Non-linear time series Models and their applications.

Abstract

The thesis is primarily concerned with the construction of non-linear time series models and their applications in real-world data. Non-linear models excel at accommodating non-Gaussian and heavy tailed distributions enabling more precise modelling of extreme events and outliers. So the analysis of financial time series requires non-linear modelling using non-Gaussian distributions. Within the range [0,1], we propose a novel distribution termed the uniform truncated Poisson distribution (UTPD) and investigate its features, parameter estimates, and applicability in real-world scenarios. There is also a comparison with the power function distribution and generalization to this distribution. The non-linear applicability of this distribution is investigated by introducing processes with the UTPD under a variety of assumptions. We build a uniform truncated Poisson autoregressive process of order 1 (UTPAR(1)) with UTPD as the marginal function. Investigates the new process's attributes, estimating methodologies, and real-world application. Another process is the uniform truncated autoregressive conditional duration process (UTPACD(1,1)). We talk about analytical characteristics and traditional techniques. Estimation and application are also looked upon. We address the analytical characteristics, traditional estimating methodologies, and real-world applications of the process. This thesis also includes spatial analysis of child mortality data using spatial lag models, spatial Durbin models, and spatial error models that incorporate non-linearity. Minification procedures with two distinct structures are presented, with UTPD acting as a marginal. The processes are known as Type I uniform truncated minification process (Type I UTPM) and Type II uniform truncated minification process (Type II UTPM). The key attributes, estimation methods, and application are also investigated. The relevance of non-linear non- Gaussian time series model is emphasized at the end of this thesis. This thesis concludes by underlining the significance of non-linear non-Gaussian time series models in time series analysis and suggesting future directions. Key Words: Truncated uniform distribution, Non-linear time series, Spatial auto-correlation, ACD, Minification process.