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.
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- Doctoral Theses [5]