Abstract
We consider a linear regression model in continuous time with predetermined stochastic regressors and a local martingale as noise process. The method of estimation of the regression parameters is inspired by the classical least-squares estimate in the discrete time setting. It is shown that under a certain condition limiting the growth of the maximal eigenvalue of the design matrix with respect to the minimal eigenvalue, this “quasi-least-squares” estimate converges with probability one to the true parameter values. The proof uses results from semimartingale theory, in particular the transformation formula and some stability properties of local martingales.
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