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

Peter Zadrozny

Econometric Theory, 1988, vol. 4, issue 1, 108-124

Abstract: 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.

Date: 1988
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