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...

The strong consistency and asymptotic normality of the maximum likelihood estimator in observation-driven models usually requires the study of the model both as a filter for the time-varying parameter and as a data generating process (DGP) for observed data. The probabilistic properties of the...

We derive computationally simple and intuitive score tests of neglected serial correlation in unobserved component univariate models using frequency domain techniques. In some common situations in which the alternative model information matrix is singular under the null, we derive one-sided...

This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons...

There is a growing literature on unit root testing in threshold autoregressive models. This paper makes two contributions to the literature. First, an asymptotic theory is developed for unit root testing in a threshold autoregression, in which the errors are allowed to be dependent and...

In this paper, we investigate the implications of the two concepts of asymmetry defined by Sichel (1993) - deepness and steepness - for first-order autoregressive processes with a Markov-switching intercept. In order to do so, we derive the two required formulas determining the coefficient of...

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of...

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identification failures that plague conventional likelihood-based inference methods. The approach exploits the moments of...

In a recent article, Xu (2008) developed the asymptotic theory for autoregressions around a polynomial trend, under nonstationary volatility. In the same article, Xu proposed a set of t-tests for the regression coefficients and claimed that these tests are asymptotically standard normal. A...