Modeling and Prediction of Exchange Rates Using Topp-Leone Burr Type X, Machine Learning and Deep Learning Models

Abstract

This paper introduces the Topp-Leone Burr X distribution (TLBXD), a novel extension of the Burr X distribution, developed within the framework of the Topp-Leone-G family. The TLBXD is designed to effectively model varying datasets, addressing the limitations of classical distributions when applied to heterogeneous data. We derived and presented key mathematical and statistical properties of the TLBXD, ensuring their clarity and applicability for practical use. A simulation study was conducted to evaluate the efficiency of different parameter estimation methods, including least squares (LS), maximum product of spacings (MPS), weighted least squares (WLS), and maximum likelihood (ML). The proposed distribution was applied to two real-world dates related to the daily exchange rates of the Nigerian Naira against the EURO and RIYAL. The TLBXD demonstrated superior performance compared to existing sub-models. In addition to the data modeling, this research also applied the proposed distribution to explore the predictive capabilities of machine learning and deep learning techniques for exchange rate forecasting. Three machine learning models, including the Extreme Gradient Boosting (XGBoost), Random Forest, and Light Gradient Boosting Machine (LightGBM) were evaluated alongside a deep learning algorithm, the Long Short-Term Memory (LSTM). The models were trained on 80% of the data set and tested on the remaining 20% to assess prediction accuracy. The results reveal that the LSTM model has significantly outperformed the machine learning models in forecasting exchange rates, as evidenced by lower root means squared errors (RMSE) and mean absolute errors (MAE) values.