Frederic Abergel, Nicolas Huth, Ioane Muni Toke
We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks correlation structure.
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On 2 November 2009, the Financial Bubble Experiment was launched within the Financial Crisis Observatory (FCO) at ETH Zurich (\url{http://www.er.ethz.ch/fco/}). In that initial report, we diagnosed and announced three bubbles on three different assets. In this latest release of 23 December 2009 in this ongoing experiment, we add a diagnostic of a new bubble developing on a fourth asset.
This is the third installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 27 bubbles in 27 different global assets; for 25 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that document of the original analysis on 2 May 2011.
This is the second installment of the Financial Bubble Experiment. Here we provide the digital fingerprint of an electronic document in which we identify 7 bubbles in 7 different global assets; for 4 of these assets, we present windows of dates of the most likely ending time of each bubble. We will provide that document of the original analysis on 1 November 2010.
Multiple-bubble testing in the cryptocurrency market: a case study of bitcoin
本文以比特币为例研究加密货币市场的多重泡沫检验问题，强调评估金融市场对投资者和研究人员的重要性。
Cross-Sectional Heterogeneity in LSTM Networks for Financial Time Series
针对金融时间序列预测中LSTM难处理横截面异质性的问题，本文提出含可学习行业嵌入的扩展LSTM模型，结合宏观金融协变量，在标普500成分股多空策略中表现优于基准模型，还通过可视化和贡献指标提升了可解释性。
Inspired by the question of identifying the start time $τ$ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised sum of the squared residuals, $χ^{2}_{np}(Φ)$, to endogenously detect the optimal fitting window size := $w^* \in [τ:\bar{t}_2]$ that should be used for calibration purposes for a fixed pseudo present time $\bar{t}_2$. The performance of the Lagrange regularisation of $χ^{2}_{np}…
Universal Dynamics of Financial Bubbles in Isolated Markets: Evidence from the Iranian Stock Market
本文通过伊朗股市的实证研究，证明孤立市场中的金融泡沫动力学具有普遍性，揭示了内生机制在泡沫形成中的主导作用。
The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for many companies, there are no dividends and fundamental value, making it difficult (if not impossible) to measure the bubbles by existing methods. Therefore, we proposed a simple but effective statistical method and three statistics (that is, C, U, V) to capture and quantify asset price bubbles, especially in immature emerging markets. To present a clear exa…
We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion (GBM) and a bubble regime represented by the stochastic super-exponential Sornette-Andersen (2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the b…
We present a detailed methodological study of the application of the modified profile likelihood method for the calibration of nonlinear financial models characterised by a large number of parameters. We apply the general approach to the Log-Periodic Power Law Singularity (LPPLS) model of financial bubbles. This model is particularly relevant because one of its parameters, the critical time $t_c$ signalling the burst of the bubble, is arguably the target of choice for dynamical risk management. However, previous calibrations of the LPPLS model have shown that the estimation of $t_c$ is in gene…
Based on the Log-Periodic Power Law (LPPL) methodology, with the universal preferred scaling factor $λ\approx 2$, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so called commodity currencies expressed in terms of the US dollar appears to take place with the oscillation pattern which largely is mirror reflected relative to oil price oscillation pattern. This documents recent strong anti-correlation between the dynamics of the oil price and of the USD. A related forecast made at the time of FENS 2015 conference (beginning of N…
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 prope…
Vector-Quantized Discrete Latent Factors Meet Financial Priors: Dynamic Cross-Sectional Stock Ranking Prediction for Portfolio Construction
本文提出PRISM-VQ模型，结合专家先验因子和向量量化离散潜在因子，通过结构条件混合专家生成时间变化因子载荷，提升横截面股票收益预测和投资组合表现。
We study the intraday behaviour of the statistical moments of the trading volume of the blue chip equities that composed the Dow Jones Industrial Average index between 2003 and 2014. By splitting that time interval into semesters, we provide a quantitative account of the non-stationary nature of the intraday statistical properties as well. Explicitly, we prove the well-known U-shape exhibited by the average trading volume-as well as the volatility of the price fluctuations-experienced a significant change from 2008 (the year of the sub-prime financial crisis) onwards. That has resulted in a fa…
Why Topological Data Analysis Detects Financial Bubbles?
本文基于LPPLS模型给出启发式论证，解释TDA为何能检测金融时间序列中的临界转变早期预警信号，并以比特币正负泡沫为例进行验证。
Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The model predicts the existence of two anomalous behaviors occurring simultaneously: (i) super-exponential price growth and (ii) volatility growth, that we refer to as the ``fearful singular bubble'' regime. Out of the 9 time series, we find that 5 pass our tests and can be characte…
A three-step machine learning approach to predict market bubbles with financial news
提出融合金融新闻NLP情绪特征、宏观经济指标与右尾单位根检验的三步集成学习框架，用于识别并预测S&P 500市场泡沫，提升预警准确性与稳健性。
Pricing assets has attracted significant attention from the financial technology community. We observe that the existing solutions overlook the cross-sectional effects and not fully leveraged the heterogeneous data sets, leading to sub-optimal performance. To this end, we propose an end-to-end deep learning framework to price the assets. Our framework possesses two main properties: 1) We propose Equity2Vec, a graph-based component that effectively captures both long-term and evolving cross-sectional interactions. 2) The framework simultaneously leverages all the available heterogeneous alpha s…
A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condition. This paper examines these claims and the robustness of the LPPL for capturing large falls in the Hang Seng stock market index, over a 30-year period, including the current global downturn. We identify 11 crashes on the Hang Seng market over the period 1970 to 2008. The fitte…
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to their allocation on the risky asset versus the risk-free asset. Noise traders are subjected to social imitation and follow momentum trading. Allowing for random time-varying herding propensity, we are able to reproduce several well-known stylized facts of financial markets such as a …
We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to ``anti-bubbles'' with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price decorated by decelerating log-periodic oscillations. We document this behaviour on the Japanese Nikkei stock index from 1990 to prese…
By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competin…
Statistical analysis of financial data most focused on testing the validity of Brownian motion (Bm). Analysis performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We inquiry in the behavior of measures of performance based on maximum drawdown movements (MDD), testing their stability when the underlying process deviates from the Bm hypothesis. In particular we consider the fractional Brownian motion (fBm), and fluctuations estimated empirically on raw market data. The case study of the rising part of s…
We extend the model of rational bubbles of Blanchard and of Blanchard and Watson to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d times d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i on any other asset j different from i has to vanish on average, i.e., must exhibit random alternative regimes of reinforcement and contrarian feedbacks. In contrast, the diagonal terms must be positive and equal on average to the inverse of the discount factor. Applying the resu…
We tested 45 indices and common stocks traded in the South African stock market for the possible existence of a bubble over the period from Jan. 2003 to May 2006. A bubble is defined by a faster-than-exponential acceleration with significant log-periodic oscillations. The faster-than-exponential acceleration characteristics are tested with several different metrics, including nonlinearity on the logarithm of the price and power law fits. The log-periodic properties are investigated in detail using the first-order log-periodic power-law (LPPL) formula, the parametric detrending method, the $(H,…
Are cryptocurrencies real financial bubbles? Evidence from quantitative analyses
研究比特币和以太坊是否为金融泡沫，运用结合LPPL模型与统计模型的方法，采用多种测试版本，发现特定时间段内两种加密货币有泡沫迹象，证实其投机泡沫高风险，方法具通用性可用于金融时间序列及相关策略。
A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a "super-bubble" (bubble on bubble) phenomenon. Identifying a potential "universal" preferred scaling…
Amid the current financial crisis, there has been one equity index beating all others: the Shanghai Composite. Our analysis of this main Chinese equity index shows clear signatures of a bubble build up and we go on to predict its most likely crash date: July 17-27, 2009 (20%/80% quantile confidence interval).
Cross-sectional topological anomaly scores and intraday return predictability in the S&P 500: A BallMapper, decoder-conditional VAE, and Function-on-Function regression approach
本文构建基于市场拓扑结构和横截面同行背景的股票级拓扑异常分数，通过函数对函数回归验证其对标普500成分股日内收益曲线的预测能力，发现异常分数具有累积、反转和分布式的预测特征。
The rapid spread of information over social media influences quantitative trading and investments. The growing popularity of speculative trading of highly volatile assets such as cryptocurrencies and meme stocks presents a fresh challenge in the financial realm. Investigating such "bubbles" - periods of sudden anomalous behavior of markets are critical in better understanding investor behavior and market dynamics. However, high volatility coupled with massive volumes of chaotic social media texts, especially for underexplored assets like cryptocoins pose a challenge to existing methods. Taking…
In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior (HB) and hence, to find out the beginning of a market bubble. In particular, classical Detrended Fluctuation Analysis (DFA), Generalized Hurst Exponent (GHE) and GM2 (one of Geometric Method-based algorithms) were applied for self-similarity exponent calculation purposes. Traditionally, researchers have been focused on identifying the beginning of a crash. I…
A taxonomy of large financial crashes proposed in the literature locates the burst of speculative bubbles due to endogenous causes in the framework of extreme stock market crashes, defined as falls of market prices that are outlier with respect to the bulk of drawdown price movement distribution. This paper goes on deeper in the analysis providing a further characterization of the rising part of such selected bubbles through the examination of drawdown and maximum drawdown movement of indices prices. The analysis of drawdown duration is also performed and it is the core of the risk measure est…
We perform an extended analysis of the distribution of drawdowns in the two leading exchange markets (US dollar against the Deutsmark and against the Yen), in the major world stock markets, in the U.S. and Japanese bond market and in the gold market, by introducing the concept of ``coarse-grained drawdowns,'' which allows for a certain degree of fuzziness in the definition of cumulative losses and improves on the statistics of our previous results on the existence of ``outliers'' or ``kings.'' Then, for each identified outlier, we check whether log-periodic power law signatures (LPPS) are pres…
This review is a partial synthesis of the book ``Why stock market crash'' (Princeton University Press, January 2003), which presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are ``outliers'': they form a class of their own as can be seen from their statistical signatures. If large financial crashes are ``outliers'', they are special and thus require a special explanation,…
The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to algorithmically detect critical changes in the scaling of the underlying complex time-series. The methodology involves the degree of multiscaling at a particular time instance, the multiscaling trend which is calculated by the Change-Point Analysis method, and a rigorous evaluation of the statistical significance of the results. Using this algorithm, we have …
Regime-Gated Residual Mixture-of-Experts for Cross-Sectional Volatility Forecasting
本文针对金融波动率的 regime 依赖性问题，提出 RG-ResMoE 架构，将 regime 信息仅用于专家路由，在美、日股票波动率预测中，该模型在精度和稳定性上均优于 MLP。
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. We define a simple statistic $s$, the normalized sum of signs of returns on a given day, to capture the degree of correlation in the system. $s$ can be seen as the order parameter of the system because if $s= 0$ there is no correlation (a disordered state), whereas for $s \ne 0$ t…
We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. L…
We present a simple agent-based model to study the development of a bubble and the consequential crash and investigate how their proximate triggering factor might relate to their fundamental mechanism, and vice versa. Our agents invest according to their opinion on future price movements, which is based on three sources of information, (i) public information, i.e. news, (ii) information from their "friendship" network and (iii) private information. Our bounded rational agents continuously adapt their trading strategy to the current market regime by weighting each of these sources of informatio…
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