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A large portion of tourist demand is conducted by air. Several air links can have intrinsic characteristics concerning the touristic demand evolution with strong non-stationary and seasonal characteristics. In this paper we implemented recent data mining techniques to model tourist demand and developed two advanced models of time-series prediction: a fractionally integrated autoregressive moving average model (ARFIMA) and a temporal genetically optimized iterative neural networks. These models originate from different methodological backgrounds and aim to evaluate different statistical properties of tourist demand (such as the existence of long-term memory, the parameters of memory depth for predictions and so on). To evaluate the proposed methodologies, three cases studies were examined that encompass three secondary airport located in the Greek Islands which exhibit different yearly and monthly demand distributions. In terms of prediction accuracy, the advanced form of temporal neural networks implemented seems to outperform the ARFIMA model. This applies to both high and low tourist demand periods. In terms of the knowledge acquired by the modeling, both approaches revealed very interesting results; the fractional dynamics observed in both the pooled data and the peak demand period, show that the tourist arrivals are not always stationary or best described as most frequently - assumed - by ARIMA models. The fractionally integrated processes fitted to the available data showed that all case studies examined have similar fractional dynamics and exhibit long term memory. This finding has significant implications to the process of modeling NSI arrivals, as it suggests the persistence of the effect of several socio-economic issues to the evolution of NSI arrivals. Moreover, the iterative approach to predicting NSI arrivals showed significant improvement to the prediction accuracy. The advanced genetic optimization implemented with regards to the look-back time window of the TLNN shows that the past could be utilized to predict the evolution of tourist demand. Nevertheless, the differences in the memory depth of the three TLNN models developed to approximate the dynamics of NSI arrivals in the three airports indicates the stochasticity of the temporal evolution of NSI arrivals during periods of low volume that significantly affect the accuracy of predictions. Finally, lack of prediction accuracy during transitional conditions reveals that, as expected, the demand evolution can have multiple causal dimensions that need to be considered in an effective methodological framework that could integrate both the temporal and causal/relational characteristics of other possible influential variables in the prediction process. Our ongoing work focuses on extending the present methodological framework to iterative neural network prediction that incorporates other socio-economic data to develop