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This paper proposes an algorithm, called sequence prediction via enhanced episode discovery (SPEED), to predict inhabitant activity in smart homes. SPEED is a variant of the sequence prediction algorithm. It works with the episodes of smart home events that have been extracted based on the on -off states of home appliances. An episode is a set of sequential user activities that periodically occur in smart homes. The extracted episodes are processed and arranged in a finite-order Markov model. A method based on prediction by partial matching (PPM) algorithm is applied to predict the next activity from the previous history. The result shows that SPEED achieves an 88.3% prediction accuracy, which is better than LeZi Update, Active LeZi, IPAM, and C4.5.