This paper discusses the constrained two stage least squares (CLS2) estimator of the parameters of ARCH models under known order. This estimator is a modified version of the two stage least squares (TSLS) estimation. The estimator is easy to obtain and fast since it involves only quadratic optimization. At the same time, the estimator has the same asymptotic efficiency as that of the TSLS estimator and the widely used quasi-maximum likelihood estimator (QMLE). Simulation results show that, even for small sample size, the performance of our estimator is better than the quasi-maximum likelihood and two stage least squares estimators.
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