This thesis provides a simulation based study on Kalman Filter estimation of time varying parameter models when nonstationary series are included in regression equation. In this study, we have performed several simulations in order to present the outcomes and ramifications of Kalman Filter estimation applied to time varying regression models in the presence of random walk series. As a consequence of these simulations, we demonstrate that Kalman Filter estimation cannot prevent the emergence of spurious regression in time varying parameter models. Furthermore, so as to detect the presence of spurious regression, we also propose a new method, which suggests penalizing Kalman Filter recursions with endogenously generated series. These series, which are created endogenously by utilizing Cochrane’s variance ratio statistic, are replaced by state evolution parameter Tt in transition equation of time varying parameter model. Consequently, Penalized Kalman Filter performs well in distinguishing nonsense relation from a true cointegrating regression.