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

Oyebayo Ridwan Olaniran, Saidat Fehintola Olaniran, Ali Rashash R. Alzahrani (), Nada MohammedSaeed Alharbi and Asma Ahmad Alzahrani
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Oyebayo Ridwan Olaniran: Department of Statistics, Faculty of Physical Sciences, University of Ilorin, Ilorin 1515, Nigeria
Saidat Fehintola Olaniran: Department of Statistics and Mathematical Sciences, Faculty of Pure and Applied Sciences, Kwara State University, Malete 1530, Nigeria
Ali Rashash R. Alzahrani: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 24382, Saudi Arabia
Nada MohammedSaeed Alharbi: Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia
Asma Ahmad Alzahrani: Department of Mathematics, Faculty of Science, Al-Baha University, Al-Baha 65779, Saudi Arabia

Mathematics, 2025, vol. 13, issue 10, 1-28

Abstract: 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.

Keywords: fractional cointegration; panel data; fixed effect models; residual-based test; Bayesian estimation; tapering; narrowband least squares (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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