The statistical behavior of wave energy at a site strongly depends on the wave characteristics. Wave energy converters fail to produce energy when there are no sufficiently available wave heights. Hence, evaluation of return periods and risk values of the minimum wave height becomes important for wave energy studies. A time index representing the minimum wave height is proposed here for ocean wave applications. Persistence plays a significant role in the calculation of return period and risk. Although ignoring the serial independence makes calculations easy, it leads to overestimations of the real status. In this paper, return periods and risk values are compared with each other by taking into consideration independent and dependent situations. Application of the study is achieved for the stations located in the Pacific Ocean and Gulf of Mexico. (C) 2008 Elsevier Ltd. All rights reserved.