The purpose of this article is to detect a possible linear and nonlinear causal relationship between the conditional stochastic volatility of log return of interbank interest rates for the BRICS countries in the period from January 2015 to October 2018. To extract the volatility of the analyzed time series, we use a stochastic volatility model with moving average innovations. To test a causal relationship between the estimated stochastic volatilities, two steps are applied. First, we used the Granger causality test and a vector autoregressive model (VAR). Secondly, we applied the nonlinear Granger causality test to the raw data to explore a new nonlinear causal relationship between stochastic volatility time series, and also applied it to the residual of the VAR model to confirm the causality detected in the first step. This study demonstrates the existence of some unidirectional/bidirectional linear/nonlinear causal relationships between the studied stochastic volatility time series.

conditional stochastic volatility, stochastic volatility model with moving average innovations, nonlinear Granger causality test.