letters. 4:1984;325-331.
43. Tiao G.C., Xu D. Robustness of maximum likelihood estimates for multistep predictions. the exponential smoothing case Biometrika. 80:1993;623-641.
44. Tiao G.C., Tsay R.S., Man K.S., Chu Y.J., Xu K.K., Lin J.L., Hsu C.M., Lin C.F., Mao C.S., Ho C.S., Liou R.W., Yang Y.F. A time series approach to econometric models of Taiwan's economy. Statistica Sinica. 8:1998;991-1044.
45. U.S. Bureau of the Census, 2000. Combined Annual and Revised Retail Trade, January 1999 Through December 1999. Current Business Reports, Series BR/99-RV. Washington, DC.
46. Wahlberg B., Ljung L. Design variables for bias distribution in transfer function estimation. IEEE Transactions on Automatic Control. AC-31:1986;134-144.
47. Walker A.M. Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series. Journal of the Australian Mathematical Society. 4:1964;363-384.
48. Whittle P. Gaussian estimation in stationary time series. Bulletin of the International Statistical Institute. 39:1962;105-129.