This paper investigates the problem of power allocation for hybrid automatic repeat request (HARQ) schemes over time-correlated Nakagami-m fading channels under outage constraint. The presence of time correlation complicates the power allocation problem due to the involvement of multiple correlated fading channels. Under a general time-correlated Nakagami-m fading channel with exponential correlation, outage probabilities for three widely adopted HARQ schemes, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are first derived. With these results, power allocation schemes are proposed to minimize the average total transmission power with guaranteed outage performance. Simulation results demonstrate the accuracy of our outage analysis and the effectiveness of our proposed power allocation schemes. It is shown that our proposed power allocation schemes can achieve significant power savings when compared with fixed power allocation. Moreover, under practical low outage constraint, the power efficiency is further improved when the time correlation is reduced and/or the fading order is increased.