Log-periodic Power Law Research Articles

A systematic review of the bubble dynamics of cryptocurrency prices

This paper surveys the academic literature concerning the formation of pricing bubbles in digital currency markets. Studies indicate that several bubble phases have taken place in Bitcoin prices, mostly during the years 2013 and 2017. Other digital currencies of primary importance, such as Ethereum and Litecoin, also exhibit several bubble phases. The Augmented Dickey Fuller (ADF) as well as the Log-Periodic Power Law (LPPL) methodology are the most frequently employed techniques for bubble detection and measurement. Based on much academic research, Bitcoin appears to have been in a bubble-phase since June 2015, while Ethereum, NEM, Stellar, Ripple, Litecoin and Dash have been denoted as possessing bubble-like characteristics since September 2015. However, this latter group possess little academic evidence supporting the presence of bubbles since early 2018. An overall perspective is provided based on a robust bibliography based on large deviations of market quotes from fundamental values that can serve as a guide to policymakers, academics and investors.

The Mechanism behind the Bursting of Financial Bubbles and Market Crashes

This article proposes to deliver an algorithm to envisage the distribution of the critical points of bubbles, may it be a financial bubble or an asset bubble. The study comprehensively examines the use of Log periodic Power law in various articles from renowned authors from the first paper that was published by Didier Sornette in 1996 to the present day. The paper scrutinizes the prerogatives and robustness of the LPPL for large market falls and the anti-bubbles that build in a market. The LPPL fit has been attempted to fit into various crashes in different stock markets that were predicted previously to establish the smooth working of the model.

Predicting the turning points of housing prices by combining the financial model with genetic algorithm.

The turning points of housing prices play a significant role in the real estate market and economy. However, because multiple factors impact the market, the prediction of the turning points of housing prices faces significant challenges. To solve this problem, in this study, a historical data-based model that incorporates a multi-population genetic algorithm with elitism into the log-periodic power law model is proposed. This model overcomes the weaknesses of multivariate and univariate methods that it does not require any external factors while achieving excellent interpretations. We applied the model to the case study collected from housing prices in Wuhan, China, from December 2016 to October 2018. To verify its reliability, we compared the results of the proposed model to those of the log-periodic power law model optimized by the standard genetic algorithm and simulated annealing, the results of which indicate that the proposed model performs best in terms of prediction. Efficiently predicting and analyzing the housing prices will help the government promulgate effective policies for regulating the real estate market and protect home buyers.

A REVIEW OF THE METHODS OF ECONOMIC AND MATHEMATICAL MODELING BASED ON THE PRINCIPLES OF ECONOPHYSICS. PART 1

A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics is given. The first part gives the concept of a financial bubble and methods for their search. The review covers the period 2010-2019. A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of information systems and mathematical methods in Economics is given. The first part gives the concept of a financial bubble and methods for finding them. At the beginning of the article, the development of econophysics is given. Therefore, using the research of physicists as a model, econophysics should begin its research not from the upper floors of an economic building (in the form of financial markets, distribution of returns on financial assets, etc.), but from its fundamental foundations or, in the words of physicists, from elementary economic objects and forms of their movement (labor, its productivity, etc.). Only in this way can econophysics find its subject of study and become a "new form of economic theory". Further, the main prerequisites of financial bubble models in the market are considered: the principle of the absence of arbitrage opportunities, the existence of rational agents, a risk-driven model, and a price-driven model. A well-known nonlinear LPPL model (log periodic power law model) was proposed. In the works of V. O. Arbuzov, it was proposed to use procedures for selecting models. Namely, basic selection, "stationarity" filtering, and spectral analysis were introduced. The results of the model were presented in the works of D. Sornette and his students. The second part gives the concept of percolation and its application in Economics. We will consider a mathematical model proposed by J. P. Bouchaud, D. Stauffer, and D. Sornette that recreates the behavior of an agent in the market and their interaction, geometrically describing a phase transition of the second kind. In this model, the price of an asset in a single time interval changes in proportion to the difference between supply and demand in this market. The key situation to study is the moment of formation of an infinite cluster on the percolation grid, since this means the collapse of the market, when the overwhelming part of agents for this market has a similar opinion about their actions to buy or sell an asset. The main characteristics of the process are the threshold probability of market collapse, as well as the empirical distribution function of price changes in this market.

Real-time prediction of Bitcoin bubble crashes

In the past decade, Bitcoin as an emerging asset class has gained widespread public attention because of their extraordinary returns in phases of extreme price growth and their unpredictable massive crashes. We apply the log-periodic power law singularity (LPPLS) confidence indicator as a diagnostic tool for identifying bubbles using the daily data on Bitcoin price in the past two years. We find that the LPPLS confidence indicator based on the daily Bitcoin price data fails to provide effective warnings for detecting the bubbles when the Bitcoin price suffers from a large fluctuation in a short time, especially for positive bubbles. In order to diagnose the existence of bubbles and accurately predict the bubble crashes in the cryptocurrency market, this study proposes an adaptive multilevel time series detection methodology based on the LPPLS model and a finer (than daily) timescale for the Bitcoin price data. We adopt two levels of time series, 1 h and 30 min, to demonstrate the adaptive multilevel time series detection methodology. The results show that the LPPLS confidence indicator based on this new method is an outstanding instrument to effectively detect the bubbles and accurately forecast the bubble crashes, even if a bubble exists in a short time. In addition, we discover that the short-term LPPLS confidence indicator being highly sensitive to the extreme fluctuations of Bitcoin price can provide some useful insights into the bubble status on a shorter time scale – on a day to week scale, while the long-term LPPLS confidence indicator has a stable performance in terms of effectively monitoring the bubble status on a longer time scale – on a week to month scale. The adaptive multilevel time series detection methodology can provide real-time detection of bubbles and advanced forecast of crashes to warn of the imminent risk in not only the cryptocurrency market but also other financial markets.

A Systematic Review of the Bubble Dynamics of Cryptocurrency Prices

This paper surveys the academic literature concerning the formation of pricing bubbles in digital currency markets. Studies indicate that several bubble phases have taken place in Bitcoin prices, mostly during the years 2013 and 2017. Other digital currencies of primary importance, such as Ethereum and Litecoin, also exhibit several bubble phases. The Augmented Dickey Fuller (ADF) as well as the Log-Periodic Power Law (LPPL) methodology are the most frequently employed techniques for bubble detection and measurement. Based on much academic research, Bitcoin appears to have been in a bubble-phase since June 2015, while Ethereum, NEM, Stellar, Ripple, Litecoin and Dash have been denoted as possessing bubble-like characteristics since September 2015. However, this latter group possess little academic evidence supporting the presence of bubbles since early 2018. An overall perspective is provided based on a robust bibliography based on large deviations of market quotes from fundamental values that can serve as a guide to policymakers, academics and investors.

Dissection of Bitcoin's multiscale bubble history from January 2012 to February 2018.

We present a detailed bubble analysis of the Bitcoin to US Dollar price dynamics from January 2012 to February 2018. We introduce a robust automatic peak detection method that classifies price time series into periods of uninterrupted market growth (drawups) and regimes of uninterrupted market decrease (drawdowns). In combination with the Lagrange Regularization Method for detecting the beginning of a new market regime, we identify three major peaks and 10 additional smaller peaks, that have punctuated the dynamics of Bitcoin price during the analysed time period. We explain this classification of long and short bubbles by a number of quantitative metrics and graphs to understand the main socio-economic drivers behind the ascent of Bitcoin over this period. Then, a detailed analysis of the growing risks associated with the three long bubbles using the Log-Periodic Power-Law Singularity (LPPLS) model is based on the LPPLS Confidence Indicators, defined as the fraction of qualified fits of the LPPLS model over multiple time windows. Furthermore, for various fictitious ‘present’ times t2 before the crashes, we employ a clustering method to group the predicted critical times tc of the LPPLS fits over different time scales, where tc is the most probable time for the ending of the bubble. Each cluster is proposed as a plausible scenario for the subsequent Bitcoin price evolution. We present these predictions for the three long bubbles and the four short bubbles that our time scale of analysis was able to resolve. Overall, our predictive scheme provides useful information to warn of an imminent crash risk.

Are Bitcoin bubbles predictable? Combining a generalized Metcalfe's Law and the Log-Periodic Power Law Singularity model.

We develop a strong diagnostic for bubbles and crashes in Bitcoin, by analysing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfe’s Law based on network properties, a fundamental value is quantified and shown to be heavily exceeded, on at least four occasions, by bubbles that grow and burst. In these bubbles, we detect a universal super-exponential unsustainable growth. We model this universal pattern with the Log-Periodic Power Law Singularity (LPPLS) model, which parsimoniously captures diverse positive feedback phenomena, such as herding and imitation. The LPPLS model is shown to provide an ex ante warning of market instabilities, quantifying a high crash hazard and probabilistic bracket of the crash time consistent with the actual corrections; although, as always, the precise time and trigger (which straw breaks the camel’s back) is exogenous and unpredictable. Looking forward, our analysis identifies a substantial but not unprecedented overvaluation in the price of Bitcoin, suggesting many months of volatile sideways Bitcoin prices ahead (from the time of writing, March 2018).

Anticipating critical transitions of the housing market: new evidence from China

ABSTRACTWe introduce a novel quantitative methodology to detect real estate bubbles and forecast their critical end time, which we apply to the housing markets of China's metropolises. Building on the Log-Periodic Power Law Singularity (LPPLS) model of self-reinforcing feedback loops, we use the quantile regression calibration approach recently introduced by two of us to build confidence intervals and explore possible distinct scenarios. We propose to consolidate the quantile regressions into the arithmetic average of the quantile-based LPPLS Confidence indicator, which accounts for the robustness of the calibration with respect to bootstrapped residuals. We make three main contributions to the literature of real estate bubbles. First, we verify the validity of the arithmetic average of the quantile-based LPPLS Confidence indicator by studying the critical times of historical housing price bubbles in the U.S., Hong Kong, U.K. and Canada. Second, the LPPLS detection methods are applied to provide early warning signals of the housing markets in some metropolises in China. Third, we determine the possible turning points of the markets in Beijing, Shanghai, Shenzhen, Guangzhou, Tianjin and Chengdu and anticipate critical transitions of China's housing markets via our multi-scales and multi-quantiles analyses. Finally, given these projections performed in February 2017, the price trajectories from March 2017 to January 2018 that became available from the time of submission to the time of revision of the present article offer quite unique genuine out-of-sample tests of the performances of our indicators.

Comparing the Supremum Augmented Dickey Fuller and Log Periodic Power Law Frameworks for Identifying Bubbles

Comparing the Supremum Augmented Dickey Fuller and Log Periodic Power Law Frameworks for Identifying Bubbles

Cryptocurrencies as financial bubbles: The case of Bitcoin

We study bubble behavior in Bitcoin prices during the years 2016 to 2018 based on two distinct testing methodologies. The Phillips et al. (2015) PSY methodology is used to identify multiple bubble periods. The log-periodic power law (LPPL) approach by Filimonov and Sornette (2013) identifies bubble growth and potential critical bubble termination times. Our results underline that bubble behavior is clearly a common and reoccurring characteristic of Bitcoin prices. A critical time point is identified to be December 6, 2017, after which neither approach provides evidence of ongoing bubble behavior.

China’s exchange rate regimes revisited and bubble detection in 2005-2015

The International Monetary Fund’s decision in 2015 to add the Renminbi to its Special Drawing Rights currency basket has in effect granted the Chinese Yuan the international reserve currency status. This study revisits China’s five exchange rate regimes in 2005-2015 and investigates the relationships among the currencies of the Chinese Yuan, the U.S. Dollar and the Euro. The Log-Periodic Power Law Singularity model is proposed as a generic parameterization to capture the super-exponential behavior in the tetrad of exchange rates of these currency pairs. The transient non-sustainable faster-than-exponential acceleration of the “CNY against USD” from August 2005 to July 2008 suggests the existence of an apparent bubble with an under-valuation. The clustered signals of LPPLS Confidence indicators for the “CNY against USD” from May 2011 to March 2012 suggest the termination of its long-term growth. The signals for the “EUR against USD” and “CNY against EUR” emerging from January 2014 to August 2015 show a tightly coupled relationship among these currency pairs. Moreover, the empirical estimates of the most possible critical time by the standard Ordinary Least Squares method and the Quantile Regression method for the time series of “CNY against USD” tends to be later than that of “CNY against EUR” in the five regimes.

Forecasting Financial Crashes: Revisit to Log-Periodic Power Law

We aim to provide an algorithm to predict the distribution of the critical times of financial bubbles employing a log-periodic power law. Our approach consists of a constrained genetic algorithm and an improved price gyration method, which generates an initial population of parameters using historical data for the genetic algorithm. The key enhancements of price gyration algorithm are (i) different window sizes for peak detection and (ii) a distance-based weighting approach for peak selection. Our results show a significant improvement in the prediction of financial crashes. The diagnostic analysis further demonstrates the accuracy, efficiency, and stability of our predictions.

The bubble and anti-bubble risk resistance analysis on the metal futures in China

This paper investigates the risk resistance ability of China’s metal futures before and after the financial crises in 2008 and 2015. The log periodic power law singularity (LPPLS) model is utilized to measure the financial bubble and anti-bubble during these periods. In addition, the risk resistance ability is quantitatively measured by the two derived parameters in the model. They control the super-exponential growth of price and describe the log-periodic acceleration of volatility, respectively. Further, we select the Shanghai Zinc (SZ) futures and the Shanghai Aluminum (SA) futures in Shanghai Futures Exchange as the objectives to empirically study their risk resistance ability during the above mentioned periods. Then, some interesting findings are concluded as follows: (1) For the China’s metal futures, the bubble risks last longer than the anti-bubble risks before and after the two financial crises. (2) The China’s metal futures have risk resistance ability in anti-bubble, but the ability is relatively weaker in bubble before and after the two financial crises. (3) The LPPLS model can efficiently predict and measure the bubble and anti-bubble of the financial products. It also gives us an access to observe the risk resistance ability of financial products by the derived parameters.

Testing for the burst of bubbles in dry bulk shipping market using log periodic power law model

Purpose The occurrence and unpredictability of speculative bubbles on financial markets, and their accompanying crashes, have confounded economists and economic historians worldwide. The purpose of this paper is to diagnose and detect the bursting of shipping bubbles ex ante, and to qualify the patterns of shipping price dynamics and the bubble mechanics, so that appropriate counter measures can be taken in advance to reduce side effects arising from bubbles. Design/methodology/approach Log periodic power law (LPPL) model, developed in the past decade, is used to detect large market falls or “crashes” through modeling of the shipping price dynamics on a selection of three historical shipping bubbles over the period of 1985 to 2016. The method is based on a nonlinear least squares estimation that yields predictions of the most probable time of the regime switching. Findings It could be concluded that predictions by the LPPL model are quite dependent on the time at which they are conducted. Interestingly, the LPPL model could have predicted the substantial fall in the Baltic Dry Index during the recent global downturn, but not all crashes in the past. It is also found that the key ingredient that sets off an unsustainable growth process for shipping prices is the positive feedback. When the positive feedback starts, the burst of bubbles in shipping would be influenced by both endogenous and exogenous factors, which are crucial for the advanced warning of the market conversion. Originality/value The LPPL model has been first applied into the dry bulk shipping market to test a couple of shipping bubbles. The authors not only assess the predictability and robustness of the LPPL model but also expand the understanding of the model and explain patterns of shipping price dynamics and bubble mechanics.

Modeling of Bubbles and Crashes with Log-Periodic Functions - The Bitcoin Case Study

This paper applies the log-periodic power law model to study the recent boom and bust episode of Bitcoin. We find that the parameter estimates for the model before the crash are quite unstable over time and across estimation windows. We argue that this lack of stability in the parameter estimates provides little support for the model’s applicability in the case of Bitcoins.

Dissection of Bitcoin's Multiscale Bubble History

We present a detailed bubble analysis of the Bitcoin to US Dollar price dynamics from January 2012 to February 2018. We introduce a robust automatic peak detection method that classifies price time series into periods of uninterrupted market growth (drawups) and regimes of uninterrupted market decrease (drawdowns). In combination with the Lagrange Regularisation Method for detecting the beginning of a new market regime, we identify 3 major peaks and 10 additional smaller peaks, that have punctuated the dynamics of Bitcoin price during the analyzed time period. We explain this classification of long and short bubbles by a number of quantitative metrics and graphs to understand the main socio-economic drivers behind the ascent of Bitcoin over this period. Then, a detailed analysis of the growing risks associated with the three long bubbles using the Log-Periodic Power Law Singularity (LPPLS) model is based on the LPPLS Confidence Indicators, defined as the fraction of qualified fits of the LPPLS model over multiple time windows. Furthermore, for various fictitious present analysis times t2, positioned in advance to bubble crashes, we employ a clustering method to group LPPLS fits over different time scales and the predicted critical times tc (the most probable time for the start of the crash ending the bubble). Each cluster is argued to provide a plausible scenario for the subsequent Bitcoin price evolution. We present these predictions for the three long bubbles and the four short bubbles that our time scale of analysis was able to resolve. Overall, our predictive scheme provides useful information to warn of an imminent crash risk.

The prediction of oil price turning points with log-periodic power law and multi-population genetic algorithm

The turning points in international oil price are the most significant and sudden corrections in prices in the world market. Accurate prediction of turning points can help governments and enterprises develop effective oil reserve strategies and economic decisions. Nevertheless, forecasting the turning points poses great challenges in both methodology and computational effort. Log-periodic power law (LPPL) is one state-of-the-art method to predict turning points. In this research, we propose an improved version of LPPL forecasting model by incorporating a method called multi-population genetic algorithm (MPGA) to search for optimal values of parameters in the LPPL model. By doing so, the improved LPPL model provided significantly superior performance in predicting the turning points compared to prior researches. To verify the quality of the improved LPPL model, we collected the data of WTI spot price in the period starting from April 2003 to November 2016 and used the improved LPPL model to predict the three turning points in this period based on the data prior to the turning points. In addition, we compared the improved LPPL model with three LPPL models that use other approaches to search for parameters, including simulated annealing, standard genetic and particle swarm optimization. We showed that the results from our LPPL model are superior to other three search approaches. We also concluded that the fluctuation of the WTI (West Texas Intermediate) spot price in March 2017 is a false alarm of a major turning point. The improved LPPL has great potential to predict future turning points.

A comparative study by using two different log-periodic power laws on acoustic emission signals from LiF specimens under compression

Abstract The deformation of solid materials up to the point of fracture is followed by acoustic emission (AE) signals. The cumulative acoustic energy released during such a process seems to generally follow a power law form, which is compatible with the view that the fracturing process is a phenomenon with developing critical dynamics. In the present work, the cumulative energy released by the AE signals emitted during the deformation of LiF samples has been calculated and fitted by two different fitting functions, which are both power laws decorated with log-periodic corrections. The comparison of the produced results would lead to the conclusion of whether each one of the two equations can produce valid acoustic energy release modeling, which can describe the fracturing procedure of solid materials and its underlying mechanics. It should be noted that one of the models managed to fit the experimental data more accurately in the majority of the cases studied. We show that both of the studied log-periodic models managed to acceptably fit the data, which means that this field of study could possible lead to new methods of predicting the time point of a material’s failure. In conclusion, this comparative study reveals that these models could be a valuable tool in cases of monitoring materials or structures being under load at the region of their mechanical tolerance.

Predicting financial market crashes using ghost singularities.

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of ‘ghosts of finite-time singularities’ is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts.