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The statistical properties of long-crested nonlinear wave time series measured in an offshore basin have been analysed in different aspects such as the distributions of surface elevation, wave crest, wave trough, and wave period. Comparison with linear, second-order and thirdorder theoretical models indicates that although bound wave effects also contribute to the deviation from a Gaussian process, it is the modulational instability that primarily determines the discrepancy in the evolution process in the presence of strong nonlinearity. Interestingly enough, wave crest is more sensitive to the quasi-resonant four-wave interaction effect than wave trough and the scaled maximal wave crest presents a linear regression model with the coefficient of kurtosis. Meanwhile, the estimation of the observed statistical properties is reconstructed on the basis of an ensemble of 100 wave series simulated by the NLS-type equations and compared favourably with the experimental results in most cases. Moreover,

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