Big data ecosystems are increasingly important for the daily activities of any type of company. They are decisive elements in the organization, so any malfunction of this environment can have a great impact on the normal functioning of the company; security is therefore a crucial aspect of this type of ecosystem. When approaching security in big data as an issue, it must be considered not only during the creation and implementation of the big data ecosystem, but also throughout its entire lifecycle, including operation, and especially when managing and responding to incidents that occur. To this end, this paper proposes an incident response process supported by a private blockchain network that allows the recording of the different events and incidents that occur in the big data ecosystem. The use of blockchain enables the security of the stored data to be improved, increasing its immutability and traceability. In addition, the stored records can help manage incidents and anticipate them, thereby minimizing the costs of investigating their causes; that facilitates forensic readiness. This proposal integrates with previous research work, seeking to improve the security of big data by creating a process of secure analysis, design, and implementation, supported by a security reference architecture that serves as a guide in defining the different elements of this type of ecosystem. Moreover, this paper presents a case study in which the proposal is being implemented by using big data and blockchain technologies, such as Apache Spark or Hyperledger Fabric.