The proper classification of major eye movements, saccades, fixations, and smooth pursuits, remains essential to utilizing eye-tracking data. There is difficulty in separating out smooth pursuits from the other behavior types, particularly from fixations. To this end, we propose a new offline algorithm, I-VDT-HMM, for tertiary classification of eye movements. The algorithm combines the simplicity of two foundational algorithms, I-VT and I-DT, as has been implemented in I-VDT, with the statistical predictive power of the Viterbi algorithm. We evaluate the fitness across a dataset of eight eye movement records at eight sampling rates gathered from previous research, with a comparison to the current state-of-the-art using the proposed quantitative and qualitative behavioral scores. The proposed algorithm achieves promising results in clean high sampling frequency data and with slight modifications could show similar results with lower quality data. Though, the statistical aspect of the algorithm comes at a cost of classification time.