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Full-Text Articles in Social and Behavioral Sciences
Asymptotic Theory For Multivariate Garch Processes, F. Comte, Offer Lieberman
Asymptotic Theory For Multivariate Garch Processes, F. Comte, Offer Lieberman
Cowles Foundation Discussion Papers
We provide in this paper asymptotic theory for the multivariate GARCH (p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p,q) process. We prove asymptotic normality of the quasi-MLE when the initial state is either stationary or fixed.
Local Polynomial Whittle Estimation, Donald W.K. Andrews, Yixiao Sun
Local Polynomial Whittle Estimation, Donald W.K. Andrews, Yixiao Sun
Cowles Foundation Discussion Papers
The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent those problems. Instead of approximating the short-run component of the spectrum, φ(λ), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a “local polynomial Whittle” (LPW) estimator. Following the work of Robinson (1995a), we establish the asymptotic bias, variance, mean-squared error (MSE), …