Analysis of cyclical behavior in time series of stock market returns
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Efficient-market hypothesis
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A relevant issue in time series analysis is the estimation of long-range dependence, that is, how much future values of a time series depend on current values. One of the ways to verify this dependence is by estimating the Hurst exponent using methods such as detrended fluctuation analysis. Here, we propose a new methodology to estimate the Hurst exponent, named leave one out detrended fluctuation analysis. Furthermore, based on this new estimator for the Hurst exponent, we propose the noise reduction by the leave one out detrended fluctuation analysis method. We apply this new denoising method to electrocardiogram noise reduction. The results presented in this work show that this new methodology outperforms the SureShrink and universal noise reduction methods.
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In this paper, we have studied electroencephalogram (EEG) activity of schizophrenia patients, in resting eyes closed condition, with detrended fluctuation analysis (DFA). The DFA gives information about scaling and long-range correlations in time series. We computed DFA exponents from 30 scalp locations of 18 male neuroleptic-naïve, recent-onset schizophrenia (NRS) subjects and 15 healthy male control subjects. Our results have shown two scaling regions in all the scalp locations in all the subjects, with different slopes, corresponding to two scaling exponents. No significant differences between the groups were found with first scaling exponent (short-range). However, the second scaling exponent (long-range) were significantly lower in control subjects at all scalp locations (p<;0.05, Kruskal-Wallis test). These findings suggest that the long-range scaling behavior of EEG is sensitive to schizophrenia, and this may provide an additional insight into the brain dysfunction in schizophrenia.
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Based on detrended fluctuation analysis (DFA), we explore the characteristics of multichannel electroencephalogram (EEG), which is recorded from many subjects performing different mental tasks. The results show that mental EEG exhibits long-range power-law correlations by calculating its scaling exponents (alpha), which can reflect the kinds of mental tasks. The scaling exponent of letter-composing is different from that of multiplication especially at positions C3 and C4, and at positions O1 and O2 the scaling exponent of rotation is also different distinctively from that of multiplication. Detrended fluctuation analysis exhibits its robustness against noises in our works. We could benefit more from the results of this paper in designing mental tasks and selecting brain areas in brain-computer interface systems
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Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.
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The market efficiency used to clarify the relationship between the information and stock prices. If the market price of any stocks reflected correctly and completely all relevant information, the market is still considered efficient. The financial market must be efficient so that it can take its role in terms of attracting investment, the Efficient Market Hypothesis (EMH) developed firstly by Paul Sammuelson in 1965 and Fama in 1970. The aims of this paper focus on to examine at the weak-form of the EMH. The weak form show that current stock market prices are fully reflects all stock market information including historical price. The problem is whether the price of FTSE Bursa Malaysia KLCI (FBMKLCI) Stock Index in Malaysia Stock Market is efficient in the weak form of Efficient Market Hypothesis? The main objective of this study is to justify weak-form of market efficiency of FTSE Bursa Malaysia KLCI (FBMKLCI) Stock Index in Malaysia Stock Market. Furthermore, the study is conducted to study whether the indexes follow the Random Walk hypothesis or not. The variable in this study is the stock market index of the FTSE Bursa Malaysia KLCI (FBMKLIC) Stock Index in Malaysia Stock Market. The samples in this study include daily, weekly and monthly closing price of the index. The analysis is observed in the range of 5 year in daily, weekly and monthly observation start from January 2012 to December 2016 with total number of 1300 observations for daily sample, 260 observations for weekly sample and 60 observations for monthly sample. The statistical test applied in this study is Descriptive Statistic, Augmented Dickey Fuller (ADF) Unit Root Test, Philips-Perron (PP) Unit Root Test, Autocorrelation Test and Runs Test.
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Capitalization-weighted index
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Detrended fluctuation analysis (DFA), a fractal analysis method which is widely used in heart rate variability (HRV) studies, is used to analyze the scaling behaviour of RR interval series of preterm neonates. The average scaling behaviour, calculated using 30000 RR intervals (3 - 4 hours), is characterized by a scaling exponent of 1.4 ± 0.1 at small scales (n ≤ 20) and a smaller exponent of 1.0 ± 0.1 at larger scales. It is shown that the scaling behaviour is not constant over such long segments and how heart rate patterns, associated with specific physiological mechanisms, contribute to the observed variation of the scaling exponents. The effect of the two most important patterns, spikes (either due to faulty peak detection or true decelerations in heart rate) and periodic fluctuations, on the scaling behaviour is investigated.
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