Continuous updating gmm
Compared to the conventional chi-square tests, the F tests are as powerful, but are much more accurate in size.
Simple, Robust and More Accurate Approaches for Cointegration Regression : Estimation and Inference This paper proposes new, simple, and more accurate statistical tests in a cointegrated system that allows for endogenous regressors and serially dependent errors.
The key difference between these two types of asymptotics is whether the number of clusters G is regarded as fixed or growing when the sample size increases.
Under the new fixed-G asymptotics, the centered two-step GMM estimator and the two continuously-updating estimators have the same asymptotic mixed normal distribution.
The approach involves first transforming the time series using a number of orthonormal basis functions in L²[0,1] that has energy concentrated at low frequencies and then running an augmented regression based on the transformed data.
The tests are extremely simple to implement as they can be carried out in exactly the same way as if the transformed regression is a classical linear normal regression.
The results suggest that the effect of market access may be lower after taking into account the randomness of the estimated optimal GMM weighting matrix. - An Accurate Comparison of One-step and Two-step Procedures in a Generalized Method of Moments Framework - According to the conventional asymptotic theory, the two-step Generalized Method of Moments (GMM) estimator and test perform at least as well as the one-step estimator and test in large samples.
Simulation shows that, in terms of both size and power, the asymptotic F tests perform as well as the nonstandard tests proposed recently by Sun (2014b) in finite samples.