Periodicity is one of the most common phenomena in the physical world. The problem of periodicity analysis (or period detection) is a research topic in several areas, such as signal processing and data mining. However, period detection is a very challenging problem, due to the sparsity and noisiness of observational datasets of periodic events. This paper focuses on the problem of period detection from sparse and noisy observational datasets. To solve the problem, a novel method based on the approximate greatest common divisor (AGCD) is proposed. The proposed method is robust to sparseness and noise, and is e?cient. Moreover, unlike most existing methods, it does not need prior knowledge of the rough range of the period. To evaluate the accuracy and e?ciency of the proposed method, comprehensive experiments on synthetic data are conducted. Experimental results show that our method can yield highly accurate results with small datasets, is more robust to sparseness and noise, and is less sensitive to the magnitude of period than compared methods.