Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

Weighted least-squares estimation for the subcritical Heston process

We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourselves to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and a natural but intractable estimator, we use a weighted least-squares estimator. We establish strong consistency and asymptotic normality for this estimator. Numerical simulations are also provided, illustrating the favorable performance of our estimation procedure.