Abstract: We have derived some matrix equations for speedy computation of the conditional covariance kernel of a discrete-time process obtained from irregularly sampling an underlying continuous-time ARMA process. These results are applicable to both stationary and non-stationary ARMA processes. We have also demonstrated that these matrix results can be useful in shedding new insights on the covariance structure of a continuous-time ARMA process.
Key words and phrases: Irregularly sampled data, Kalman filter, stochastic differential equations.