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Purpose: The purpose of this paper is to investigate the influence of the real interest rates, inflation and risk premium on the time deposit rates of banks in the dual banking system in Malaysia. Design/methodology/approach: The data consists of 1-, 6- and 12-month average time deposit rates of conventional and Islamic banks over the period of January 2000 to June 2017. The cointegration methodologies are used to explore links between the time deposit rates, real rates, inflation and risk premium. The causality tests to test causality linkages between pairs of variables are also applied. The generalised forecast error variance decomposition based on the error correction model is conducted to analyse the impact of variables variation on the deposit rates. Findings: The results show the presence of two cointegration vectors in the deposit rates, real rates, inflation and risk premium, for both conventional and Islamic bank rates. Causality tests reveal that deposit rates are caused by inflation and risk premium in a one-way causality. The results of variance decomposition highlight the importance of inflation and risk premium in explaining the variations in the bank deposit rates. For the conventional bank, inflation shocks play the most important role in explaining the movements of the deposit rates. In Islamic banks, the major determinant's largest influence is the risk premium. Between the two bank rates, Islamic bank rates receive more influence from the explanatory variables in the long-run compared to conventional bank rates. The real rates have no noticeable effect on the variance of time deposit rates for both banks. Originality/value: This study presents new evidence on the relationship between time deposit rates and the three explanatory variables, which are the real interest rates, inflation and risk premium, for both conventional and Islamic banks in Malaysia. The dual banking system allows exploring the similarities and differences between conventional and Islamic banks in Malaysia in terms of the linkages between the variables. [ABSTRACT FROM AUTHOR]