Bayesian Tapered Narrowband Least Squares for Fractional Cointegration Testing in Panel Data

Fractional cointegration has been extensively examined in time series analysis, but its extension to heterogeneous panel data with unobserved heterogeneity and cross-sectional dependence remains underdeveloped. This paper develops a robust framework for testing fractional cointegration in heterogeneous panel data, where unobserved heterogeneity, cross-sectional dependence, and persistent shocks complicate traditional approaches. We propose the Bayesian Tapered Narrowband Least Squares (BTNBLS) estimator, which addresses three critical challenges: (1) spectral leakage in long-memory processes, mitigated via tapered periodograms; (2) precision loss in fractional parameter estimation, resolved through narrowband least squares; and (3) unobserved heterogeneity in cointegrating vectors ( θ i ) and memory parameters ( ν , δ ), modeled via hierarchical Bayesian priors. Monte Carlo simulations demonstrate that BTNBLS outperforms conventional estimators (OLS, NBLS, TNBLS), achieving minimal bias (0.041–0.256), near-nominal coverage probabilities (0.87–0.94), and robust control of Type 1 errors (0.01–0.07) under high cross-sectional dependence ( ρ = 0.8 ), while the Bayesian Chen–Hurvich test attains near-perfect power (up to 1.00) in finite samples. Applied to Purchasing Power Parity (PPP) in 18 fragile Sub-Saharan African economies, BTNBLS reveals statistically significant fractional cointegration between exchange rates and food price ratios in 15 countries ( p < 0.05 ), with a pooled estimate ( θ ^ = 0.33 , p < 0.001 ) indicating moderate but resilient long-run equilibrium adjustment. These results underscore the importance of Bayesian shrinkage and spectral tapering in panel cointegration analysis, offering policymakers a reliable tool to assess persistence of shocks in institutionally fragmented markets.