Nonlinear exponential autoregressive time series models with conditional heteroskedastic errors with applications to economics and finance

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models, which have many advantages. Nevertheless, an issue which has been raised is whether there exist other models that can explain and forecast real data better than linear ones. In this thesis, new nonlinear time series models are suggested, which consist of a nonlinear conditional mean model, such as an ExpAR or an Extended ExpAR, and a nonlinear conditional variance model, such as an ARCH or a GARCH. Since new models are introduced, simulated series of the new models are presented, as it is important in order to see what characteristics real data which could be explained by them should have. In addition, the models are applied to various stationary and nonstationary economic and financial time series and are compared to the classic AR-ARCH and AR-GARCH models, in terms of fitting and forecasting. It is shown that, although it is difficult to beat the AR-ARCH and AR-GARCH models, the ExpAR and Extended ExpAR models and their special cases, combined with conditional heteroscedastic errors, can be useful tools in fitting, describing and forecasting nonlinear behaviour in financial and economic time series, and can provide some improvement in terms of both fitting and forecasting compared to the AR-ARCH and AR-GARCH models.