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摘要翻译：
对数周期幂律(LPPL)是内生泡沫期间资产价格的模型。如果怀疑泡沫正在发展，资产价格可以在数字上符合LPPL定律。最好的解决方案可以表明泡沫是否正在进行，如果是，泡沫的临界时间（即泡沫预计破裂的时间）。因此，LPPL模型只有在数据能够用精确且计算效率高的算法拟合模型时才是有用的。本文主要讨论LPPL非线性最小二乘拟合的计算效率和精度。具体来说，我们提出了一种用于LPPL最小二乘拟合的并行Levenberg-Marquardt算法(LMA)，它加快了对历史和合成价格序列的序列LMA的四倍以上的计算。此外，我们分离出LPPL最小二乘拟合的一个线性子结构，它可以与雅可比的精确计算配对，给出了Levenberg-Marquardt阻尼因子的新设置，并描述了一种选择初始解的启发式方法。
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英文标题：
《Computational LPPL Fit to Financial Bubbles》
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作者：
Vincenzo Liberatore
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最新提交年份：
2011
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. If the on-going development of a bubble is suspected, asset prices can be fit numerically to the LPPL law. The best solutions can then indicate whether a bubble is in progress and, if so, the bubble critical time (i.e., when the bubble is expected to burst). Consequently, the LPPL model is useful only if the data can be fit to the model with algorithms that are accurate and computationally efficient. In this paper, we address primarily the computational efficiency and secondarily the precision of the LPPL non-linear least-square fit. Specifically, we present a parallel Levenberg-Marquardt algorithm (LMA) for LPPL least-square fit that sped up computation of more than a factor of four over a sequential LMA on historical and synthetic price series. Additionally, we isolate a linear sub-structure of the LPPL least-square fit that can be paired with an exact computation of the Jacobian, give new settings for the Levenberg-Marquardt damping factor, and describe a heuristic method to choose initial solutions.
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PDF链接：
https://arxiv.org/pdf/1003.2920
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