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The Long-term Memory In Financial Markets The Fractal Approach

Posted on:2018-04-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:D Y LiFull Text:PDF
GTID:1319330518959901Subject:Finance
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In 1980 s,IT technology experienced rapid developments and it provides researchers in financial field with tons of data,which bring researchers new opportunities to study the microstructure of financial markets and request improved statistical tools to handle these data.Similar mass data has been analyzed by physicists in the past half century and plenty of experiences have been accumulated from the study of statistical mechanics,phase transitions,nonlinear dynamics,and disordered systems.Concepts such as power law distribution,correlation,scaling,continuous time series,and stochastic processes have been widely applied and relative statistical tools are well developed.Researchers with physics backgrounds apply these useful tools to the analysis of financial markets.This interdisciplinary field of finance,statistics and physics is known as statistical finance or Econphysics.In this field,the study of the long-term memory,based on the fractal theory,improves the research framework of the classic finance theory.The efficient market hypothesis is one of the most important corner stones in finance,which argues that asset prices fully reflect all available history information and it is impossible to "beat the market" consistently on a risk-adjusted basis because market prices are expected only react to new information and the excess returns are eliminated by arbitragers in a very short period.On the basis of the Fractal theory,Mandelbrot(1975)and Peters(1994)adopt the Hurst exponent and fractal dimension as an indicator to measure the long-term memory.The empirical results using these tools indicate that the long-term memory persists in the majorty of the return series of assets,foreigh exchange and bond markets.Despite the extent of the memory is weak,but it significantly persists for a long time and is not eliminated by arbitragers.The long-term memory of the return series is one of the most ubiquitous market anomalies in financial markets.Matteo(2005)adopts the generalized Hurst exponent to measure the long-term memory of stock,currency and bond markets.The result indicates that the long-term memory of the return series of these markets is identified and shows multi-fractal characteristic;the memory of mature markets is less significant,indicating these markets are more efficient;the value of the Hurst exponent is close to 0.5 and the market price series follows the random walk.The emerging markets are less efficient and the memory is statistically significant.The empirical evidence of the persistence of the long-term memory brings new questions for researchers from the EMH School.Since the tools of measuring the long-term memory and non-linear time series are introduced to the finance field,the time series and relative econometrics tools achieve new developments.Granger et al.(1980)proposes the ARFIMA model derived from the ARIMA model,which provides a sophisticated time series tool for fractal time series.Moreover,the Chaos theory,thermodynamics model and system dynamics model,which have been fully developed in the physic field,are adopted in finance fields to investigate the herding behavior and the complex system in financial markets.These tools enrich research methods in the finance field.This paper focuses on the long-term memory of the return series in financial markets.First,the measure tools,like rescaled analysis,detrended fluctuation analysis and generalized Hurst exponents,are introduced.These tools will be used to analyze the market efficieny later.The contributions of this paper are detailed described as below:1)The phenomonen that Initial under-reaction and delayed over-reaction is studied.The Hurst exponent is the nature method to measure the scale-dependent trend for all scales,and this unique advantage is used to investigate the 44 important markets.The empirical results of local trends of all scales are documented.In classic finance studies,limited by the tools,only results of several pre-selected scales are illustrated.The fractal theory can be used to verify the local trends of all scales in an easy and straightforward way.Empirical results illustrate that assets,which are able to provide the long enough history data,share the same pattern that these markets are under initial under-reaction and delayed over-reaction.The scale-dependent trend switches from the momentum to the mean reversion,which implies that non-periodic cycles exist in financial markets.This pattern can be partly explained by the economic cycles.However,the empirical results of this paper illustrate that the currency markets show the same pattern.Since currency markets are only weakly correlated with the economic cycles,indicating that other internal mechanism of the market leads to this result and this pattern can not be fully explained by economics cycles.2)In this paper,the source of the market liquidity and the causes of the long-term memory are studies from a perspective of the market microstructure.The efficient market hypothsis states that noise traders are the source of market liquidity.By comparison,the fractal market hypothesis argues that the self-similar structure and the diversity of the investment horizons provide liquidity for market traders.Investors with various investment horizons hold their investment position for different periods.Due to the differences of the holding periods,they have different expected returns and tend to hold positions with different directions,and provide each other liquidity by trading in different directions.This theory argues that the expected returns for the market are divergent even if all investors are assumed to be rational investors,and the divergence provides the market with liquidity.By comparion,the liquidity provided by the noise traders is possibly a small fraction.Based on this assumption,an experiment is designed using the agent-based model to simulate the effect caused by the divergence of investors.The result indicates that the market shows the properties of a complex system,and the return series has a significant long-term memory;the diversity of investment horizons plays an important role in the source of the market liquidity.The more divergent the investment horizons are,the more liquid the market is.This simulation result helps explain the influence of the hetergenous structure of financial markets to the market stability and liquidity and contributes to the study of the market crush caused by the sudden missing of market liquidity.3)In this paper,an investment strategy using the Hurst exponents is proposed.When the value of the Hurst exponent(H)of the market return is larger than 0.5,it indicates that the recent market trend is likely to continue in the future;H < 0.5 indicates that the recent trend is likely to reverse.This property of the Hurst exponent can be used to forecast the future market movement.The proposed strategy is verified based on the simulation,the daily data of the Chinese market and the high-frequency data of NYMEX crude oil.The result of Monte Carlo simulation indicates that this strategy achieves the best performance when the long-term memory is in great strength.However,for most mature markets,which are relatively efficient with a weak long-term memory,the efficiency of this strategy is not significant.The empirical results based on the Chinese market data indicate that the components of Shanghai index are significantly long-term correlated.However,the correlation is not strong enough to guarrantee the excess return.The transaction cost larger than 4‰ can fully offset the strategy return.Moreover,the value of the Hurst exponent decreases in the 2010-2014 period,indicating the increasement of the market efficiency.The result based on the high-frequency data of NYMEX crude oil shows the consistent result.The empirical results from both the daily data and high frequency data support the efficient market hypothesis and the long-term memory of these markets is significant in a statistical but not economical way.Moreover,the long-term trend of the market is proved to be time-varying,which further reduces the performance of the proposed method.Even in a market with no transaction cost,the strategy may fail to obtain a positive return due to the time-varying trend.Because when the market shows a long-term trend,but the trend needs to be confirmed with more data,the investors exploiting the trend face the dilemma: the forecast based on limited data performs slightly better than flipping a coin;waiting for more data to confirm the trend may miss the opportunity.The trend may change and the investors are possibly always one step behind it.
Keywords/Search Tags:long-term memory, market efficiency, Hurst exponent
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