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This research focuses on studying the return and volatility of CSR indices. Four models namely ARFIMA, ARFIMA-GARCH, ARFIMA-FIGARCH and ARFIMA-HYGARCH were applied to investigate the long-memory process in these indices. This paper provides investors with knowledge of CSR indices? time-series data structure, and identifies the most suitable model for volatility estimation. The dataset included 16 CSR indices in terms of environmental, social and corporate governance performance (ESG) under four categories regarding different regional markets in the world. The results show that all the indices exhibit long-memory process, which indicates that predicting their CSR index volatilities in the future to gain excess profits is feasible. In addition, based on log-likelihood values, ARFIMA-HYGARCH appears as the best fitting model to estimate the long-memory effect over the other GARCH models. This paper acknowledges the increasing importance of CSR in selecting investment portfolios to not just maximize returns, but to also promote responsible financing.

Fractional Integration in Corporate Social Responsibility Indices: A FIGARCH and HYGARCH Approach