Who’s more efficient and drives others? Profit sharing rates vs. deposit rates

We investigate the existence of the explosive behavior, long memory and causal impacts for the Islamic and conventional banking sectors in Türkiye during the 2012–2023 period. The procedure detects multiple bubble episodes in all maturities of profit-sharing rates and shorter maturities of deposit rates, mostly intensified after 2017, Islamic banking has longer-lived bubble episodes than conventional banking, and the duration decreases as the maturity increases. We find that the Hurst exponent is significantly greater than 0.50 for Islamic banking, while its magnitude decreases and goes below 0.50 for the maturity longer than 3 months in the conventional banking as the maturity increases in the full sample period. Conventional banking rates are more efficient, and the level of efficiency rises as maturity increases. We find bidirectional causalities between the 1-month maturities and report one-way short-run causal flows from the conventional banking rates for other three maturities. Multifaceted implications for investors and policymakers are discussed in detail.