On the consistency of estimators for non-stationary observation-driven time-varying parameters

This thesis considers two bivariate non-stationary observation-driven time-varying parameter models where the time-varying parameter is modeled as a univariate random walk. We prove that the quasi-maximum likelihood estimator of the static parameters of these models is consistent. Also, we establish that the estimator of the timevarying parameter, obtained by plugging the quasi-maximum likelihood estimator into the filtering equation, converges in probability to the true time-varying parameter. A similar investigation for otherwise equivalent parameter-driven time-varying parameter models was done by Johansen and Tabor (2017). Their results are comparable to those found in our study. We examine to what extent the asymptotic results we found hold in finite samples by conducting a Monte Carlo simulation study. As an example, we also consider an application using data on consumption and income.