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摘要翻译：
本文对金融泡沫的Johansen-Ledoit-Sornette模型的对数周期幂律公式进行了简单的变换，将其简化为一个仅包含三个非线性参数的函数。由于修正后的成本函数具有良好的光滑性，在模型适合于经验数据的情况下，通常只有一个最小值，因此该变换显著降低了拟合过程的复杂性，并极大地提高了其稳定性。我们用一个附加的从属过程来补充该方法，该过程将两个非线性参数从属于可以被认为是最关键的非线性参数，即定义为泡沫结束的临界时间t_c$和崩溃发生的最可能时间。这进一步降低了搜索的复杂性，并提供了校准结果的直观表示。在我们提出的方法中，元启发式搜索不再是必要的，人们可以只求助于严格的受控局部搜索算法，导致效率的显著提高。对2007年1月至2008年3月上证综合指数(SSE)的实证检验说明了我们的发现。
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英文标题：
《A Stable and Robust Calibration Scheme of the Log-Periodic Power Law
Model》
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作者：
Vladimir Filimonov, Didier Sornette
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time $t_c$ defined as the end of the bubble and the most probably time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings.
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PDF链接：
https://arxiv.org/pdf/1108.0099
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