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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。一个主要的开放问题是验证价格序列中LPPL的存在性和估计LPPL参数。每日LPPL收益通常比实测价格收益小数量级，这一事实使估计变得复杂，表明噪声掩盖了潜在的LPPL动态。然而，如果噪声是均值恢复，它将很快抵消后续的测量。本文试图利用LPPL和均值回复的频域特性来抑制价格序列中的均值回复噪声。首先，我们计算了均值恢复噪声的频谱，并设计了噪声参数的估计器。然后，我们将LPPL谱分解为幂律和对数周期两个主要特征，导出了LPPL谱。我们比较了历史泡沫期间的价格谱和噪声谱。一般而言，低频噪声也很强，即使LPPL支持价格动态，LPPL也会被噪声所掩盖。
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英文标题：
《Financial LPPL Bubbles with Mean-Reverting Noise in the Frequency Domain》
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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：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price returns, suggesting that noise obscures the underlying LPPL dynamics. However, if noise is mean-reverting, it would quickly cancel out over subsequent measurements. In this paper, we attempt to reject mean-reverting noise from price sequences by exploiting frequency-domain properties of LPPL and of mean reversion. First, we calculate the spectrum of mean-reverting \ou noise and devise estimators for the noise's parameters. Then, we derive the LPPL spectrum by breaking it down into its two main characteristics of power law and of log-periodicity. We compare price spectra with noise spectra during historical bubbles. In general, noise was strong also at low frequencies and, even if LPPL underlied price dynamics, LPPL would be obscured by noise.
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PDF链接：
https://arxiv.org/pdf/1009.4835
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