A thesis
Submitted to the council of the college of Administration &Economics\ University of Karbala as partial fulfillment of the requirements for the Master degree in Statistics Sciences
By
Hani Ali Abai
Supervision
Prof. Dr. Basim Sh. Msallam
The thesis aimed to estimate the Smooth Transition Kink Regression (STKR) model using several entropy-based estimation methods grounded in Shannon’s principle, namely the Generalized Maximum Entropy (GME) method and the Differential Entropy (DE) method. In addition, some conventional estimation approaches were employed, including the Nonlinear Least Squares (NLLS) method and the Bootstrap Procedure via Grid Search. After presenting the theoretical foundations, mathematical derivations, and computational algorithms of these methods, Monte Carlo simulation experiments were conducted to investigate their performance in estimating the parameters of the STKR model. Prior to implementing the simulations, the design of the simulation experiments was carefully specified by selecting four different sample sizes representing small, medium, and large cases (n=25,50,75,100), as well as three different levels for the number of explanatory variables in the assumed models (k=2,3,5). Accordingly, the simulation study included three different hypothetical models in order to compare the efficiency of the estimation methods under various data conditions. In addition, several supporting statistical tests were employed, such as the Terasvirta Linearity Test, which was used to verify the presence of nonlinearity in the relationship between the variables, and the Wald Test, which was applied to examine the statistical significance of the kink point in the model. All computational procedures and simulations were implemented using the MATLAB programming language. The results of the simulation experiments indicated the superiority of the Generalized Maximum Entropy (GME) method across all simulation experiments, sample sizes, and assumed models. In the applied part of the study, the dataset used in the thesis was obtained from the Iraq Stock Exchange for a period of 120 trading days, as it represents the official financial market that reflects trading movements and investment activities in Iraq. The dependent variable was Risk, while the explanatory variables included Return as the main kink variable, Trading Volume, and Market Volatility. The descriptive statistics of the data indicated sufficient variation to conduct econometric analysis. Furthermore, the results of the Terasvirta linearity test showed that the relationship between risk and the explanatory variables is not linear, but rather exhibits gradual nonlinearity of the smooth transition type, which supports the suitability of applying the STKR model. The Wald Test also confirmed the presence of a statistically significant difference between the effect of return before and after the kink point, indicating the existence of a meaningful kink in the relationship under study. The estimation results of the model revealed that the intercept and the return coefficients before and after the transition are statistically significant, with the effect of return after the kink point being greater than its effect before the kink point. This finding suggests that the sensitivity of risk to return increases once return exceeds a certain threshold. On the other hand, the coefficients of trading volume and market volatility were found to be statistically insignificant, indicating that the main source of nonlinearity in the model is concentrated in the return variable. Meanwhile, trading volume and market volatility play supportive explanatory roles without representing primary sources of structural change or transition .
