Utilization of Directional Time Series with Practical Application

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

Roqaea Ali Talib Mohamed Al-Khasbak

Supervision
Asst. Prof.  Dr. Enas                                Asst.Prof. Zainb

Abdul Hafedh Mohammed                    Hasan Abood

Abstract

This study aims to analyze directional time series using nonlinear autoregressive models (TAR) and traditional linear models (AR) to determine the most accurate and appropriate model for describing the money supply data of the Central Bank of Iraq. The study focused on nonlinear models (TAR(1) and TAR(2)) as well as linear models (AR(1) and AR(2)). The maximum likelihood estimation (MLE) method was employed to estimate the model parameters and test their predictive efficiency. The models were evaluated using various criteria, including the Akaike Information Criterion (AIC), the Corrected Akaike Information Criterion (CAIC), and the Bayesian Information Criterion (BIC). These criteria serve as essential tools for assessing the overall performance of models in terms of predictive accuracy and parameter efficiency.                                                                                                    

The study utilized monthly money supply data from the Central Bank of Iraq, obtained from the Statistics and Reports Division, covering 21 years (2004–2024) and consisting of 246 observations.                                    

The results showed that the TAR(2) model significantly outperformed the other models, delivering superior performance in capturing sudden shifts in the money supply data. It achieved the lowest mean squared error (MSE) and the best values for AIC, CAIC, and BIC among all the models used. Although the TAR(1) model demonstrated good performance, it was less effective compared to TAR(2) in handling more complex shifts. In contrast, the linear models (AR(1) and AR(2)) were unable to accurately capture these sudden shifts, potentially leading to the loss of critical information, making them less suitable for data analysis .         

This study highlights the effectiveness of the TAR(2) model in analyzing money supply data, emphasizing the importance of utilizing nonlinear models in complex economic environments .                                            

Utilization of Directional Time Series with Practical Application

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

Roqaea Ali Talib Mohamed Al-Khasbak

Supervision
Asst. Prof.  Dr. Enas                                Asst.Prof. Zainb

Abdul Hafedh Mohammed                    Hasan Abood

Abstract

This study aims to analyze directional time series using nonlinear autoregressive models (TAR) and traditional linear models (AR) to determine the most accurate and appropriate model for describing the money supply data of the Central Bank of Iraq. The study focused on nonlinear models (TAR(1) and TAR(2)) as well as linear models (AR(1) and AR(2)). The maximum likelihood estimation (MLE) method was employed to estimate the model parameters and test their predictive efficiency. The models were evaluated using various criteria, including the Akaike Information Criterion (AIC), the Corrected Akaike Information Criterion (CAIC), and the Bayesian Information Criterion (BIC). These criteria serve as essential tools for assessing the overall performance of models in terms of predictive accuracy and parameter efficiency.                                                                                                    

The study utilized monthly money supply data from the Central Bank of Iraq, obtained from the Statistics and Reports Division, covering 21 years (2004–2024) and consisting of 246 observations.                                    

The results showed that the TAR(2) model significantly outperformed the other models, delivering superior performance in capturing sudden shifts in the money supply data. It achieved the lowest mean squared error (MSE) and the best values for AIC, CAIC, and BIC among all the models used. Although the TAR(1) model demonstrated good performance, it was less effective compared to TAR(2) in handling more complex shifts. In contrast, the linear models (AR(1) and AR(2)) were unable to accurately capture these sudden shifts, potentially leading to the loss of critical information, making them less suitable for data analysis .         

This study highlights the effectiveness of the TAR(2) model in analyzing money supply data, emphasizing the importance of utilizing nonlinear models in complex economic environments .