Most real word systems such as world economy, stock market, and medical applications, contain a series of dynamic and complex phenomena. One of common methods to understand these systems is to build a model and analyze the behavior of the system. In this paper, we investigated methods for best clustering over time series data. As a first step for clustering, BIC (Bayesian Information Criterion) approximation is used to determine the number of clusters. A search technique to improve clustering efficiency is also suggested by analyzing the relationship between data size and BIC values. For clustering, two methods, model-based and similarity based methods, are analyzed and compared. A number of experiments have been performed to check its validity using real data(stock price). BIC approximation measure has been confirmed that it suggests best number of clusters through experiments provided that the number of data is relatively large. It is also confirmed that the model-based clustering produces more reliable clustering than similarity based ones.