This paper analyzes autoregressive time series models where the errors are assumed to be martingale difference sequences that satisfy an additional symmetry condition on their fourth order moments. Under these conditions Quasi Maximum Likelihood estimators of the autoregressive parameters are no longer efficient in the GMM sense. The main result of the paper is the construction of efficient semiparametric instrumental variables estimators for the autoregressive parameters. The optimal instruments are linear functions of the innovation sequence.
Efficient Instrumental Variables Estimation for Autoregressive Models with Conditional HeteroskedasticityGuido Kuersteiner ,
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Efficient Instrumental Variables Estimation for Autoregressive Models with Conditional Heteroskedasticity