Statistical Analysis of Poisson Bifurcated Autoregressive Modeling

Abstract

This study evaluates the Poisson Bifurcated Autoregressive (PBAR) model for analyzing time-varying count data, focusing on exchange rate datasets from Anglophone countries. As an extension of the traditional Bifurcated Autoregressive (BAR) model, the PBAR model incorporates a Poisson-distributed error term, enabling it to capture non-Gaussian features and bifurcating structures common in degenerate economic data. Using historical exchange rates from the Central Bank of Nigeria’s Statistical Bulletin, the study compares the PBAR and BAR models based on Akaike Information Criterion (AIC), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE). Results show the PBAR model consistently achieves better fit and accuracy. For Equatorial Guinea (XAF), PBAR recorded an AIC of 0.4077, MAE of 0.249, and RMSE of 0.875, while the BAR model had values of 0.4694, 0.847, and 1.075, respectively. Similarly, for Ghana (GHS), PBAR produced an AIC of 0.3500, MAE of 0.152, and RMSE of 1.026, outperforming BAR’s values of 0.4207, 1.080, and 1.086. Across all datasets, the PBAR model demonstrated improved accuracy and robustness. These findings highlight the PBAR model’s advantage in forecasting non-linear, bifurcating time series. The study concludes that PBAR offers a significant enhancement over traditional models, making it well-suited for financial econometrics applications where accurate modeling of count-based, irregular data is essential