Estimating multivariate ARCH parameters by two-stage least-squares method

This paper discusses the asymptotic properties of the two-stage least-squares (TSLS) estimator of the parameters of multivariate autoregressive conditional heteroscedasticity (ARCH) model. The estimator is easy to obtain since it involves solving sets of linear equations. It will be shown that, under some conditions, this TSLS estimator is asymptotically consistent and its rate of convergence is the same as that of the quasi maximum likelihood estimator (QMLE). At the same time, the computational load of the TSLS estimator is extremely lower than that of the QMLE. The performance of the TSLS estimator will be evaluated and compared with QMLE using simulations. Simulation results show that the performances of the two estimators are comparable, even for small data records.