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Distributed lag regression by an almost periodic design matrix

Published online by Cambridge University Press:  14 July 2016

M. J. Katzoff  and
R. H. Shumway
M. J. Katzoff
Affiliation:
NHI Modeling Group, Social Security Administration
R. H. Shumway
Affiliation:
The George Washington University, Washington, D.C.
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Abstract

Frequency domain estimation and tests of hypotheses are considered for a general multivariate distributed lag regression model. The usual vector of regression functions is replaced by a matrix of almost periodic functions, a case for which the terms appearing in the frequency domain estimators have well-defined limits. Asymptotic distributions and consistency are established for the regression coefficients and error spectra. A test statistic is proposed for the no regression hypothesis which is asymptotically central under the null hypothesis and converges to infinity under the alternative. In the multivariate case, a product of beta-distributed variables is obtained.

Keywords

STATIONARY TIME SERIESFINITE FOURIER TRANSFORMTESTS OF HYPOTHESESASYMPTOTIC DISTRIBUTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 4 , December 1978 , pp. 759 - 773
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Anderson, T. W. (1971) The Statistical Analysis of Time Series. Wiley, New York.Google Scholar
[2] Besicovitch, A. S. (1958) Almost Periodic Functions. Dover, New York.Google Scholar
[3] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[4] Brillinger, D. R. (1969) A search for a relationship between monthly sunspot numbers and certain climactic series. Bull. I.S.I., Proc. 37th Session , XLIII(1), 293–307.Google Scholar
[5] Corduneanu, C. (1968) Almost Periodic Functions. Wiley, New York.Google Scholar
[6] Goodman, N. R. (1963) Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Ann. Math. Statist. 34, 152–177.Google Scholar
[7] Grenander, U. and Rosenblatt, M. (1957) Statistical Analysis of Stationary Time Series. Wiley, New York.Google Scholar
[8] Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
[9] Holevo, A. S. (1971) Estimators of an almost periodic time signal. Theory Prob. Appl. 16, 249–263.Google Scholar
[10] Khatri, C. G. (1965) Classical statistical analysis based on a certain multivariate complex Gaussian distribution. Ann. Math. Statist. 36, 98–114.Google Scholar
[11] Kirkendall, N. (1974) Large Sample Finite Approximations in an Infinite Dimensional Distributed Lag Model. Ph.D. Dissertation, The George Washington University.Google Scholar
[12] Koopmans, H. L. (1974) The Spectral Analysis of Time Series. Academic Press, New York.Google Scholar
[13] Shumway, R. H. (1970) Applied regression and analysis of variance for stationary time series. J. Amer. Statist. Assoc. 65, 1527–1546.Google Scholar
[14] Wahba, G. (1969) Estimation of the coefficient in a multidimensional distributed lag model. Econometrica 37, 398–407.Google Scholar