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Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies

Published online by Cambridge University Press:  18 October 2010

Peter Zadrozny
Peter Zadrozny
Affiliation:
U.S., Bureau of the Census
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Extract

For purposes of maximum likelihood estimation, we show how to compute the Gaussian likelihood function when the data are generated by a higher-order continuous-time vector ARMAX model and are observed as stocks and flows at different frequencies. Continuous-time ARMAX models are analogous to discrete-time autoregressive moving-average models with distributed-lag exogenous variables. Stocks are variables observed at points in time and flows are variables observed as integrals over sampling intervals. We derive the implied state-space model of the discrete-time data and show how to use it to compute the Gaussian likelihood function with Kalman-filtering, prediction-error, decomposition of the data.

Type
Articles
Information
Econometric Theory , Volume 4 , Issue 1 , April 1988 , pp. 108 - 124
Copyright
Copyright © Cambridge University Press 1988

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