At this stage, it is common knowledge that cryptocurrency prices are indeed, a bubble. However, does modern-day finance have the tools to detect explosive behaviour in absence of a fundamental value?
Glad to have worked with Shane Jose to release a paper in a bid to answer the aforementioned question!
Stochastic computation graphs provide a framework for automatically deriving unbiased gradient estimators. They generalize backpropagation to deal with random variables by treating the computation graph as a DAG with both deterministic and stochastic nodes. This allows gradients to be computed through expectations, enabling techniques like policy gradients for reinforcement learning and variational inference. The document describes several policy gradient methods that use stochastic computation graphs to compute gradients, including SVG(0), SVG(1), and DDPG. These methods have been successfully applied to robotics tasks and driving.
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This document introduces new epidemiological measures for multilevel studies, including the median risk ratio, median hazard ratio, and median beta. It begins with an introduction and overview of intraclass correlation coefficients and variance partition coefficients. It then provides formulas for calculating the new measures based on binomial, Poisson, and Cox proportional hazards multilevel models. Examples are shown using real data on breast cancer and families to demonstrate how to compute and interpret the median odds ratio, median risk ratio, and median hazard ratio. The document concludes by discussing applications of the new measures to other data types like count and survival data.
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International Journal of Computational Science and Information Technology (...ijcsity
International Journal of Computational Science and Information Technology (IJCSITY) focuses on Complex systems, information and computation using mathematics and engineering techniques. This is an open access peer-reviewed journal will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the area of Computation theory and applications. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and advancement in the area of advanced Computation and its applications
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In this work, a Chaotic based Pteropus algorithm (CPA) has been proposed for solving optimal reactive power problem. Pteropus algorithm imitates deeds of the Pteropus. Normally Pteropus while flying it avoid obstacles by using sonar echoes, particularly utilize time delay. To the original Pteropus algorithm chaotic disturbance has been applied and the optimal capability of the algorithm has been improved in search of global solution. In order to augment the population diversity and prevent early convergence, adaptively chaotic disturbance is added at the time of stagnation. Furthermore, exploration and exploitation capability of the proposed algorithm has been improved. Proposed CPA technique has been tested in standard IEEE 14,300 bus systems & real power loss has been considerably reduced.
This document presents distributed algorithms for k-truss decomposition of large graphs. It begins with introducing the problem of k-truss decomposition and definitions. It then describes how k-truss decomposition can be performed using traditional sequential algorithms. It proposes two distributed algorithms: MRTruss, which uses MapReduce but has limitations; and i-MRTruss, an improved version that aims to address the issues with MRTruss. The document outlines the different sections that will evaluate these distributed algorithms and experimentally analyze their performance.
This document discusses analyzing time-series data using a case-crossover study design and conditional logistic regression. It begins with concepts of individual versus population risk, the case-crossover design which uses a subject's other time periods as controls, and how the data structure changes. It then reviews basic linear regression, logistic regression, and conditional logistic regression. Finally, it discusses practical issues and demonstrates using the season package in R to conduct case-crossover analyses and conditional logistic regression.
A new transformation into State Transition Algorithm for finding the global m...Michael_Chou
To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization
problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of
numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.
Stochastic computation graphs provide a framework for automatically deriving unbiased gradient estimators. They generalize backpropagation to deal with random variables by treating the computation graph as a DAG with both deterministic and stochastic nodes. This allows gradients to be computed through expectations, enabling techniques like policy gradients for reinforcement learning and variational inference. The document describes several policy gradient methods that use stochastic computation graphs to compute gradients, including SVG(0), SVG(1), and DDPG. These methods have been successfully applied to robotics tasks and driving.
New Epidemiologic Measures in Multilevel Study: Median Risk Ratio, Median Haz...Jinseob Kim
This document introduces new epidemiological measures for multilevel studies, including the median risk ratio, median hazard ratio, and median beta. It begins with an introduction and overview of intraclass correlation coefficients and variance partition coefficients. It then provides formulas for calculating the new measures based on binomial, Poisson, and Cox proportional hazards multilevel models. Examples are shown using real data on breast cancer and families to demonstrate how to compute and interpret the median odds ratio, median risk ratio, and median hazard ratio. The document concludes by discussing applications of the new measures to other data types like count and survival data.
Cost versus distance_in_the_traveling_sa_79149olimpica
The document analyzes solutions to the Traveling Salesman Problem (TSP) on a 532-city instance using five local search heuristics. It finds that lower-cost solutions tend to be closer to the optimal tour and to other good solutions, supporting the idea that TSP solution spaces have a "globally convex" or "big valley" structure. The optimal tour is located near the center of the main cluster of good solutions.
International Journal of Computational Science and Information Technology (...ijcsity
International Journal of Computational Science and Information Technology (IJCSITY) focuses on Complex systems, information and computation using mathematics and engineering techniques. This is an open access peer-reviewed journal will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the area of Computation theory and applications. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and advancement in the area of advanced Computation and its applications
Chaotic based Pteropus algorithm for solving optimal reactive power problemIJAAS Team
In this work, a Chaotic based Pteropus algorithm (CPA) has been proposed for solving optimal reactive power problem. Pteropus algorithm imitates deeds of the Pteropus. Normally Pteropus while flying it avoid obstacles by using sonar echoes, particularly utilize time delay. To the original Pteropus algorithm chaotic disturbance has been applied and the optimal capability of the algorithm has been improved in search of global solution. In order to augment the population diversity and prevent early convergence, adaptively chaotic disturbance is added at the time of stagnation. Furthermore, exploration and exploitation capability of the proposed algorithm has been improved. Proposed CPA technique has been tested in standard IEEE 14,300 bus systems & real power loss has been considerably reduced.
This document presents distributed algorithms for k-truss decomposition of large graphs. It begins with introducing the problem of k-truss decomposition and definitions. It then describes how k-truss decomposition can be performed using traditional sequential algorithms. It proposes two distributed algorithms: MRTruss, which uses MapReduce but has limitations; and i-MRTruss, an improved version that aims to address the issues with MRTruss. The document outlines the different sections that will evaluate these distributed algorithms and experimentally analyze their performance.
This document discusses analyzing time-series data using a case-crossover study design and conditional logistic regression. It begins with concepts of individual versus population risk, the case-crossover design which uses a subject's other time periods as controls, and how the data structure changes. It then reviews basic linear regression, logistic regression, and conditional logistic regression. Finally, it discusses practical issues and demonstrates using the season package in R to conduct case-crossover analyses and conditional logistic regression.
A new transformation into State Transition Algorithm for finding the global m...Michael_Chou
To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization
problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of
numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.
The document discusses complex models for analyzing random variables using fractional moments and complex Hurst exponents. It begins with background on variance, covariance, and Hurst exponents. It then explains how complex Hurst exponents allow calculating fractional moments and higher-order information to better analyze relationships between variables. Applications discussed include analyzing gas emissions in coal mines, vegetation changes over time using NDVI maps, stock market fluctuations, and autonomous vehicle networks. Several academic papers and theses utilizing these complex models are also summarized.
This document discusses smoothed particle hydrodynamics (SPH), a Lagrangian numerical method for simulating fluid flows. SPH uses discrete particles that move with the fluid and sample hydrodynamic properties by averaging values over neighboring particles. The document outlines the basic concepts of SPH, including how it approximates continuous fields with discrete particles and calculates spatial derivatives. It also discusses how SPH can be used to model astrophysical phenomena through numerical simulations since laboratory experiments are often impossible at astrophysical scales.
ders 3.3 Unit root testing section 3 .pptxErgin Akalpler
The document discusses various unit root tests used to determine if a time series is stationary or non-stationary. It describes the Dickey-Fuller test and Augmented Dickey-Fuller test, which test for a unit root in a time series. The Augmented Dickey-Fuller test extends the Dickey-Fuller test by including lagged difference terms to account for autocorrelation. The tests are used to distinguish between trend-stationary and difference-stationary processes, which have different implications for forecasting and detecting spurious relationships between variables.
This document is a thesis that examines potential cointegration among biotech stocks. It begins with an introduction that provides background on cointegration and discusses how little is known about cointegration of individual stocks. The document then reviews relevant theoretical frameworks for unit root testing and cointegration testing. It also discusses characteristics of biotech stocks and criteria for stock valuation. The empirical analysis will apply unit root and cointegration tests to selected biotech stock data. The results may provide insights into whether these stocks share a common stochastic trend.
Efficient steganography techniques are needed for the security of digital information over the Internet and for secret data communication. Therefore, many techniques are proposed for steganography. One of these intelligent techniques is Particle Swarm Optimization (PSO) algorithm. Recently, many modifications are made to Standard PSO (SPSO) such as Human-Based Particle Swarm Optimization (HPSO). Therefore, this paper presents image steganography using HPSO in order to find best locations in image cover to hide text secret message. Then, a comparison is done between image steganography using PSO and using HPSO. Experimental results on six (256×256) cover images and different size of secret massages, prove that the performance of the proposed image steganography using HPSO has been improved in comparison with using SPSO.
OPTIMAL GLOBAL THRESHOLD ESTIMATION USING STATISTICAL CHANGE-POINT DETECTIONsipij
Aim of this paper is reformulation of global image thresholding problem as a well-founded statistical
method known as change-point detection (CPD) problem. Our proposed CPD thresholding algorithm does
not assume any prior statistical distribution of background and object grey levels. Further, this method is
less influenced by an outlier due to our judicious derivation of a robust criterion function depending on
Kullback-Leibler (KL) divergence measure. Experimental result shows efficacy of proposed method
compared to other popular methods available for global image thresholding. In this paper we also propose
a performance criterion for comparison of thresholding algorithms. This performance criteria does not
depend on any ground truth image. We have used this performance criterion to compare the results of
proposed thresholding algorithm with most cited global thresholding algorithms in the literature.
This document provides a summary of a presentation on applications of complex models for analyzing variance, covariance, and their use in autonomous vehicles. Some key points:
- Complex models allow calculating fractional moments and Hurst indexes with complex values, providing more information than real values alone.
- These techniques can be applied in various industries like engineering, agriculture, finance, research, and more.
- Autonomous buses use multiple sensor systems at different distances to gradually slow down as objects are detected.
- Complex fractional models have been used to predict gas emissions and analyze vegetation indexes over time. Stock market analysis and network anomaly detection were also mentioned.
The document describes a study that uses fuzzy logic to predict porosity from well log data. It discusses (1) normalizing the input data, (2) using subtractive clustering to identify clusters and membership functions, and (3) developing fuzzy rules with Gaussian membership functions to relate inputs like density, sonic, and neutron logs to the output of porosity. The results showed fuzzy logic predictions of porosity were more accurate than those from multiple linear regression on the same well log data.
Historical Simulation with Component Weight and Ghosted Scenariossimonliuxinyi
This document proposes two strategies to improve historical simulation (HS) for calculating Value-at-Risk (VaR): 1) A "ghosted scenario" approach that doubles the number of scenarios by treating the reflection of each historical return as a separate scenario. 2) A two-component EWMA scheme that assigns different weights to recent vs. older scenarios to balance response speed and use of historical data. The strategies aim to address deficiencies in HS like under-responsiveness to recent events and issues with insufficient data. An integrated approach combining ghosted scenarios and the two-component EWMA is presented as improving HS while imposing only minor additional computational costs.
Firefly Algorithm, Stochastic Test Functions and Design OptimisationXin-She Yang
This document describes the Firefly Algorithm, a metaheuristic optimization algorithm inspired by the flashing behavior of fireflies. It summarizes the main concepts of the algorithm, including how firefly attractiveness varies with distance, and provides pseudocode for the algorithm. It also introduces some new test functions with singularities or stochastic components that can be used to validate optimization algorithms. As an example application, the Firefly Algorithm is used to find the optimal solution to a pressure vessel design problem.
This document discusses testing the normality assumption of log-returns for stock prices. It summarizes that the Black-Scholes model, widely used in pricing derivatives, assumes log-returns are normally distributed. The author tests this assumption on over 1000 company stock prices from the Nasdaq composite index using Kolmogorov-Smirnov, Shapiro-Wilk, and Anderson-Darling goodness-of-fit tests for normality with daily, weekly, and monthly price data from 2000-2011.
DETECTION OF RELIABLE SOFTWARE USING SPRT ON TIME DOMAIN DATAIJCSEA Journal
In Classical Hypothesis testing volumes of data is to be collected and then the conclusions are drawn which may take more time. But, Sequential Analysis of statistical science could be adopted in order to decide upon the reliable / unreliable of the developed software very quickly. The procedure adopted for this is, Sequential Probability Ratio Test (SPRT). In the present paper we proposed the performance of SPRT on Time domain data using Weibull model and analyzed the results by applying on 5 data sets. The parameters are estimated using Maximum Likelihood Estimation.
Identification of Outliersin Time Series Data via Simulation Studyiosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Optimal Estimations of Photometric Redshifts and SED Fitting Parametersjulia avez
This document discusses optimizing photometric redshift and spectral energy distribution (SED) fitting parameters from galaxy data. The researcher compares photometric redshift values from the EAZY code to spectroscopic redshift data from NASA to improve photometric redshift estimates. Gaussian fitting is used to model redshift probability distributions, with the best results found using a "golden sample" of 585 galaxies meeting signal-to-noise criteria in at least 13 bands.
This document describes algorithms for detecting single radio pulses in real-time using graphics processing units (GPUs). It presents two new algorithms that use incomplete sets of boxcar filters to detect pulses at accelerated speeds with minimal signal loss. The algorithms were tested on simulated data and were found to process data 266-500 times faster than real-time on GPUs, detecting pulses with a mean 7% reduction in signal power.
This document presents a method for comparing the degree of short-circuiting in different reactor types called the "distance method". It uses residence time distribution curves and 13 short-circuiting indexes to compare an experimental high rate pond (HRP) and continuous stirred-tank reactor (CSTR). The results show some short-circuiting in the HRP based on the tracer appearance time and peak time. The distance method calculates the distances between experimental reactors and ideal reactors for each index, quantifying the degree of short-circuiting. This allows for comparison between different reactor types. The study aims to develop a simple, practical method to make such comparisons possible.
Application of smooth transition autoregressive (star) models for exchange rateAlexander Decker
This document discusses applying Smooth Transition Autoregressive (STAR) models to analyze exchange rate data. Specifically, it evaluates the suitability of Logistic STAR (LSTAR) and Exponential STAR (ESTAR) models. The document outlines the methodology for testing whether exchange rate data exhibits linear or nonlinear properties. It describes testing procedures that involve estimating an auxiliary regression model based on a Taylor series expansion to detect nonlinear behavior. The study applies these LSTAR and ESTAR models to exchange rate data to determine which model provides a better fit and explanation of deviations from the mean exchange rate. The document concludes that an ESTAR model provides the best adjustment for the analyzed exchange rate data series.
Garch Models in Value-At-Risk Estimation for REITIJERDJOURNAL
Abstract:- In this study we investigate volatility forecasting of REIT, from January 03, 2007 to November 18, 2016, using four GARCH models (GARCH, EGARCH, GARCH-GJR and APARCH). We examine the performance of these GARCH-type models respectively and backtesting procedures are also conducted to analyze the model adequacy. The empirical results display that when we take estimation of volatility in REIT into account, the EGARCH model, the GARCH-GJR model, and the APARCH model are adequate. Among all these models, GARCH-GJR model especially outperforms others.
This document summarizes a research paper that proposes using a two-step sequential probability ratio test (SPRT) approach to analyze software reliability growth model (SRGM) data. Specifically, it applies the approach to the Half Logistic Software Reliability Growth Model (HLSRGM). The SPRT approach allows drawing conclusions about software reliability from sequential or continuous monitoring of failure data, potentially reaching conclusions more quickly than traditional hypothesis testing. Equations are provided for determining acceptance, rejection, and continuation regions based on comparing observed failure counts to lines derived from the HLSRGM mean value function. The approach is applied to five sets of existing software failure data to analyze results.
This paper proposes combining a bottom-up visual pedestrian detector with a top-down fuzzy logic reasoning framework to improve detection performance. The bottom-up detector uses corner features and data mining to identify pedestrians. The top-down framework takes detector outputs as logical facts and applies fuzzy logic rules to associate detections with a confidence level. Detections with lower confidence are removed, adding global constraints. The approach demonstrates increased detection performance over using either method alone on a challenging dataset.
Fabular Frames and the Four Ratio ProblemMajid Iqbal
Digital, interactive art showing the struggle of a society in providing for its present population while also saving planetary resources for future generations. Spread across several frames, the art is actually the rendering of real and speculative data. The stereographic projections change shape in response to prompts and provocations. Visitors interact with the model through speculative statements about how to increase savings across communities, regions, ecosystems and environments. Their fabulations combined with random noise, i.e. factors beyond control, have a dramatic effect on the societal transition. Things get better. Things get worse. The aim is to give visitors a new grasp and feel of the ongoing struggles in democracies around the world.
Stunning art in the small multiples format brings out the spatiotemporal nature of societal transitions, against backdrop issues such as energy, housing, waste, farmland and forest. In each frame we see hopeful and frightful interplays between spending and saving. Problems emerge when one of the two parts of the existential anaglyph rapidly shrinks like Arctic ice, as factors cross thresholds. Ecological wealth and intergenerational equity areFour at stake. Not enough spending could mean economic stress, social unrest and political conflict. Not enough saving and there will be climate breakdown and ‘bankruptcy’. So where does speculative design start and the gambling and betting end? Behind each fabular frame is a four ratio problem. Each ratio reflects the level of sacrifice and self-restraint a society is willing to accept, against promises of prosperity and freedom. Some values seem to stabilise a frame while others cause collapse. Get the ratios right and we can have it all. Get them wrong and things get more desperate.
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The document discusses complex models for analyzing random variables using fractional moments and complex Hurst exponents. It begins with background on variance, covariance, and Hurst exponents. It then explains how complex Hurst exponents allow calculating fractional moments and higher-order information to better analyze relationships between variables. Applications discussed include analyzing gas emissions in coal mines, vegetation changes over time using NDVI maps, stock market fluctuations, and autonomous vehicle networks. Several academic papers and theses utilizing these complex models are also summarized.
This document discusses smoothed particle hydrodynamics (SPH), a Lagrangian numerical method for simulating fluid flows. SPH uses discrete particles that move with the fluid and sample hydrodynamic properties by averaging values over neighboring particles. The document outlines the basic concepts of SPH, including how it approximates continuous fields with discrete particles and calculates spatial derivatives. It also discusses how SPH can be used to model astrophysical phenomena through numerical simulations since laboratory experiments are often impossible at astrophysical scales.
ders 3.3 Unit root testing section 3 .pptxErgin Akalpler
The document discusses various unit root tests used to determine if a time series is stationary or non-stationary. It describes the Dickey-Fuller test and Augmented Dickey-Fuller test, which test for a unit root in a time series. The Augmented Dickey-Fuller test extends the Dickey-Fuller test by including lagged difference terms to account for autocorrelation. The tests are used to distinguish between trend-stationary and difference-stationary processes, which have different implications for forecasting and detecting spurious relationships between variables.
This document is a thesis that examines potential cointegration among biotech stocks. It begins with an introduction that provides background on cointegration and discusses how little is known about cointegration of individual stocks. The document then reviews relevant theoretical frameworks for unit root testing and cointegration testing. It also discusses characteristics of biotech stocks and criteria for stock valuation. The empirical analysis will apply unit root and cointegration tests to selected biotech stock data. The results may provide insights into whether these stocks share a common stochastic trend.
Efficient steganography techniques are needed for the security of digital information over the Internet and for secret data communication. Therefore, many techniques are proposed for steganography. One of these intelligent techniques is Particle Swarm Optimization (PSO) algorithm. Recently, many modifications are made to Standard PSO (SPSO) such as Human-Based Particle Swarm Optimization (HPSO). Therefore, this paper presents image steganography using HPSO in order to find best locations in image cover to hide text secret message. Then, a comparison is done between image steganography using PSO and using HPSO. Experimental results on six (256×256) cover images and different size of secret massages, prove that the performance of the proposed image steganography using HPSO has been improved in comparison with using SPSO.
OPTIMAL GLOBAL THRESHOLD ESTIMATION USING STATISTICAL CHANGE-POINT DETECTIONsipij
Aim of this paper is reformulation of global image thresholding problem as a well-founded statistical
method known as change-point detection (CPD) problem. Our proposed CPD thresholding algorithm does
not assume any prior statistical distribution of background and object grey levels. Further, this method is
less influenced by an outlier due to our judicious derivation of a robust criterion function depending on
Kullback-Leibler (KL) divergence measure. Experimental result shows efficacy of proposed method
compared to other popular methods available for global image thresholding. In this paper we also propose
a performance criterion for comparison of thresholding algorithms. This performance criteria does not
depend on any ground truth image. We have used this performance criterion to compare the results of
proposed thresholding algorithm with most cited global thresholding algorithms in the literature.
This document provides a summary of a presentation on applications of complex models for analyzing variance, covariance, and their use in autonomous vehicles. Some key points:
- Complex models allow calculating fractional moments and Hurst indexes with complex values, providing more information than real values alone.
- These techniques can be applied in various industries like engineering, agriculture, finance, research, and more.
- Autonomous buses use multiple sensor systems at different distances to gradually slow down as objects are detected.
- Complex fractional models have been used to predict gas emissions and analyze vegetation indexes over time. Stock market analysis and network anomaly detection were also mentioned.
The document describes a study that uses fuzzy logic to predict porosity from well log data. It discusses (1) normalizing the input data, (2) using subtractive clustering to identify clusters and membership functions, and (3) developing fuzzy rules with Gaussian membership functions to relate inputs like density, sonic, and neutron logs to the output of porosity. The results showed fuzzy logic predictions of porosity were more accurate than those from multiple linear regression on the same well log data.
Historical Simulation with Component Weight and Ghosted Scenariossimonliuxinyi
This document proposes two strategies to improve historical simulation (HS) for calculating Value-at-Risk (VaR): 1) A "ghosted scenario" approach that doubles the number of scenarios by treating the reflection of each historical return as a separate scenario. 2) A two-component EWMA scheme that assigns different weights to recent vs. older scenarios to balance response speed and use of historical data. The strategies aim to address deficiencies in HS like under-responsiveness to recent events and issues with insufficient data. An integrated approach combining ghosted scenarios and the two-component EWMA is presented as improving HS while imposing only minor additional computational costs.
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This document describes the Firefly Algorithm, a metaheuristic optimization algorithm inspired by the flashing behavior of fireflies. It summarizes the main concepts of the algorithm, including how firefly attractiveness varies with distance, and provides pseudocode for the algorithm. It also introduces some new test functions with singularities or stochastic components that can be used to validate optimization algorithms. As an example application, the Firefly Algorithm is used to find the optimal solution to a pressure vessel design problem.
This document discusses testing the normality assumption of log-returns for stock prices. It summarizes that the Black-Scholes model, widely used in pricing derivatives, assumes log-returns are normally distributed. The author tests this assumption on over 1000 company stock prices from the Nasdaq composite index using Kolmogorov-Smirnov, Shapiro-Wilk, and Anderson-Darling goodness-of-fit tests for normality with daily, weekly, and monthly price data from 2000-2011.
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In Classical Hypothesis testing volumes of data is to be collected and then the conclusions are drawn which may take more time. But, Sequential Analysis of statistical science could be adopted in order to decide upon the reliable / unreliable of the developed software very quickly. The procedure adopted for this is, Sequential Probability Ratio Test (SPRT). In the present paper we proposed the performance of SPRT on Time domain data using Weibull model and analyzed the results by applying on 5 data sets. The parameters are estimated using Maximum Likelihood Estimation.
Identification of Outliersin Time Series Data via Simulation Studyiosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
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This document presents a method for comparing the degree of short-circuiting in different reactor types called the "distance method". It uses residence time distribution curves and 13 short-circuiting indexes to compare an experimental high rate pond (HRP) and continuous stirred-tank reactor (CSTR). The results show some short-circuiting in the HRP based on the tracer appearance time and peak time. The distance method calculates the distances between experimental reactors and ideal reactors for each index, quantifying the degree of short-circuiting. This allows for comparison between different reactor types. The study aims to develop a simple, practical method to make such comparisons possible.
Application of smooth transition autoregressive (star) models for exchange rateAlexander Decker
This document discusses applying Smooth Transition Autoregressive (STAR) models to analyze exchange rate data. Specifically, it evaluates the suitability of Logistic STAR (LSTAR) and Exponential STAR (ESTAR) models. The document outlines the methodology for testing whether exchange rate data exhibits linear or nonlinear properties. It describes testing procedures that involve estimating an auxiliary regression model based on a Taylor series expansion to detect nonlinear behavior. The study applies these LSTAR and ESTAR models to exchange rate data to determine which model provides a better fit and explanation of deviations from the mean exchange rate. The document concludes that an ESTAR model provides the best adjustment for the analyzed exchange rate data series.
Garch Models in Value-At-Risk Estimation for REITIJERDJOURNAL
Abstract:- In this study we investigate volatility forecasting of REIT, from January 03, 2007 to November 18, 2016, using four GARCH models (GARCH, EGARCH, GARCH-GJR and APARCH). We examine the performance of these GARCH-type models respectively and backtesting procedures are also conducted to analyze the model adequacy. The empirical results display that when we take estimation of volatility in REIT into account, the EGARCH model, the GARCH-GJR model, and the APARCH model are adequate. Among all these models, GARCH-GJR model especially outperforms others.
This document summarizes a research paper that proposes using a two-step sequential probability ratio test (SPRT) approach to analyze software reliability growth model (SRGM) data. Specifically, it applies the approach to the Half Logistic Software Reliability Growth Model (HLSRGM). The SPRT approach allows drawing conclusions about software reliability from sequential or continuous monitoring of failure data, potentially reaching conclusions more quickly than traditional hypothesis testing. Equations are provided for determining acceptance, rejection, and continuation regions based on comparing observed failure counts to lines derived from the HLSRGM mean value function. The approach is applied to five sets of existing software failure data to analyze results.
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Digital, interactive art showing the struggle of a society in providing for its present population while also saving planetary resources for future generations. Spread across several frames, the art is actually the rendering of real and speculative data. The stereographic projections change shape in response to prompts and provocations. Visitors interact with the model through speculative statements about how to increase savings across communities, regions, ecosystems and environments. Their fabulations combined with random noise, i.e. factors beyond control, have a dramatic effect on the societal transition. Things get better. Things get worse. The aim is to give visitors a new grasp and feel of the ongoing struggles in democracies around the world.
Stunning art in the small multiples format brings out the spatiotemporal nature of societal transitions, against backdrop issues such as energy, housing, waste, farmland and forest. In each frame we see hopeful and frightful interplays between spending and saving. Problems emerge when one of the two parts of the existential anaglyph rapidly shrinks like Arctic ice, as factors cross thresholds. Ecological wealth and intergenerational equity areFour at stake. Not enough spending could mean economic stress, social unrest and political conflict. Not enough saving and there will be climate breakdown and ‘bankruptcy’. So where does speculative design start and the gambling and betting end? Behind each fabular frame is a four ratio problem. Each ratio reflects the level of sacrifice and self-restraint a society is willing to accept, against promises of prosperity and freedom. Some values seem to stabilise a frame while others cause collapse. Get the ratios right and we can have it all. Get them wrong and things get more desperate.
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In World Expo 2010 Shanghai – the most visited Expo in the World History
https://www.britannica.com/event/Expo-Shanghai-2010
China’s official organizer of the Expo, CCPIT (China Council for the Promotion of International Trade https://en.ccpit.org/) has chosen Dr. Alyce Su as the Cover Person with Cover Story, in the Expo’s official magazine distributed throughout the Expo, showcasing China’s New Generation of Leaders to the World.
University of North Carolina at Charlotte degree offer diploma Transcripttscdzuip
办理美国UNCC毕业证书制作北卡大学夏洛特分校假文凭定制Q微168899991做UNCC留信网教留服认证海牙认证改UNCC成绩单GPA做UNCC假学位证假文凭高仿毕业证GRE代考如何申请北卡罗莱纳大学夏洛特分校University of North Carolina at Charlotte degree offer diploma Transcript
In a tight labour market, job-seekers gain bargaining power and leverage it into greater job quality—at least, that’s the conventional wisdom.
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"Does Foreign Direct Investment Negatively Affect Preservation of Culture in the Global South? Case Studies in Thailand and Cambodia."
Do elements of globalization, such as Foreign Direct Investment (FDI), negatively affect the ability of countries in the Global South to preserve their culture? This research aims to answer this question by employing a cross-sectional comparative case study analysis utilizing methods of difference. Thailand and Cambodia are compared as they are in the same region and have a similar culture. The metric of difference between Thailand and Cambodia is their ability to preserve their culture. This ability is operationalized by their respective attitudes towards FDI; Thailand imposes stringent regulations and limitations on FDI while Cambodia does not hesitate to accept most FDI and imposes fewer limitations. The evidence from this study suggests that FDI from globally influential countries with high gross domestic products (GDPs) (e.g. China, U.S.) challenges the ability of countries with lower GDPs (e.g. Cambodia) to protect their culture. Furthermore, the ability, or lack thereof, of the receiving countries to protect their culture is amplified by the existence and implementation of restrictive FDI policies imposed by their governments.
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South Dakota State University degree offer diploma Transcriptynfqplhm
办理美国SDSU毕业证书制作南达科他州立大学假文凭定制Q微168899991做SDSU留信网教留服认证海牙认证改SDSU成绩单GPA做SDSU假学位证假文凭高仿毕业证GRE代考如何申请南达科他州立大学South Dakota State University degree offer diploma Transcript
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Econometric Investigation into Cryptocurrency Price Bubbles in Bitcoin and Ethereum
1. Econometric Investigation into Cryptocurrency Price
Bubbles in Bitcoin and Ethereum
Siddharth Hitkari & Shane Jose
Trinity College, University of Dublin
April 2018
Abstract
This paper delves into testing bubble activity in Bitcoin and Ethereum prices as well as
linking these explosive responses to real-world events through a three-pronged model,
consisting of recursive, rolling and reverse recursive ADF tests. Rolling and reverse
recursive ADF models prove highly credible in detecting ‘irrational exuberance’. Ad-
ditionally, our results indicate a low degree of complementarity between Bitcoin and
Ethereum, which is often overstated due to sporadic events.
Keywords: Asset-price Bubbles; Cryptocurrency; Augmented Dickey-Fuller
1. Introduction
Nobel laureate in economics, Robert Shiller, remarked earlier this year that while Bitcoin
was a ‘really clever idea’, it would not become a permanent part of the financial world
(Monaghan, 2018). The wild swings in the prices of cryptocurrencies have been a matter
of much on-going academic deliberation and polarisation. Such incessant and intriguing
volatility forms the epicentre of the motivation for this paper wherein we aim to detect
cryptocurrency price bubbles in Bitcoin and Ethereum.
However, detecting bubbles in cryptocurrencies is particularly challenging given an ab-
sence of fundamental value which was empirically confirmed by Cheah and Fry (2015). This
implies that traditional asset-pricing approaches developed by West (1987), Diba and Gross-
man (1988) cannot be implemented. Furthermore, Evans’ (1991) critique highlights the
limitations of standard unit-root procedures in detecting periodically collapsing bubbles.
As a result, we follow right-tailed approaches of recursive and rolling ADF testing success-
fully developed by Phillips, Wu and Yu (2011) and Phillips, Shi and Yu (2013) respectively.
We supplement this approach with a right-tailed reverse recursive ADF test developed by
2. Andrews and Kim (2006) to test for end-of-sample bubble activity. The aforementioned tests
form the cornerstone of our model which is explained in Section 3, while Section 4 mentions
the empirical results which successfully detect explosiveness in Bitcoin and Ethereum. In
Section 5, we delve into the economic interpretation of our results and draw parallels with
real-world events to validate our findings, before concluding in Section 6.
2. Description of data set
Count Max Min Range Std.dev Variance Skewness Kurtosis
BTC 2807 9.87008 -2.99573 12.8658 2.92341 8.54634 -.694872 2.84611
ETH 962 7.23347 -.8675006 8.10097 2.245559 5.042536 .109551 1.878663
2011 2012 2013 2014 2015 2016 2017
0
5
10
Year
Price
(a) Bitcoin
2015 2016 2017 2018
0
2
4
6
8
Year
Price
(b) Ethereum
Fig. 1. Log-Price Trends
The sample period for Bitcoin price data is 19th July 2011 to 23rd March 2018, consist-
ing of 2807 daily observations. Similarly, the sample period for Ethereum price data is 6th
August 2015 to 23rd March 2018, consisting of 962 daily observations. Inconsistent pricing
across crypto-exchanges can be attributed to a highly speculative pricing mechanism cou-
pled with their non-stationary explosive behaviour. Bitcoin pricing varies across exchanges
on degrees of volatility, volumes of transactions as well as ‘infrastructural’ technicalities that
certain exchanges face (Pilani and Haselton, 2017). It is for this reason that the histori-
cal data extracted for both, Bitcoin and Ethereum, was a weighted average obtained from
BitcoinAverage.com.
In order to correct for skewness and accurately estimate results, we took the natural log
of the currency prices and linearized the time-series data. Doing so, additionally aided in
2
3. reducing the scaling dimension of these time-series trends through providing stricter con-
ditions. Intuitively, despite having reduced the range-scale, a high degree of volatility can
be observed in the short time intervals in both cases and this will be verified empirically,
subsequently in this paper.
3. Empirical Approach
3.1. Optimal Lag Selection
While too few lags would inadequately eliminate residual serial correlation, too many lags
could cause biases in the model coefficients through higher standard errors (Brooks, 2014).
Optimal lag-order selection was executed by extrapolating the number of optimal lags
for each of the ‘maximum-lag values’ chosen. The maximum-lag values arbitrarily belonged
to the set {5, 8, 12, 15, 20, 24}. For each of these 6 statistics, the optimal lags (lag∗
) were
compared across each information criterion (IC), AIC, HQIC and SBIC. Most ICs agreed on
the optimal-lag value for the log-prices of both cryptocurrencies.
The Hannah-Quinn Information Criterion (HQIC) remained consistent at lag∗
= 8 for
Bitcoin, and the Schwarz Bayesian Information Criterion (SBIC) did not deviate from lag∗
=
1 for Ethereum, regardless of the maximum-lag chosen. Furthermore, Ivanov and Kilian
(2005), provide evidence for the HQIC rendering the most accurate results (in comparison
to other ICs) for large sample sizes; while SBIC performs better for smaller sample sizes.
This conjecture is consistent with our datasets – 2807 time-series observations for Bitcoin
and 962 for Ethereum.
3.2. The Model
In order to detect explosive behaviour in Bitcoin and Ethereum prices, we adopt the
models previously successfully deployed by Phillips, Wu and Yu (2011) and Phillips, Shi and
Yu (2013). For each time series pt (log of Bitcoin/Ethereum prices), we apply the Augmented
Dickey-Fuller test for a unit-root (H0 : δ = 1) against the alternative of an explosive root
(H0 : δ > 1). We, then, estimate the following regression by OLS for expanding and rolling
windows:
pt = αp + δpt−1 +
Q
q=1
ωq∆pt−q + p,t, p,t ≈ iid(0, σ2
p) (1)
where Q is the number of optimal lags chosen and the error term, , is normally and
independently distributed.
3
4. 3.2.1. Unit-Root Testing
Taking into account the endogeneity of the regressor pt−1, standard unit root-root tests
like Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) allow for lags ∆pt to be
included as regressors1
.
The null hypothesis without drift is chosen as the true process by treating the time-
variable as exogenous (drift = 0) and by obtaining non-zero means of cryptocurrency log-
prices (signifying the presence of a constant in the regression).
3.2.2. Forward Recursive Augmented Dickey-Fuller Test
Phillips, Wu and Yu (2011) proposed a forward recursive method to detect exuberance in
asset price series during an inflationary phase which is especially effective in cases of a single
bubble episode in the sample data2
. They develop a reduced form right-tailed approach to
bubble detection which focuses on the mildly explosive (submartingale) behaviour captured
by the alternative hypothesis.
Phillips et al. (2011) develop a test that entails a forward expanding sequence of samples
with a pre-decided initial window size (r0). The starting point (r1) is fixed at 0 while the
endpoint of the sample (r2) increases (from r0) recursively by 1 observation until r2 is equal
to the entire sample size. The supremum ADF (SADF) statistic is the largest ADF statistic
obtained by conducting a forward recursive ADF test across all subsamples and is defined
as:
SADF(r0) = supr2∈[r0,1][ADFr2
0 ] (2)
Our selection of the initial window size (r0) at 10% of the sample size (2807) for BTC was
consistent with that of Phillips et al. (2011). Given the smaller sample set for ETH (962),
we decided to take a larger value (15%) for r0 in order to reliably detect explosive behaviour.
3.2.3. Rolling Augmented Dickey-Fuller Test
Phillips, Shi and Yu (2013) postulate that in cases where the sample period includes mul-
tiple episodes of exuberance and collapse, the SADF test may have low explanatory power.
The complex nonlinear structure of a bubble with multiple collapsing episodes coupled with
SADFs reliance on the initial sample size selected (Shi, 2010), increases the risk of a false
positive.
1
The PP test additionally redresses unidentified heteroskedasticity, but is less accurate than the ADF
test in finite datasets (Davidson and MacKinnon, 2004).
2
Phillips, Wu and Yu (2011) successfully applied the SADF approach on to NASDAQ prices in the 1990s
to detect explosive behaviour
4
5. Phillips et al. (2013) highlight that this weakness is more prominent in analyzing long
time series or rapidly changing market data, where more than one episode of exuberance
is suspected. To overcome this pitfall, they propose an alternative approach, Generalised
Supremum ADF (GSADF) test, by allowing the starting point of each subsample to change.
Similar to forward recursive ADF test in essence, rolling ADF test is built on the premise
that now both, the start (r1) and endpoints (r2), are not static. They expand in increments
(of one) such that a fixed-sized window of subsamples is rolled forward in each regression.
The GSADF statistic is the largest ADF statistic obtained by conducting the rolling ADF
test across all subsamples and is defined as:
GSADF(r0) = sup
r2∈[r0,1]
r1∈[0,r2−r0][ADFr2
r1
] (3)
3.2.4. Reverse Recursive Augmented Dickey-Fuller Test
According to Astill et al. (2016), the reverse (or ‘backward’) recursive ADF test has a
higher level of explanatory power in detecting an end-of-sample bubble as opposed to either
a forward or a rolling ADF. More importantly, this approach is robust to serial correlation
and conditional heteroskedasticity (Andrews and Kim, 2006).
This test is similar to the forward recursive in having a fixed initial window size (r0) and
repeatedly generating ADF statistical values for the corresponding regressions of every sub-
sample. However, we now fixate the endpoint (r2) of our sample and proceed by recursively
incrementing our start-point (r1) backwards until the entire sample has been included. This
is the Reverse SADF (RSADF) and is defined as:
RSADF(r0) = supr1∈[0,1−r0][ADFr
1
1] (4)
4. Empirical Results
The results from both, the ADF and PP tests, fail to reject the null hypothesis of a unit
root process. Intuitively, this makes sense as standard unit root procedures fail to detect
bubbles in the presence of multiple/collapsing bubbles due to mean-reversion issues (Evans,
1991).
Given the limitations of standard unit root procedures, we resort to conducting the
standard ADF on smaller subsamples through econometric approaches developed by Phillips,
Wu and Yu (2011) and Phillips Shi and Yu (2013). While the forward recursive ADF statistics
fail to reject the null hypothesis for Ethereum, they detect financial exuberance in Bitcoin
prices at the 95% level of significance.
5
6. Table 1: Test statistics for Log-Bitcoin Prices (Lags=8)
Test Test Statistic 1% C.V. 5% C.V. 10% C.V.
ADF 2.354 3.430 2.860 2.570
PP 2.046 3.430 2.860 2.570
Recursive ADF 2.873** 3.430 2.860 2.570
Rolling ADF 4.496*** 3.458 2.879 2.570
R-Recursive ADF 2.799* 3.458 2.879 2.570
***
p < 0.01, **
p < 0.05, *
p < 0.1
Table 2: Test statistics for Log-Ethereum Prices (Lags=1)
Test Test Statistic 1% C.V. 5% C.V. 10% C.V.
ADF 0.446 3.430 2.860 2.570
PP 0.102 3.430 2.860 2.570
Recursive ADF 2.270 3.430 2.860 2.570
Rolling ADF 6.432*** 3.495 2.877 2.577
R-Recursive ADF 3.496*** 3.495 2.877 2.577
***
p < 0.01, **
p < 0.05, *
p < 0.1
2011 2014 2017
0
1
2
3
Year
Recursive-ADFt-stat
(a) Recursive ADF (Ln-BTC)
99% C.I.
95% C.I.
90% C.I.
2011 2014 2017
0
2
4
Year
Rolling-ADFt-stat
(b) Rolling ADF (Ln-BTC)
99% C.I.
95% C.I.
90% C.I.
2011 2014 2017
0
1
2
3
Year
R-RADFt-stat
(c) R-Recursive ADF (Ln-BTC)
99% C.I.
95% C.I.
90% C.I.
Jan2016
Jun2016
Jan2017
Jun2017
Jan2018
0
1
2
Year
Recursive-ADFt-stat
(d) Recursive ADF (Ln-ETH)
99% C.I.
95% C.I.
90% C.I.
Jan2016
Jun2016
Jan2017
Jun2017
Jan2018
0
2
4
6
Year
Rolling-ADFt-stat
(e) Rolling ADF (Ln-ETH)
99% C.I.
95% C.I.
90% C.I.
Jan2016
Jun2016
Jan2017
Jun2017
Jan2018
0
1
2
3
Year
R-RADFt-stat
(f) R-Recursive ADF (Ln-ETH)
99% C.I.
95% C.I.
90% C.I.
Fig. 2. Time-Series Analysis on Bitcoin and Ethereum
6
7. Rolling ADF statistics, on the other hand, provide an even stronger evidence for bubble
activity in both, Bitcoin and Ethereum, at the 99% level of significance.
Interestingly, despite rejecting the null hypothesis, the rolling ADF test fails to capture
bubble formation towards the latter end of the sample. Contextually, this result is particu-
larly counter-intuitive given the meteoric rise in cryptocurrency prices and volatility in 2017.
Reverse recursive ADF statistics provide statistical evidence for the explosive behaviour in
Bitcoin and Ethereum but more importantly, this test captures end-of-sample instability in
both cryptocurrencies.
5. Analysis and Discussion
Historically3
, there have been 5 instances of major price shocks in Bitcoin (Roberts,
2018) dating back to the Chinese government’s decision to ban financial institutions’ usage
of Bitcoin in March 2013. Bitcoin’s price soared from $30 to $230 over the span of a few
months but collapsed by 71% in a single day during April 2013. Following this collapse,
Bitcoin prices recovered and rallied, witnessing a ten-fold rise to reach $1150 before tumbling
to less than $500 in December 2013. The closure of Mt. Gox (Bitcoin’s biggest exchange at
the time) in February 2014, on the account of hacking, caused another major sell-off wherein
Bitcoin prices dropped by 49% and this doldrums period lasted till 2016 (Roberts, 2018).
As graphically illustrated in Fig. 2(b), rolling ADF statistics exceed their respective critical
values to successfully detect these three bubbles.
Reverse recursive ADF statistics (Fig. 2(c)) capture not only Bitcoin’s crash by 68% in
June 2011 but also Bitcoin’s historical price run of 2017 – theoretically, linking it to the end-
of-sample price explosiveness. The reverse recursive ADF test successfully detects the year-
long persistent exuberance in Bitcoin which temporarily culminated in September 2017. This
was due to the Chinese government’s crackdown on ‘Initial Coin Offerings’ causing Bitcoin’s
price to plummet by 37%. Contextually, this crash was crucial in highlighting China’s de
facto monopoly in cryptocurrency mining (Roberts, 2018). Despite this relatively ‘minor’
blip, Fig. 2(c) effectively captures a steeper upward trend (after November 2017) followed
by a steep crash towards the end of 2017. This can be explained by Bitcoin prices flash
spiking from $2,000 to $20,000 on 7th December4
before nose-diving in January 2018 due to
a major sell-off discussed later in this section5
.
However, our findings fail to detect relatively smaller bubbles in Bitcoin prices such as the
3
Until December 2017
4
Prices rose by more than 900% in a 12-month period.
5
Roubini, who predicted the 2008 financial crisis, labels this event as “The Mother of all Bubbles and
Biggest Bubble in Human History”
7
8. summer sell-off of 2017. This can be rationalised through our selection of 280 observations as
the window size. While this is too large a window to capture smaller bubble activity, it elimi-
nates the possibility of falsely identifying explosive behaviour through seasonal idiosyncratic
price fluctuations.
Conversely, the rolling ADF test empirically detects wild swings in Ethereum prices
throughout 2016. The interpretation of this empirical data is consistent with the economic
narrative that Ethereum was trading at $21.50, a 2000% increase YTD6
in June 2016, when
attacks on ‘Distributed Autonomous Organisation7
’ caused the price to face heavy head-
winds. A relatively smaller window size of 144 observations allows us to detect more in-
stances of explosiveness in Ethereum prices. The biggest spike in the rolling ADF statistics
(see Fig. 2(e)) relates to the Thanksgiving hard forking – Ethereum network splitting into
two transaction histories – following which, the price hit a 9-month low in December 2016
(Bovaird, 2016).
Ethereum, according to Goldman Sachs, has dwarfed Bitcoin and Dutch tulipmania to
become the biggest bubble in history (Hargreaves, 2018). Ethereum’s stratospheric price
rise by over 2,300% in 2017 was halted by a flash-crash when it’s price plunged by 99.9%
within seconds on 22nd June 2017. The flash-crash was triggered by a multi-million dollar
sell order on GDAX (a leading Ethereum exchange) which executed 800 stop-loss orders,
thereby creating a domino effect (Williams-Grut, 2017). Both, rolling ADF and reverse
recursive ADF statistics (Fig. 2(e) and 2(f)), successfully detect the occurrence of this crash
and the precursive price explosiveness at the 99% significance level.
Ethereum prices dramatically escalated to $1000 in January 2018 after a Russian bank
(under Vladimir Putin’s tutelage) embraced blockchain technology through striking a deal8
with Ethereum CEO. This dramatic price rise, September 2017 onwards, was a classic exam-
ple of highly speculative Ethereum trading. As illustrated in Fig. 2(e), rolling ADF statistics
successfully detect this bubble behaviour across the aforementioned timespan (at the 99%
critical level).
After reaching all-time highs, Bitcoin and Ethereum prices experienced a series of troughs
in January 2018 following Facebook and Google’s decision to ban cryptocurrency advertise-
ments (Williams-Grut, 2018). While it is common for financial assets to show explosive
behaviour following major announcements, cryptocurrencies (due to an absence of funda-
mental value) are more erratic in their behaviour. Momentum and signalling effects play
a pivotal role in determining the demand (and in turn, prices) for cryptocurrencies. For
6
year-to-date
7
The DAO is aimed to develop an Ethereum-based vehicle through which other projects in the ecosystem
could be crowdfunded (Bovaird, 2016).
8
The deal led to the creation of ‘Ethereum Russia’ through Ethereum forking
8
9. instance, the rallying prices of Bitcoin and Ethereum, in late 2017, were driven by positive
expectations originating from favourable developments in South Korea/Japan and Russia
respectively. Rolling (for Bitcoin) and reverse recursive (for Ethereum) ADF statistics trace
a time-period which roughly coincides with the crash in both cryptocurrencies.
This raises a bigger question – do Bitcoin and Ethereum persistently exhibit correlated
trends? Our empirical results for the last bubble ostensibly suggest a correlation between
Bitcoin and Ethereum. Rather, this implies a spurious relationship and it would be a fallacy
to deduce a strong correlation between the two. Antonopoulos (2017) and Toren (2017) noted
that Bitcoin’s relationship with Ethereum, unlike other cryptocurrencies, is underlined by
the fundamental technological differences between the two. Antonopoulos further stated that
while Ethereum and Bitcoin compete indirectly in the short-run, they operate in segmented
markets and do not compete in the long-run. Independent and unassociated global events
might steer simultaneous price movements in Bitcoin and Ethereum temporarily. However,
it is crucial to highlight the existence of low complementarity between the two.
6. Conclusion
It is beyond an iota of doubt that Bitcoin, along with other cryptocurrencies, is a series
of giant bubbles which is destined to end in grief (Krugman, 2018). We followed the right-
tail ADF approaches of recursive, rolling and reverse recursive testing – all of which have
been extensively developed in literature to detect explosiveness. Through rolling and reverse
recursive ADF tests, we successfully detected and compared multiple collapsing and end-
of-sample bubbles respectively. This enabled us to rationalise meteoric runs of Bitcoin and
Ethereum in 2017 which were halted by major announcements. Contextually, our results
ascertained ‘irrational exuberance’ in both cryptocurrencies. This reiterates their highly
speculative behaviour wherein the aggressive price swings are even more pronounced due to
the absence of a fundamental value.
Interestingly, a reverse rolling ADF test could pose as a possible extension to empirically
investigating cryptocurrency bubbles. This could potentially serve as a single foolproof test
that could deliver robust results in detecting periodically collapsing as well as end-of-sample
bubbles.
Lastly, we emphasize the existence of low complementarity between Bitcoin and Ethereum
which can often be eclipsed in the wake of sporadic global shocks that affect all cryptocur-
rencies alike, albeit transiently.
9
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10