Many econometric models that are commonly used in empirical financial and economic applications are linear. However, the existing literature provides several indications that nonlinear models may be more appropriate to describe relationships encountered in real phenomena. Excess kurtosis, volatility clustering, sensitivity of estimated parameters to alternative specifications of the estimation period are all points towards the presence of nonlinearities in financial and economic time series. Therefore, more complex models are needed in order to overcome the limitations of the linear regression models to deal with these stylized facts. This thesis examines some non-standard parametric time series models which aim at capturing several features of time series of interest, not accounted for by the usual models of the econometric literature. The first class of models considered here are autoregressive models (AR) whose parameters are autoregressive or moving average (MA) processes themselves. Already in 1973 Belsley and Kuh (1973) argued: "The rationales for time varying parameter models are several. For one, the true coefficients themselves can often be viewed directly as the outcome of a stochastic process... Second, even when the underlying parameters are stable, situations arise in which a time-varying coefficient approach will prove to be effective. Such is the case when there are specification errors, such as excluded variables or linear approximations of curvilinear forms'.