As the fastest growing sector within the international tourism industry, having grown at roughly double the rate of international tourism as a whole, the cruise liner business has shown impressive growth in the North American and European markets. For port management purposes, as well as for transport policy, it is essential to be able to forecast accurately cruise passenger arrivals and their variability. In the presence of time-varying variances (or volatility), it is crucial to model such volatility in order to provide sensible forecast intervals in addition to the forecast themselves. Time-varying volatility in port management is important because governments and businesses need to be aware of the uncertainty associated with the number of cruise passenger arrivals and their associated growth. In calculating income elasticities, port taxes and tourist taxes, it is essential to obtain accurate estimates of cruise passenger arrivals and their volatility. Moreover, in an international context in which natural disasters, terrorism, crime and ethnic conflicts, among others, have significant impacts on tourism, it is crucial to assess the persistence of shocks on cruise passenger arrivals for effective crisis management plans, including different forms of co-operation among ports facing similar shocks. Appropriate models are required to enable optimal private and public decision making in designing ports for cruise ships. Daily cruise passenger arrivals data for the three major ports in the Balearic Islands, Spain, namely Palma, Ibiza and Mahon, for the period 1997-2006, as well as for the high cruise season for each island,are analyzed using alternative conditional mean and conditional volatility models in order to provide empirical support for purposes of optimal decision making. Four different types of asymmetries are analyzed according to the positive and negative shocks to daily cruise passenger arrivals, as well as from distinctions between the high and low cruise seasons. The estimates of cruise passenger arrivals and their volatility are generally found to be sensible and to have valid statistical properties. Likelihood ratio tests of the constancy of coefficients in the high and low cruise seasons indicate that the weekly delayed response of cruise passenger arrivals differ significantly spatially across islands and temporally across seasons.