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ARMA Memory Index Modeling of Economic Time Series

Published online by Cambridge University Press:  18 October 2010

Herman J. Bierens
Herman J. Bierens
Affiliation:
Free University, Amsterdam
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Abstract

In this paper, it will be shown that if we condition a k-variate rational-valued time series process on its entire past, it is possible to capture all relevant information on the past of the process by a single random variable. This scalar random variable can be formed as an autoregressive moving average of past observations; Since economic data are usually reported in a finite number of digits, this result applies to virtually all economic time series. Therefore, economic time series regressions generally take the form of a nonlinear function of an autoregressive moving average of past observations. This approach is applied to model specification testing of nonlinear ARX models.

Type
Articles
Information
Econometric Theory , Volume 4 , Issue 1 , April 1988 , pp. 35 - 59
Copyright
Copyright © Cambridge University Press 1988

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References

REFERENCES

1.Andrews, D.A zero-one result for the least squares estimator. Econometric Theory 1 (1985): 85–96.CrossRefGoogle Scholar
2.Bierens, H.J.Robust methods and asymptotic theory in nonlinear econometrics. New York: Springer Verlag, 1981.CrossRefGoogle Scholar
3.Bierens, H.J.A uniform weak law of large numbers under ø-mixing with application to nonlinear least squares estimation. Statistica Neerlandica 36 (1982): 81–86.Google Scholar
4.Bierens, H.J.Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of the American Statistical Association 77 (1983): 699–707.CrossRefGoogle Scholar
5.Bierens, H.J.Model specification testing of time series regressions. Journal of Econometrics 26 (1984): 323–353.Google Scholar
6.Bierens, H.J. (1987) Kernel estimators of regression functions. In Bewley, T.F. (ed.), Advances in Econometrics Fifth World Congress, Vol. I: 99–144. Cambridge: Cambridge University Press.Google Scholar
7.Bierens, H.J.ARMAX model specification testing, with an application to unemployment in the Netherlands. Journal of Econometrics 35 (1987); 161–190.CrossRefGoogle Scholar
8.Billingsley, P.Convergence of probability measures. New York: John Wiley, 1968.Google Scholar
9.Chung, K.L.A course in probability theory. New York-London: Academic Press, 1974.Google Scholar
10.Devroye, L.P.The uniform convergence of the Nadaraya-Watson regression function estimate. Canadian Journal of Statistics 6 (1978); 179–191.CrossRefGoogle Scholar
11.Devroye, L.P. & Wagner, T.J.. Distribution-free consistency results in nonparametric discrimination and function estimation. Annals of Statistics 8 (1980): 231–239.Google Scholar
12.Domowitz, I. & White, H.. Misspecified models with dependent observations. Journal of Econometrics 20 (1982): 35–58.CrossRefGoogle Scholar
13.Dunford, N. & Schwartz, J.T.. Linear operators, Part I., General theory. New York: Wiley Interscience, 1957.Google Scholar
14.Ibragimov, I.A. & Linnik, Yu. V.. Independent and stationary sequences of random variables. Groningen: Wolters-Noordhoff, 1971.Google Scholar
15.Rissanen, J.Modeling by shortest data description. Automatica 14 (1978): 465–471.Google Scholar
16.Rissanen, J. Consistent order estimation of autoregressive processes by shortest description of data. In Jacobs, O. et al. (eds.), Analysis and optimization of stochastic systems, 451–461. New York: Academic Press, 1980.Google Scholar
17.Rissanen, J.A universal prior for integers and estimation by minimum description length. Annals of Statistics 11 (1983): 416–431.Google Scholar
18.Royden, H.L.Real analysis. London: Macmillan, 1968.Google Scholar
19.Sargent, T.J. & Sims, C.A.. Business cycle modeling without pretending to have too much a priori economic theory. In Sims, C.A. (ed.), New Methods in Business Cycle Research; Proceedings from a Conference, 45–109. Minneapolis: Federal Reserve Bank of Minneapolis, 1977.Google Scholar
20.Sims, C.A.Macroeconomics and reality. Econometrica 48 (1980): 1–48.Google Scholar
21.Sims, C.A. An autoregressive index model for the U.S., 1948–1975. In Kmenta, J. & Ramsey, J.B. (eds.), Large-scale macro-econometric models, 283–327. Amsterdam: North Holland, 1981.Google Scholar
22.White, H. & Domowitz, I.. Nonlinear regression with dependent observations. Econometrica 52 (1984): 143–161.CrossRefGoogle Scholar