We extend the generalized method of moments to a setting where a subset of the parameters may vary over time with unknown dynamics. We approximate the true unknown dynamics by an updating scheme that is driven by the influence function of the conditional criterion function at time t. The updates...

We extend the generalized method of moments to a setting where a subset of the parameters may vary over time with unknown dynamics. We approximate the true unknown dynamics by an updating scheme that is driven by the influence function of the conditional criterion function at time t. The updates...

We establish the strong consistency and asymptotic normality of the maximum likelihood estimator for time-varying parameter models driven by the score of the predictive likelihood function. We formulate primitive conditions for global identification, invertibility, strong consistency, and...

We investigate the information theoretic optimality properties of the score function of the predictive likelihood as a device to update parameters in observation driven time-varying parameter models. The results provide a new theoretical justification for the class of generalized autoregressive...

We develop a new parameter stability test against the alternative of observation driven generalized autoregressive score dynamics. The new test generalizes the ARCH-LM test of Engle (1982) to settings beyond time-varying volatility and exploits any autocorrelation in the likelihood scores under...

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...

We study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximum power against the unit root null, give rise to different optimal...

The maximum likelihood estimator based on Student's t distribution is generally thought to be robust to outliers in the regression errors. This paper shows that this is true if the degrees of freedom parameter is kept fixed. In contrast, if the degrees of freedom parameter is also estimated from...

In the present paper we confine ourselves to proposing tests for smooth transition nonlinearity in the presence ou outliers. We consider outlier robust estimation techniques to modify the tests developed by Luukkonen et al

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...