In this work, we tackle the problem of ternary eye movement classification, which aims to separate fixations, saccades and smooth pursuits from the raw eye positional data. The efficient classification of these different types of eye movements helps to better analyze and utilize the eye tracking data. Different from the existing methods that detect eye movement by several pre-defined threshold values, we propose a hierarchical Hidden Markov Model (HMM) statistical algorithm for detecting fixations, saccades and smooth pursuits. The proposed algorithm leverages different features from the recorded raw eye tracking data with a hierarchical classification strategy, separating one type of eye movement each time. Experimental results demonstrate the effectiveness and robustness of the proposed method by achieving competitive or better performance compared to the state-of-the-art methods.