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May, 1975 Continuous Time Regressions with Discrete Data
P. M. Robinson
Ann. Statist. 3(3): 688-697 (May, 1975). DOI: 10.1214/aos/1176343131


A general continuous time distributed lag model is considered. The problem is that of estimating the parameters of the kernel when, as is often the case, the available data consist not of a continuous record but of discrete observations recorded at regular intervals of time. Fourier transformation of the model and insertion of the computable, discrete Fourier transforms of the variables produce an approximate model which is of non-linear regression type and is relatively easy to handle. Estimators are proposed and their asymptotic properties established, assuming principally that the variables are stationary and ergodic and that an "aliasing" condition on the independent variable is satisfied. The results of the paper imply a theory for the estimation of rather general continuous time systems, involving the operations of differentiation, integration and translation through time.


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P. M. Robinson. "Continuous Time Regressions with Discrete Data." Ann. Statist. 3 (3) 688 - 697, May, 1975.


Published: May, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0305.62042
MathSciNet: MR431569
Digital Object Identifier: 10.1214/aos/1176343131

Primary: 62E20
Secondary: 42A68 , 62M10 , 62M15

Keywords: Asymptotic theory , Fourier methods , non-linear regressions , Stationary processes

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 3 • May, 1975
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