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In this paper, a metacognitive octonion-valued neural network (Mc-OVNN) learning algorithm and its application to diverse time series prediction are presented. The Mc-OVNN is comprised of two components: the octonion-valued neural network that represents the cognitive component and the metacognitive component that serves to self-regulate the learning algorithm. At each epoch, the metacognitive component decides if, how, and when learning occurs. The algorithm deletes unneeded samples and only stores those that will be used. This decision is determined by the octonion magnitude and the seven phases. To evaluate the Mc-OVNN algorithm’s performance, it is applied to five real-world forecasting problems: the power consumption of a home in Honolulu, HI, USA, Box and Jenkins J series, Euro to Algerian Dinar (DZ) real-time conversion rates, the Mackey–Glass equation, and Europe Brent oil price prediction in a time series. When comparing the Mc-OVNN to other relevant techniques, Mc-OVNN displays its capability for efficient time series prediction. The real-time evaluation of the proposed algorithm is presented using the power consumption of a home in Boumerdès, Algeria, as a case study. [ABSTRACT FROM AUTHOR]