Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used...

A new model for time-varying spatial dependencies is introduced. It forms an extension to the popular spatial lag model and can be estimated conveniently by maximum likelihood. The spatial dependence parameter is assumed to follow a generalized autoregressive score (GAS) process. The theoretical...

We study the performance of alternative methods for calculating in-sample confidence and out of-sample forecast bands for time-varying parameters. The in-sample bands reflect parameter uncertainty only. The out-of-sample bands reflect both parameter uncertainty and innovation uncertainty. The...

We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The...

We introduce a new model for time-varying spatial dependence. The model extends the well-known static spatial lag model. All parameters can be estimated conveniently by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimator for the...

The multivariate analysis of a panel of economic and financial time series with mixed frequencies is a challenging problem. The standard solution is to analyze the mix of monthly and quarterly time series jointly by means of a multivariate dynamic model with a monthly time index: artificial...

We characterize the dynamic properties of Generalized Autoregressive Score (GAS) processes by identifying regions of the parameter space that imply stationarity and ergodicity. We show how these regions are affected by the choice of parameterization and scaling, which are key features of GAS...

We first consider an extension of the generalized autoregressive conditional heteroskedasticity (GARCH) model that allows for a more flexible weighting of financial squared-returns for the filtering of volatility. The parameter for the squared-return in the GARCH model is time-varying with an...

Locally explosive behavior is observed in many economic and financial time series when bubbles are formed. We introduce a time-varying parameter model that is capable of describing this behavior in time series data. Our proposed model can be used to predict the emergence, existence and burst of...

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...