Abstract: Fractal dimension is used broadly in fractal analysis for time series. Lots of calculating methods are available, but fully comparison of them is rarely reported in literature. In this study, the most common methods of estimating the fractal dimension for time series directly in the time domain are analyzed and compared over synthetic data（WCF time series）. The accuracy, efficiency and dependence on data length are evaluated for each method. Simulation and measurement results indicate that the FA, DFA and Higuchi methods outperform others in accuracy comparison. When it comes to efficiency, Katz, Sevcik and Castiglioni methods have the highest performance. In analysis of dependence on data length, 4，096 is found to be the just length with which most methods could get a stable estimating value. Especially for FA, DFA and Higuchi methods, whose estimated value coincide with theory value well. Therefore, the Higuchi and DFA methods outshine than others in calculating fractal dimension, and they should be taken precedence in related computing.

Key words: fractal dimension, Higuchi, Detrended Fluctuation Analysis（DFA）, Fluctuation Analysis（FA）, accuracy, efficiency, data length

摘要： 分形维数在一维时间序列的分形特性分析中应用非常广泛，其计算方法多种多样，但是相关计算方法的全面对比鲜见文献报道。针对常用的八种一维时间序列分形维数计算方法，以WCF合成时间序列为研究对象，分别就算法的准确性和效率，对数据长度的依赖性进行分析对比。结果表明：准确性较好的三种算法是FA，DFA和Higuchi算法；而运算效率最高的是Sevcik，Katz和Castiglioni算法，但是它们的准确性偏低，而FA和Higuchi算法在计算时间上略微增加，但准确性比较高；在数据长度为4 096点时，各算法的计算值基本稳定，尤其是FA、Higuchi和DFA算法，在数据长度为4 096点时，计算值与理论值比较吻合。由此可以得出结论，Higuchi和DFA算法在计算一维时间序列的分形维数时性能优越，在相关的计算中优先选择。

关键词: 分形维数, Higuchi, 去趋势波动分析, 波动分析, 准确性, 效率, 数据长度