Analysis of market returns using multifractal time series and agent-based simulation

Multifractal detrended fluctuation analysis of ionospheric total electron content data during solar minimum and maximum

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 65:39-52 (2015) - DOI: https://doi.org/10.3354/cr01321 Contribution to the CR Special: 'Modelling climate change impacts for food security' Multifractal analysis of meteorological time series to assess climate impacts Piotr Baranowski1,*, Jaromir Krzyszczak1, Cezary Slawinski1, Holger Hoffmann2, Jerzy Kozyra3, Anna Nieróbca3, Krzysztof Siwek4, Andrzej Gluza4 1Institute of Agrophysics, Polish Academy of Sciences, ul. Doświadczalna 4, 20-290 Lublin, Poland 2Institute of Crop Science and Resource Conservation (INRES), Katzenburgweg 5, 53115 Bonn, Germany 3Institute of Soil Science and Plant Cultivation, State Research Institute, Czartoryskich 8, 24-100 Pulawy, Poland 4Faculty of Earth Sciences and Spatial Management, UMCS, al. Kraśnicka 2cd, 20-718 Lublin, Poland *Corresponding author: pbaranow@ipan.lublin.pl ABSTRACT: Agro-meteorological quantities are often in the form of time series, and knowledge about their temporal scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice versa. However, the scaling analysis of these quantities is complicated due to the presence of localized trends and nonstationarities. The objective of this study was to characterise scaling properties (i.e. statistical self-similarity) of the chosen agro-meteorological quantities through multifractal detrended fluctuation analysis (MFDFA). For this purpose, MFDFA was performed with 11322 measured time series (31 yr) of daily air temperature, wind velocity, relative air humidity, global radiation and precipitation from stations located in Finland, Germany, Poland and Spain. The empirical singularity spectra indicated their multifractal structure. The richness of the studied multifractals was evaluated by the width of their spectrum, indicating considerable differences in dynamics and development. In log-log plots of the cumulative distributions of all meteorological parameters the linear functions prevailed for high values of the response, indicating that these distributions were consistent with power-law asymptotic behaviour. Additionally, we investigated the type of multifractality that underlies the q-dependence of the generalized Hurst exponent by analysing the corresponding shuffled and surrogate time series. For most of the studied meteorological parameters, the multifractality is due to different long-range correlations for small and large fluctuations. Only for precipitation does the multifractality result mainly from broad probability function. This feature may be especially valuable for assessing the effect of change in climate dynamics. KEY WORDS: Multifractal analysis · Time series · Agro-meteorological parameters Full text in pdf format Supplementary material PreviousNextCite this article as: Baranowski P, Krzyszczak J, Slawinski C, Hoffmann H and others (2015) Multifractal analysis of meteorological time series to assess climate impacts. Clim Res 65:39-52. https://doi.org/10.3354/cr01321 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 65. Online publication date: September 28, 2015 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2015 Inter-Research.

Multifractal analysis provides a detailed approach to examine complex systems with varying scaling behaviors across multiple time scales. In this article, multifractal detrended fluctuation analysis (MFDFA) is applied to the index returns of Netflix from 2019 to 2024. The purpose is to uncover the multifractal nature of financial data through analyzing original, shuffled and surrogate time series and to identify sources of multifractality, particularly focusing on the roles of fat-tailed distributions and temporal correlations. This article finds out that even after shuffling, which disrupts time-dependent correlations, the multifractality still remains or even intensifies. Meanwhile, the surrogate data is investigated to study the sources of multifractality. The results show that Netflix stock returns exhibit clear multifractal properties, primarily driven by fat-tailed distributions rather than long-term correlations. In general, multifractal detrended fluctuation analysis provides important insights into the complex dynamics of financial markets, and it demonstrates how multifractal analysis can reveal underlying structures that traditional methods often overlook. These findings have implications for better risk management and market analysis by acknowledging the critical role of extreme events and distributional characteristics in stock market behavior.

In this paper, we propose the multifractal detrending fluctuation analysis based on [Formula: see text]-norm constrain (MF-DFN). We assess the performance of the proposed algorithm by constructing a [Formula: see text]-model based multiplicative cascades time series. We calculate the generalized [Formula: see text] exponent [Formula: see text], [Formula: see text] exponent [Formula: see text], singularity exponent [Formula: see text] and multifractal spectrum [Formula: see text] for multifractal detrended fluctuation analysis (MF-DFA) and MF-DFN, respectively. We notice that under different norm constraints, the distribution of multifractal characteristics is quite different. Appropriate norm constraints can make the multifractal characteristics of time series described more accurately. Based on the analytical solution curve, the distribution of different multifractal numerical curves determines the correct selection of norm constraint value. In this study, using a combination of norms [Formula: see text] and [Formula: see text], the depicted numerical curves almost overlap the theoretical curve, which shows that the proposed MF-DFN is superior to MF-DFA. To eliminate the influence of specific time series, we reset parameters [Formula: see text] and [Formula: see text] in [Formula: see text]-model. Various experimental results also show the effectiveness of the proposed MF-DFN. In addition, we also verify the efficiency of the proposed MF-DFN by using the practical application. The experimental results show that our proposed method plays a significant role in ECG classification.

A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation

Text emotion classification system based on multifractal methods

This paper investigates the traffic flow time series observed on the Beijing second ring road over a period of about 27 days, from 0:00 a.m. on 12/6/2006 to 16:00 p.m. on 1/1/2007. With the aid of the multifractal detrended fluctuation analysis (MF-DFA) method, the multifractality of the traffic flow series is shown in this paper. Furthermore, the multifractal spectrum is employed in studying the time series, which shows the strong degree of multifractality in the time series.

Based on the mathematical arguments formulated within the multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in the uncorrelated time series from the Gaussian basin of attraction, the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations, and the fatter distribution tails of fluctuations may broaden the width of the singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series-temporal correlations or broad distribution tails-is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the central limit theorem.

Recently, many lines of investigation in neuroscience and statistical physics have converged to raise the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG) signals is nonlinear, with self-affine dynamics, while scalp-recorded EEG signals themselves are nonstationary. Therefore, traditional methods of EEG analysis may miss many properties inherent in such signals. Similarly, fractal analysis of EEG signals has shown scaling behaviors that may not be consistent with pure monofractal processes. In this study, we hypothesized that scalp-recorded human EEG signals may be better modeled as an underlying multifractal process. We utilized the Physionet online database, a publicly available database of human EEG signals as a standardized reference database for this study. Herein, we report the use of multifractal detrended fluctuation analysis on human EEG signals derived from waking and different sleep stages, and show evidence that supports the use of multifractal methods. Next, we compare multifractal detrended fluctuation analysis to a previously published multifractal technique, wavelet transform modulus maxima, using EEG signals from waking and sleep, and demonstrate that multifractal detrended fluctuation analysis has lower indices of variability. Finally, we report a preliminary investigation into the use of multifractal detrended fluctuation analysis as a pattern classification technique on human EEG signals from waking and different sleep stages, and demonstrate its potential utility for automatic classification of different states of consciousness. Therefore, multifractal detrended fluctuation analysis may be a useful pattern classification technique to distinguish among different states of brain function.

Climate dynamics were assessed using multifractal detrended fluctuation analysis (MF-DFA) for sites in Finland, Germany and Spain across a latitudinal transect. Meteorological time series were divided into the two subsets (1980–2001 and 2002–2010) and respective spectra of these subsets were compared to check whether changes in climate dynamics can be observed using MF-DFA. Additionally, corresponding shuffled and surrogate time series were investigated to evaluate the type of multifractality. All time series indicated underlying multifractal structures with considerable differences in dynamics and development between the studied locations. The source of multifractality of precipitation time series was two-fold, coming from the width of the probability function to a greater extent than for other time series. The multifractality of other analyzed meteorological series was mainly due to long-range correlations for small and large fluctuations. These results may be especially valuable for assessing the change of climate dynamics, as we found that larger changes in asymmetry and width parameters of multifractal spectra for divided datasets were observed for precipitation than for other time series. This suggests that precipitation is the most vulnerable meteorological quantity to change of climate dynamics.

Water, in its various forms, is considered a key parameter in climate change studies. Water vapor is recognized as the most important natural greenhouse gas playing a vital role in the hydrological cycle. Thus, studying air humidity fluctuations may contribute towards a deeper understanding of the radiative and thermodynamic processes that take part in the Earth’s atmosphere. Traditional statistical analysis is not always efficient to describe complex physical processes with high temporal variability. In addition, a more thorough study of the variations of climatic parameters requires examination of their time series fluctuations over multiple time scales. Fractal theory offers robust solutions that satisfy the above requirements. In this work, the Multifractal Detrended Fluctuation Analysis (MF-DFA) is used in order to investigate the intrinsic dynamics of daily relative humidity time series over the Greek region from a nonlinear perspective. The scaling properties and the multifractal structure of the time series are studied by examining the fluctuation function, the multifractal spectrum and the Hurst exponent.

Ensuring the safety of transmission line towers is vital for human safety, power supply, economic development, and environmental protection. This study specifically examines how temperature affects tower inclination. Multifractal detrended cross-correlation analysis (MF-DCCA) is a combination of multifractal detrended fluctuation analysis (MF-DFA) and DCCA that reveals the multifractal features of two cross-correlated non-stationary signals. This paper adopts the MF-DCCA tool to investigate the cross-correlations between the internal temperature of an inclination sensor device and the posture of a transmission line tower. The tilt angle data in the x- and y-axes are used to measure the posture of the transmission line tower. We start by using Pearson correlation to assess the relationship between temperature and two inclination angles, followed by verifying their correlation with a p-value below 0.05 using first-order linear fitting. We initially assess the multifractal features of three time series using MF-DFA before MF-DCCA analysis. All exhibit multifractal traits with H(2)<0.5, indicating negative persistence, especially notable in the temperature series. Finally, we adopt the MF-DCCA approach to examine the multifractal cross-correlation between tilt-angle time series and temperature time series, and the results indicate the negative persistence of the cross-correlation between the time series. Furthermore, the multifractal cross-correlation of temperature and inclination data on the y-axis was also found to be stronger than on the x-axis based on features of the scaling exponent and symmetry exponent.

The ongoing COVID-19 shocked financial markets globally, including China’s crude oil future market, which is the third-most traded crude oil futures after WTI and Brent. As China’s first crude oil futures are accessible to foreign investors, the Shanghai crude oil futures (SC) have attracted significant interest since launch at the Shanghai International Energy Exchange. The impact of COVID-19 on the new crude oil futures is an important issue for investors and policy makers. Therefore, this paper studies the short-term influence of COVID-19 pandemic on SC via multifractal analysis. We compare the market efficiency of SC before and during the pandemic with the multifractal detrended fluctuation analysis and other commonly used random walk tests. Then, we generate shuffled and surrogate data to investigate the components of multifractal nature in SC. And we examine cross-correlations between SC returns and other financial assets returns as well as SC trading volume changes by the multifractal detrended cross-correlation analysis. The results show that market efficiency of SC and its cross-correlations with other assets increase significantly after the outbreak of COVID-19. Besides that, the sources of its multifractal nature have changed since the pandemic. The findings provide evidence for the short-term impacts of COVID-19 on SC. The results may have important implications for assets allocation, investment strategies and risk monitoring.

Uncertain systems are those wherein some variability is observed, meaning that different observations of the system will produce different measurements. Studying such systems demands the use of statistical methods over multiple measurements, which allows overcoming the uncertainty, based on the premise that a single measurement is not representative of the system’s behavior. In such cases, the current multifractal detrended fluctuation analysis (MFDFA) method cannot offer confident conclusions. This work presents multi-signal MFDFA (MS-MFDFA), a novel methodology for accurately characterizing uncertain systems using the MFDFA algorithm, which enables overcoming the uncertainty of the system by simultaneously considering a large set of signals. As a case study, we consider the problem of characterizing software (Sw) consumption. The difficulty of the problem mainly comes from the complexity of the interactions between Sw and hardware (Hw), as well as from the high uncertainty level of the consumption measurements, which are affected by concurrent Sw services, the Hw, and external factors such as ambient temperature. We apply MS-MFDFA to generate a signature of the Sw consumption profile, regardless of the execution time, the consumption levels, and uncertainty. Multiple consumption signals (or time series) are built from different Sw runs, obtaining a high frequency sampling of the instant input current for each of them while running the Sw. A benchmark of eight Sw programs for analysis is also proposed. Moreover, a fully functional application to automatically perform MS-MFDFA analysis has been made freely available. The results showed that the proposed methodology is a suitable approximation for the multifractal analysis of a large number of time series obtained from uncertain systems. Moreover, analysis of the multifractal properties showed that this approach was able to differentiate between the eight Sw programs studied, showing differences in the temporal scaling range where multifractal behavior is found.

Multifractal detrended fluctuation analysis (MFDFA) method can examine higher-dimensional fractal and multifractal characteristics hidden in time series. However, removal of local trends in MFDFA is based on discontinuous polynomial fitting, resulting in pseudo-fluctuation errors. In this paper, we propose a two-stage modified MFDFA for multifractal analysis. First, an overlap moving window (OMW) algorithm is introduced to divide time series of the classic MFDFA method. Second, detrending by polynomial fitting local trend in traditional MFDFA is replaced by ensemble empirical mode decomposition (EEMD)-based local trends. The modified MFDFA is named OMW-EEMD-MFDFA. Then, the performance of the OMW-EEMD-MFDFA method is assessed by extensive numeric simulation experiments based on a p-model of multiplicative cascading process. The results show that the modified OMW-EEMD-MFDFA method performs better than conventional MFDFA and OMW-MFDFA methods. Lastly, the modified OMW-EEMD-MFDFA method is applied to explore multifractal characteristics and multifractal sources of daily precipitation time series data at the Mapoling and Zhijiang stations in Dongting Lake Basin. Our results showed that the scaling properties of the daily precipitation time series at the two stations presented a long-range correlation, showing a long-term persistence of the previous state. The strong q-dependence of H ( q ) and τ ( q ) indicated strong multifractal characteristics in daily precipitation time series data at the two stations. Positive Δ f values demonstrate that precipitation may have a local increasing trend. Comparing the generalized Hurst exponent and the multifractal strength of the original precipitation time series data with its shuffled and surrogate time series data, we found that the multifractal characteristics of the daily precipitation time series data were caused by both long-range correlations between small and large fluctuations and broad probability density function, but the broad probability density function was dominant. This study may be of practical and scientific importance in regional precipitation forecasting, extreme precipitation regulation, and water resource management in Dongting Lake Basin.