scholarly journals Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 634 ◽  
Author(s):  
Pietro Murialdo ◽  
Linda Ponta ◽  
Anna Carbone
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Long Range ◽  
Financial Time Series ◽  
Moving Average ◽  
Social Systems ◽  
Long Run ◽  
Characteristic Behaviour ◽  
Correlation Parameters ◽  
Average Cluster

A perspective is taken on the intangible complexity of economic and social systems by investigating the dynamical processes producing, storing and transmitting information in financial time series. An extensive analysis based on the moving average cluster entropy approach has evidenced market and horizon dependence in highest-frequency data of real world financial assets. The behavior is scrutinized by applying the moving average cluster entropy approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). An extensive set of series is generated with a broad range of values of the Hurst exponent H and of the autoregressive, differencing and moving average parameters p , d , q . A systematic relation between moving average cluster entropy and long-range correlation parameters H, d is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter d ≃ 0.05 , d ≃ 0.15 and d ≃ 0.25 are consistent with moving average cluster entropy results obtained in time series of DJIA, S&P500 and NASDAQ. The findings clearly point to a variability of price returns, consistently with a price dynamics involving multiple temporal scales and, thus, short- and long-run volatility components. An important aspect of the proposed approach is the ability to capture detailed horizon dependence over relatively short horizons (one to twelve months) and thus its relevance to define risk analysis indices.

scholarly journals Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1125
Author(s):  
Rytis Kazakevičius ◽  
Aleksejus Kononovicius ◽  
Bronislovas Kaulakys ◽  
Vygintas Gontis
Keyword(s):  
Financial Markets ◽  
Long Range ◽  
Markov Processes ◽  
Point Processes ◽  
First Passage Time ◽  
Moving Average ◽  
Social Systems ◽  
Passage Time ◽  
Stable Motion ◽  
Non Gaussian

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

scholarly journals A Comparison of Hurst Exponent Estimators in Long-range Dependent Curve Time Series

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Han Lin Shang
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Moving Average ◽  
Estimation Method ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Finite Sample ◽  
Long Run ◽  
Finite Sample Bias

AbstractThe Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by constructing an estimate of the long-run covariance function, which we use, via dynamic functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of functional time series. Within the context of functional autoregressive fractionally integrated moving average (ARFIMA) models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

scholarly journals A case study of the residual-based cointegration procedure

2003 ◽  
Vol 7 (1) ◽  
pp. 29-48
Author(s):  
Riccardo Biondini ◽  
Yan-Xia Lin ◽  
Michael Mccrae
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Real Life ◽  
Arima Models ◽  
Financial Time ◽  
Long Run ◽  
Data Generating Process ◽  
Finance Theory ◽  
The Relationship

The study of long-run equilibrium processes is a significant component of economic and finance theory. The Johansen technique for identifying the existence of such long-run stationary equilibrium conditions among financial time series allows the identification of all potential linearly independent cointegrating vectors within a given system of eligible financial time series. The practical application of the technique may be restricted, however, by the pre-condition that the underlying data generating process fits a finite-order vector autoregression (VAR) model with white noise. This paper studies an alternative method for determining cointegrating relationships without such a pre-condition. The method is simple to implement through commonly available statistical packages. This ‘residual-based cointegration’ (RBC) technique uses the relationship between cointegration and univariate Box-Jenkins ARIMA models to identify cointegrating vectors through the rank of the covariance matrix of the residual processes which result from the fitting of univariate ARIMA models. The RBC approach for identifying multivariate cointegrating vectors is explained and then demonstrated through simulated examples. The RBC and Johansen techniques are then both implemented using several real-life financial time series.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

An Optimal Band for Prediction of Buy and Sell Signals and Forecasting of States

2015 ◽  
Vol 2 (2) ◽  
pp. 33-53
Author(s):  
Vivek Vijay ◽  
Parmod Kumar Paul
Keyword(s):  
Time Series ◽  
Linear Function ◽  
Markov Models ◽  
Stock Exchange ◽  
Financial Time Series ◽  
Moving Average ◽  
Linear Optimization ◽  
Optimization Technique ◽  
Price Series ◽  
Security Price

A trading band, based on historical movements of a security price, suggests buy or sell pattern. Bollinger band is one of the most famous bands based on moving average and volatility of the security. The authors define a new trading band, namely Optimal Band, to forecast the buy or sell signals. This optimal band uses a linear function of local and absolute extrema of a given financial time series. The parameters of this linear function are then estimated by simple linear optimization technique. The authors then define different states using various upper and lower values of Bollinger band and the optimal band. The approach of Markov and Hidden Markov Models are used to forecast the future states of given time series. The authors apply all the techniques on the closing price of Bombay stock exchange and intra-day price series of crude oil and Nifty stock exchange.

scholarly journals Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 441 ◽  
Author(s):  
Maria C. Mariani ◽  
Peter K. Asante ◽  
Md Al Masum Bhuiyan ◽  
Maria P. Beccar-Varela ◽  
Sebastian Jaroszewicz ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Series Data ◽  
Financial Time Series ◽  
Seismic Station ◽  
Volcanic Eruptions ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

Nonlinear Complexity and Chaotic Behaviors on Finite-Range Stochastic Epidemic Financial Dynamics

2019 ◽  
Vol 29 (06) ◽  
pp. 1950083
Author(s):  
Guochao Wang ◽  
Shenzhou Zheng ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Financial Time Series ◽  
Logistic Map ◽  
Entropy Method ◽  
Finite Range ◽  
Price Model ◽  
Nonlinear Complexity ◽  
Proposed Model ◽  
Real Market

In this paper, a novel stochastic financial price model, based on the theory of finite-range stochastic interacting epidemic system, is proposed to reproduce the nonlinear dynamic mechanism of price fluctuations in financial markets. To better understand the complexity behavior of the proposed model, we develop a new entropy-based approach called index fluctuation fuzzy entropy (IFFE) and construct four measure criteria. The effectiveness of this approach is experimentally validated by logistic map time series, white noise time series, [Formula: see text] noise time series and six financial time series. Moreover, the largest Lyapunov exponents and Kolmogorov–Sinai entropy method are applied to analyze the chaotic property of the proposed model. To verify the rationality of the proposed model, the same analyses for the real market data are comparatively investigated with the simulation ones. The empirical results reveal that the novel financial price model is able to reproduce some important features of the financial markets.

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