Time-varying Hurst Exponent Research Articles

한국 탄소배출권 시장의 효율성 분석

As the development of technologies that can reduce carbon emissions and the conversion of energy production methods have not produced particularly meaningful effects, major countries have high expectations for the effect of regulating the total amount of carbon emissions through the carbon emission market. Since Korea is a country that emits a lot of greenhouse gases, it operates a carbon emission market with a large transaction volume. For this market to show the expected effect, the movement of the emission permit price must be efficient. So this study analyzed whether the carbon emission market in Korea is efficient, comparing it with the European emission market. To this end, the time-varying Hurst exponent was measured using daily data of Korea's KAU and Europe's EUA Futures markets. The main results are summarized as follows. First, the degree of informational efficiency of the price movement of carbon emission market is time-varying. Second, in both the Korean and European carbon markets, transaction prices did not move randomly at many times, and there were many inefficient periods in both markets. Third, the long memory characteristics were stronger and the inefficiency was more severe in the KAU market than in the EUA market. Fourth, although the informational efficiency of KAU market has generally improved since 2022, it has not yet reached the level of efficiency implied by the efficient market hypothesis. These results mean that despite the government's efforts so far, the emission trading market is not functioning sufficiently. Therefore, it is necessary to continuously improve the emission trading system in a way that can reduce carbon emissions through the market function.

Measuring conditional correlation between financial markets' inefficiency

<abstract><p>Assuming that stock prices follow a multi-fractional Brownian motion, we estimated a time-varying Hurst exponent ($ h_t $). The Hurst value can be considered a relative volatility measure and has been recently used to estimate market inefficiency. Therefore, the Hurst exponent offers a level of comparison between theoretical and empirical market efficiency. Starting from this point of view, we adopted a multivariate conditional heteroskedastic approach for modeling inefficiency dynamics in various financial markets during the 2007 financial crisis, the COVID-19 pandemic and the Russo-Ukranian war. To empirically validate the analysis, we compared different stock markets in terms of conditional and unconditional correlations of dynamic inefficiency and investigated the predicted power of inefficiency measures through the Granger causality test.</p></abstract>

Fuzzy clustering of time series with time-varying memory

Little attention has been devoted to the long memory among the different data features considered for clustering time series. Following previous literature, we measure the long memory of a time series through the estimated Hurst exponent. However, we exploit the fact that a constant value for the Hurst exponent h is unrealistic in many practical examples. In this paper, assuming that the time series follows a multifractional Brownian motion, we estimate a time-varying Hurst exponent used as the input for a fuzzy clustering procedure. Motivated by the relevance of long memory in finance, the usefulness of the proposed clustering procedure is shown with an application to stock prices.

Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framework

In this study, we conduct a rolling window approach to wavelet-filtered (denoised) S&P500 returns (2000−2020) to obtain time-varying Hurst exponents. We discuss implications of Hurst exponent dynamics such as the complete invalidity of the efficient market hypothesis (EMH), an explicative rationale for momentum crashes and potentials for crises predictability. We analyse the dynamics of the Hurst exponents by applying a novel nonlinear dynamics analysis framework for non-stationary and nonlinear time series. The latter framework includes statistical tests, a recurrence quantification analysis (RQA), a wavelet multi-resolution analysis (MRA) and a multifractal detrended fluctuation analysis (MFDFA) paired with subsequent multifractal analyses. Besides, we display empirical findings taken out of the academic literature and critically elaborate on the impact of our findings and future prospects.

Multifractional Brownian motion characterization based on Hurst exponent estimation and statistical learning.

This paper proposes an approach for the estimation of a time-varying Hurst exponent to allow accurate identification of multifractional Brownian motion (MFBM). The contribution provides a prescription for how to deal with the MFBM measurement data to solve regression and classification problems. Theoretical studies are supplemented with computer simulations and real-world examples. Those prove that the procedure proposed in this paper outperforms the best-in-class algorithm.

Time series clustering based on time-varying Hurst exponent

We consider the problem of clustering time series which are assumed to possess the long term memory. We propose an approach based on combining the results obtained by applying different methods for estimating time-varying Hurst exponent and apply it to Euro exchange rates. Firstly, we fit AR-GARCH models to every time series to reduce bias of rescaled range analysis method. We only consider model with residuals, in which no autocorrelation and ARCH effect is present; among them we choose the model with the lowest value of the Bayesian information criterion. Afterwards, we estimate the Hurst exponent from the residuals by means of the rolling window approach using four different estimation methods. Vectors of Hurst exponents are clustered for each of the four cases and the clusters are compared in order to obtain the final clustering.

Frontier Markets, Liberalization and Informational Efficiency: Evidence from Vietnam

This paper examines the equity market opening in Vietnam, a frontier market that has taken gradual steps of relaxing capital control, by analysing whether liberalization policies in the period 2009–15 have had an impact on informational efficiency. We applied time-varying Hurst exponent during the liberalization period and tested Adaptive Market Hypothesis. The results confirm the role of foreign investors in improving the local market’s efficiency, however, the findings show that the liberalization does not always result in the increase of foreign participation, which then has a limited impact on the efficiency. The study also indicates the importance of governance policies, along with liberalization policies, in completing market structure and market dynamics, that promote equity price reflects truly firm’s intrinsic value.

Representativeness Heuristic in Stock Market: Measurement and Its Predictive Ability

ABSTRACT This paper measures representativeness heuristic by the irrational part of time-varying Hurst exponent, and empirically tests the validity of measurement including its predictive ability for one-month-ahead excess return in the Chinese stock market. Our preliminary analyses suggest that the representativeness heuristic is a “new” firm-specific characteristic and is possibly related (not consistent) with momentum. It confirms that the measurement of representativeness heuristic is valid. Further researches show that the representativeness heuristic has the predictive ability for one-month-ahead excess return. Meanwhile, multiple robustness tests are constructed to prove these results.

Hurst Dynamics of S&P500 Returns: Implications and Impact on Market Efficiency, Long Memory, Multifractality and Financial Crises Predictability

In this study, we apply a rolling window approach to wavelet-filtered (denoised) S&P500 returns (2000–2020) to obtain time varying Hurst exponents. We analyse the dynamics of the Hurst exponents by applying statistical tests (e.g., for stationarity, Gaussianity and self-similarity), a recurrence quantification analysis (RQA) and a wavelet multi-resolution analysis (MRA). Moreover, we discuss the implications of Hurst dynamics in terms of market efficiency, long memory, multifractal properties and financial crises predictability. Besides, we display academic literature by applying a bibliometric- and referring citation network analysis, state research streams and critically elaborate on the impact and future prospects.

Bayesian analysis of static and dynamic Hurst parameters under stochastic volatility

Despite the fact that the use of Hurst exponent is well-established, few attempts have been made to embed this parameter in a wider framework to account for stylized facts in stock returns. For example, fat tails and volatility clustering are well known to exist in financial time series, yet a comprehensive model involving the Hurst exponent is unavailable. In this paper, we generalize standard fractional Brownian motion to account for time-varying conditional heteroskedasticity when the Hurst parameter is static or, alternatively, when it also evolves over time, in which case we use a multi-fractional Brownian motion. The generalized model delivers persistence parameters for both time-varying volatility as well as time-varying Hurst exponents. In an application to Eurostoxx-50 (daily data for 1990–2018) we find that once we allow for time variation in the Hurst parameter, the persistence of conditional variances is substantially smaller. Model comparison shows that there are aspects introduced by the Hurst exponent that are not captured by stochastic volatility or other models with time-varying conditional variances. Log-predictive densities are used to compare different models out-of-sample.

Does Crude Oil Market Efficiency Improve After the Lift of the U.S. Export Ban? Evidence From Time-Varying Hurst Exponent

On 18 December 2015, the 40-year old U.S. crude oil export ban was repealed. Since then U.S. crude and oil producers were allowed to reach the global market. In this paper, we study if the crude oil market efficiency increases after the lift of the export ban via the Centered Detrending Moving average Analysis (CDMA) and the Detrended Fluctuation Analysis (DFA). We examine the time-varying market inefficiency from 2011 to 2020 with different rolling windows. The results indicate that WTI becomes inefficient after the lift in medium-term. Though in short and long-term, there is evidence for the improvement of the degree of market efficiency. Generally, the WTI market presents mixed efficiency behavior at different time horizons. In one-year window, the degree of efficiency on Brent decreased while there isn’t enough evidence to conclude that Brent market efficiency increased or decreased in medium and long term. In this sense, the lift of the ban might have significant impact on WTI but not on Brent.

Dynamic evolution of sentiments in Never Let Me Go: Insights from multifractal theory and its implications for literary analysis

Abstract The moods, feelings, and attitudes represented in a novel will resonate in the reader by activating similar sentiments. It is generally accepted that sentiment analysis can capture aspects of such moods, feelings, and attitudes and can be used to summarize a novel’s plot in a story arc. With the availability of a number of algorithms to automatically extract sentiment-based story arcs, new approaches for their utilization becomes pertinent. We propose to use nonlinear adaptive filtering and fractal analysis in order to analyze the narrative coherence and dynamic evolution of a novel. Using Never Let Me Go by Kazuo Ishiguro, the winner of the 2017 Nobel Prize for Literature as an illustrative example, we show that: (1) nonlinear adaptive filtering can extract a story arc that reflects the tragic trend of the novel; (2) the story arc displays persistent dynamics as measured by the Hurst exponent at short and medium timescales; (3) the plot’s dynamic evolution is reflected in the time-varying Hurst exponent. We argue that these findings are indicative of the potential that multifractal theory has for computational narratology and large-scale literary analysis. Specifically that the global Hurst exponent of a story arc is an index of narrative coherence that can identify bland, incoherent, and coherent narratives on a continuous scale. And, further, that the local time-varying Hurst exponent captures variation of a novel’s plot such that the extrema have specific narratological interpretations.

MF-DCCA between molecular properties and aqueous solubility

In this paper, we propose a framework, based on Multi-Fractal De-trended Fluctuation Cross-Correlation Analysis (MF-DCCA), to investigate the cross-correlation features between the molecular properties and aqueous solubility using the data set of Delaney-processed widely used for Deep Learning (DL). The molecular properties of Minimum Degree, Number of H-Bond Donors, Number of Rings, Number of Rotatable bonds and Polar Surface Area have a weak power-law cross-correlation with aqueous solubility; the Molecular Weight has a weak long-range cross-correlation. Obvious oscillation of long-range cross-correlation captures through a sliding window approach between molecular properties and aqueous solubility based on the pseudo-time series. Experimental comparison of time-varying cross-correlation widths shows that window widths are more robust to time-varying Hurst exponent. This work can provide a reference for reducing the data dimension for neural network molecular property prediction tasks and help in high-accuracy predicting molecular aqueous solubility on DL.

Multifractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting

Gradual degradation of the bearing vibration signal is usually studied as a nonstationary stochastic time series. Roller bearings are working at high speed in a heavy load environment so that the combination of bearing faults gradually degraded during the rotation might lead to unpredicted catastrophic accidents. The degradation process has the property of long-range dependence (LRD), so that the fractional Brownian motion (fBm) is taken into account for a prediction model. Because of the dramatic changes in the bearing degradation process, the Hurst exponent that describes the fBm will change during the degradation process. A priori Hurst value of the conventional fBm in the prediction is fixed, thus inducing a minor accuracy of the prediction. To avoid this problem, we propose an improved prediction method. Based on the following steps, at the initial data processing, a skip-over factor is selected as the characteristics parameter of the bearing degradation process. A multifractional Brownian motion (mfBm) replaces the fBm for the degradation modeling. We will show that also our mfBm has the same property of long-range dependence as the fBm. Moreover, a time-varying Hurst exponent H(t) is taken to replace the constant H in fBm. Finally, we apply the quantum-behaved partial swarm optimization (QPSO) to optimize H(t) for a finite interval. Some tests and corresponding experimental results will show that our model QPSO + mfBm have a much better performance on the prediction effect than fBm.

Analysis of the efficiency of Hong Kong REITs market based on Hurst exponent

At present, as China promotes the virtuous circle of housing leasing market, Real Estate Investment Trusts (REITs) has become an important investment and financing tool. In this paper, Hurst exponent is used to examine the efficiency of Hong Kong REITs market in China, and time-varying Hurst exponent is used to explore the dynamic changes of its efficiency. The empirical results of the Hong Kong REITs market show that the Hong Kong REITs market has not yet reached weak efficiency, and it is basically in a state of inefficiency from November 25 2005 to October 10, 2018, with only three times approximate to weak-form efficiency, but the duration is very short. Furthermore, compared with the Hong Kong stock market and the real estate market, the degree of efficiency of the Hong Kong REITs market is the lowest. Finally, on this basis, some countermeasures and suggestions for the development of China’s REITs market are put forward. This paper not only enriches the study of REITs market, but also provides the relevant basis for investors to make investment decisions.

Examining Efficiencies of Indian ADRs and their Underlying Stocks

In this article, the efficient market hypothesis (EMH) is tested for US and Indian stock markets and Indian American depositary receipts (ADRs) and their underlying stocks. The approach used to observe changing market efficiency is time-varying Hurst exponent. The Hurst values have been calculated after filtering the financial asset return series for short-term dependence and volatility. Rolling window approach has been used to calculate Hurst exponent and observe time-varying long-range dependence. The data are filtered by autoregressive-generalized autoregressive conditional heteroscedasticity (AR-GARCH) method. The empirical results suggest that US stock market is more efficient than Indian stock market. All the ADRs, their underlying stocks and markets of both the countries have shown varying efficiency. The change in efficiency of Indian ADRs is more when compared to their underlying stocks, which suggests that stock of a company listed on stock indices of different countries may show different pace of evolution of efficiency depending on maturity of the market.

The influence of trading volume on market efficiency: The DCCA approach

For a single market, the cross-correlation between market efficiency and trading volume, which is an indicator of market liquidity, is attentively analysed. The study begins with creating time series of market efficiency by applying time-varying Hurst exponent with one year sliding window to daily closing prices. The time series of trading volume corresponding to the same time period used for the market efficiency is derived from one year moving average of daily trading volume. Subsequently, the detrended cross-correlation coefficient is employed to quantify the degree of cross-correlation between the two time series. It was found that values of cross-correlation coefficient of all considered stock markets are close to 0 and are clearly out of range in which correlation being considered significant in almost every time scale. Obtained results show that the market liquidity in term of trading volume hardly has effect on the market efficiency.

Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion

The Hurst exponent (H) is widely used to quantify long range dependence in time series data and is estimated using several well known techniques. Recognizing its ability to remove trends the Detrended Fluctuation Analysis (DFA) is used extensively to estimate a Hurst exponent in non-stationary data. Multifractional Brownian motion (mBm) broadly encompasses a set of models of non-stationary data exhibiting time varying Hurst exponents, H(t) as against a constant H. Recently, there has been a growing interest in time dependence of H(t) and sliding window techniques have been used to estimate a local time average of the exponent. This brought to fore the ability of DFA to estimate scaling exponents in systems with time varying H(t), such as mBm. This paper characterizes the performance of DFA on mBm data with linearly varying H(t) and further test the robustness of estimated time average with respect to data and technique related parameters. Our results serve as a bench-mark for using DFA as a sliding window estimator to obtain H(t) from time series data.

TIME-VARYING LONG MEMORIES OF THE CHINESE CURRENCY AND STOCK MARKETS BASED ON THE HURST EXPONENT

Based on the daily return and volatility series of the Chinese yuan (RMB)/US dollar (USD) exchange rate and the Shanghai Stock Composite Index, the time-varying long memories of the Chinese currency and stock markets are investigated by comprehensively using the rescaled range (R/S), the modified R/S, and the detrended fluctuation analysis methods. According to the results drawn: (1) the efficiency of the Chinese currency market has not improved significantly, whereas the efficiency of the Chinese stock market has improved steadily, (2) volatility series presents longer memory than return series either in the Chinese currency or stock market and (3) the time-varying Hurst exponent of the Chinese currency market is sensitive to the reform that enhances the flexibility of the RMB exchange rate. Moreover, we find that short-term bidirectional Granger causal relationship exists, but no long-run equilibrium relationship between the time-varying Hurst exponents of the Chinese currency and stock markets was found based on the Granger causality and cointegration tests, respectively.

Long Memory Features Evolve in the Time-varying Process in Asia-pacific Foreign Exchange Markets

We investigated the presence of, and changes in, long memory features in the returns and volatility dynamics of six Asia-Pacific foreign exchange markets (Australian dollar, Japanese yen, Korean won, New Zealand dollar, Singaporean dollar, and Taiwan dollar) using time-varying Hurst exponents. In particular, instead of relying on a single static measure of long memory, we explored time-varying long memory features over time to assess changes in market efficiency by analyzing the returns and volatility of the markets. Furthermore, considering a time-varying rolling approach, we estimated values of the Hurst exponent for time windows with 1,000 observations (about 4 years of data) in each window. The estimation results indicated that both the returns and the volatility series possessed strong long memory features and that the degree of the long memory features changed over time. Additionally, the Hurst exponent showed an upward trend during the 1997 Asian currency crisis and 2008 global financial crisis, indicating that exchange rate markets became inefficient and predictable during the financial crisis.