Statistical properties of information flow in financial time series

The Local Fractal Properties of the Financial Time Series on the Polish Stock Exchange Market

We investigate the local fractal properties of the financial time series based on the evolution of the Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. Calculating the local Hurst exponent for the WIG time series we find an interesting dependence between the behavior of the local fractal properties of the WIG time series and the crashes appearance on the financial market.

Financial time-series analysis: A brief overview

Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount of data available, either for free in the Internet or commercially. Financial time-series analysis is of great interest to practitioners as well as to theoreticians, for making inferences and predictions. Furthermore, the stochastic uncertainties inherent in financial time-series and the theory needed to deal with them make the subject especially interestin…

Hausdorff clustering of financial time series

A clustering procedure, based on the Hausdorff distance, is introduced and tested on the financial time series of the Dow Jones Industrial Average (DJIA) index.

Markov Chains application to the financial-economic time series prediction

In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of aftereffect or memory. The technology proposes prediction with the hierarchy of time discretization intervals and splicing procedure for the prediction results at the different frequency levels to the single prediction output time series. The hierarchy of time discretizations gives a possibility to use fractal properties of the given time series to make prediction on the different frequen…

Superstatistics with cut-off tails for financial time series

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capable of describing the statistical properties of real financial time series. In addition, we present an option pricing formula with respect to superstatistics.

A statistical physics perspective on criticality in financial markets

Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believed to be critical by analogy to physical systems but few statistically founded evidence have been given. Through a data-based methodology and comparison to simulations inspired by statistical physics of complex systems, we show that the Dow Jones and indices sets are not rigorousl…

Option Pricing from Wavelet-Filtered Financial Series

We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most ($\simeq$ 99.6%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times…

Conditional Probability as a Measure of Volatility Clustering in Financial Time Series

In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as the central feature. In this paper we propose an appropriately defined conditional probability as a new measure of volatility clustering. We test this measure by applying it to different stock market data, and we uncover a rich temporal structure in volatility fluctuations described very well by a scaling relation. The scale factor used in the scaling provi…

Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations

The mesoscopic organization of complex systems, from financial markets to the brain, is an intermediate between the microscopic dynamics of individual units (stocks or neurons, in the mentioned cases), and the macroscopic dynamics of the system as a whole. The organization is determined by "communities" of units whose dynamics, represented by time series of activity, is more strongly correlated internally than with the rest of the system. Recent studies have shown that the binary projections of various financial and neural time series exhibit nontrivial dynamical features that resemble those o…

Gaussian process imputation of multiple financial series

In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly analysed. We focus on learning the relationships among financial time series by modelling them through a multi-output Gaussian process (MOGP) with expressive covariance functions. Learning these market dependencies among financial series is crucial for the imputation and prediction of financial observations. The proposed model is validated experimentally on …

金融时间序列的复杂性：多重分形与多尺度熵分析

Complexity of Financial Time Series: Multifractal and Multiscale Entropy Analyses

本研究运用MF-DFA和RCMSE方法对比分析比特币、外汇、黄金和天然气的价格时间序列复杂性，发现比特币复杂度最高，或与其对数收益率的强非线性相关，为市场风险与可预测性研究提供参考。

Forecasting non-stationary financial time series through genetic algorithm

We utilize a recently developed genetic algorithm, in conjunction with discrete wavelets, for carrying out successful forecasts of the trend in financial time series, that includes the NASDAQ composite index. Discrete wavelets isolate the local, small scale variations in these non-stationary time series, after which the genetic algorithm's predictions are found to be quite accurate. The power law behavior in Fourier domain reveals an underlying self-affine dynamical behavior, well captured by the algorithm, in the form of an analytic equation. Remarkably, the same equation captures the trend o…

Multiple Time Series Ising Model for Financial Market Simulations

In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated.

Financial Series Prediction: Comparison Between Precision of Time Series Models and Machine Learning Methods

Precise financial series predicting has long been a difficult problem because of unstableness and many noises within the series. Although Traditional time series models like ARIMA and GARCH have been researched and proved to be effective in predicting, their performances are still far from satisfying. Machine Learning, as an emerging research field in recent years, has brought about many incredible improvements in tasks such as regressing and classifying, and it's also promising to exploit the methodology in financial time series predicting. In this paper, the predicting precision of financial…

Statistical Properties of Demand Fluctuation in the Financial Market

We examine the out-of-equilibrium phase reported by Plerou {\it et. al.} in Nature, {\bf 421}, 130 (2003) using the data of the New York stock market (NYSE) between the years 2001 --2002. We find that the observed two phase phenomenon is an artifact of the definition of the control parameter coupled with the nature of the probability distribution function of the share volume. We reproduce the two phase behavior by a simple simulation demonstrating the absence of any collective phenomenon. We further report some interesting statistical regularities of the demand fluctuation of the financial mar…

Intra-day variability of the stock market activity versus stationarity of the financial time series

We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart. Hence, we proved that the day seasonality of inter-transaction times extends the memory of as well the process itself as its absolute value. That is, both processes relaxation to zero is longer.

Domain Specific Concept Drift Detectors for Predicting Financial Time Series

Concept drift detectors allow learning systems to maintain good accuracy on non-stationary data streams. Financial time series are an instance of non-stationary data streams whose concept drifts (market phases) are so important to affect investment decisions worldwide. This paper studies how concept drift detectors behave when applied to financial time series. General results are: a) concept drift detectors usually improve the runtime over continuous learning, b) their computational cost is usually a fraction of the learning and prediction steps of even basic learners, c) it is important to st…

Multifractal dynamics of stock markets

We present a comparative analysis of multifractal properties of financial time series built on stock indices from developing (WIG) and developed (S&P500) financial markets. It is shown how the multifractal image of the market is altered with the change of the length of time series and with the economic situation on the market. We emphasize that the proper adjustment of scaling range for multiscaling power laws is essential to obtain the multifractal image of time series. We analyze in this paper multifractal properties of real financial time series using Hölder $f(α)$ representation and multif…

Record statistics of financial time series and geometric random walks

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $α$ lying in the range $1.5 \le α\le 1.8$. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that from the empirical stock data.

Wavelet Correlation Coefficient of 'strongly correlated' financial time series

In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two variables. In econophysics correlation coefficient forms important input to evolve hierarchial tree and minimum spanning tree of financial data.

Evidence and Behaviour of Support and Resistance Levels in Financial Time Series

This paper investigates the phenomenon of support and resistance levels (SR levels) in financial time series, which act as temporary price barriers that reverses price trends. We develop a heuristic discovery algorithm for this purpose, to discover and evaluate SR levels for intraday price series. Our simple approach discovers SR levels which are able to reverse price trends statistically significantly. Asset price entering SR levels with higher number of price bounces before are more likely to bounce on such SR levels again. We also show that the decay aspect of the discovered SR levels as de…

Financial Time Series Data Processing for Machine Learning

This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It proposes an empirical test based on the capability to learn simple data relationship with simple models. It also speaks about the data split method specific to time series, avoiding unwanted overfitting and proposes various labelling for classification and regression.

A relative information approach to financial time series analysis using binary $N$-grams dictionaries

Here we present a novel approach to statistical analysis of financial time series. The approach is based on $n$-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their information capacity using relative entropy. A specific quantization of (originally continuous) financial data is considered: so called binary quantization. Possible applications of the proposed technique include market event study with the $n$-grams of higher information value. The finite length of the input data presents certain computational and theoretical challe…

Measuring multiscaling in financial time-series

We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of synthetic time-series with known properties. We use the results from the synthetic time-series to interpret the measure of multifractality of real log-returns time-series. The main finding is that the aggregation horizon of the returns can introduce a strong bias effect on the measure of multifractality. This effect can become especially important when retu…

An extended Speculation Game for the recovery of Hurst exponent of financial time series

The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be anti-persistent to the initial price, resulting in the quite small value of Hurst exponent of price change. To overcome this problem, we extend the speculation game by introducing a perturbative part to the price change with the consideration of other effects besides pure specula…

Permutation approach, high frequency trading and variety of micro patterns in financial time series

Permutation approach is suggested as a method to investigate financial time series in micro scales. The method is used to see how high frequency trading in recent years has affected the micro patterns which may be seen in financial time series. Tick to tick exchange rates are considered as examples. It is seen that variety of patterns evolve through time; and that the scale over which the target markets have no dominant patterns, have decreased steadily over time with the emergence of higher frequency trading.

Order patterns, their variation and change points in financial time series and Brownian motion

Order patterns and permutation entropy have become useful tools for studying biomedical, geophysical or climate time series. Here we study day-to-day market data, and Brownian motion which is a good model for their order patterns. A crucial point is that for small lags (1 up to 6 days), pattern frequencies in financial data remain essentially constant. The two most important order parameters of a time series are turning rate and up-down balance. For change points in EEG brain data, turning rate is excellent while for financial data, up-down balance seems the best. The fit of Brownian motion wi…

Properties of low variability periods in financial time series

Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of reveling more details about time-series than the traditional multi-affine analysis. We have applied this scaling analysis to financial time series: a number of daily currency and stock index time series. The results show a good scaling behaviour for different model parameters. The analysis of high-frequency USD-EUR …

Financial Time Series Prediction Using Deep Learning

In this work we present a data-driven end-to-end Deep Learning approach for time series prediction, applied to financial time series. A Deep Learning scheme is derived to predict the temporal trends of stocks and ETFs in NYSE or NASDAQ. Our approach is based on a neural network (NN) that is applied to raw financial data inputs, and is trained to predict the temporal trends of stocks and ETFs. In order to handle commission-based trading, we derive an investment strategy that utilizes the probabilistic outputs of the NN, and optimizes the average return. The proposed scheme is shown to provide s…

Clustering Financial Time Series: How Long is Enough?

Researchers have used from 30 days to several years of daily returns as source data for clustering financial time series based on their correlations. This paper sets up a statistical framework to study the validity of such practices. We first show that clustering correlated random variables from their observed values is statistically consistent. Then, we also give a first empirical answer to the much debated question: How long should the time series be? If too short, the clusters found can be spurious; if too long, dynamics can be smoothed out.

Non-Stationarity in Financial Time Series and Generic Features

Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe limitations for approaches in the spirit of standard equilibrium statistical mechanics and thermodynamics. Nevertheless, we show that there are similar generic features which we uncover in the empirical return distributions for whole markets. We explain our findings by setting up a random matrix model.

From turbulence to financial time series

We develop a framework especially suited to the autocorrelation properties observed in financial times series, by borrowing from the physical picture of turbulence. The success of our approach as applied to high frequency foreign exchange data is demonstrated by the overlap of the curves in Figure (1), since we are able to provide an analytical derivation of the relative sizes of the quantities depicted. These quantities include departures from Gaussian probability density functions and various two and three-point autocorrelation functions.

An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series

We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative) correlation. We show in an explorative study that both types of this dependence show up in real world financial data.

Quantile Correlations: Uncovering temporal dependencies in financial time series

We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After establishing an empirical overview we compare the quantile-based correlation function to stochastic processes from the GARCH family and find striking differences. This motivates us to propose the quantile-based correlation function as a powerful tool to assess the agreements between stochastic processes and empirical data.

Data Normalization for Bilinear Structures in High-Frequency Financial Time-series

Financial time-series analysis and forecasting have been extensively studied over the past decades, yet still remain as a very challenging research topic. Since the financial market is inherently noisy and stochastic, a majority of financial time-series of interests are non-stationary, and often obtained from different modalities. This property presents great challenges and can significantly affect the performance of the subsequent analysis/forecasting steps. Recently, the Temporal Attention augmented Bilinear Layer (TABL) has shown great performances in tackling financial forecasting problems…

On the non-stationarity of financial time series: impact on optimal portfolio selection

We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing to take into account po…

A study on the leverage effect on financial series using a TAR model: a Bayesian approach

This research shows that under certain mathematical conditions, a threshold autoregressive model (TAR) can represent the leverage effect based on its conditional variance function. Furthermore, the analytical expressions for the third and fourth moment of the TAR model are obtained when it is weakly stationary.

Simulating financial time series using attention

Financial time series simulation is a central topic since it extends the limited real data for training and evaluation of trading strategies. It is also challenging because of the complex statistical properties of the real financial data. We introduce two generative adversarial networks (GANs), which utilize the convolutional networks with attention and the transformers, for financial time series simulation. The GANs learn the statistical properties in a data-driven manner and the attention mechanism helps to replicate the long-range dependencies. The proposed GANs are tested on the S&P 500 in…

Modeling Financial Time Series using LSTM with Trainable Initial Hidden States

Extracting previously unknown patterns and information in time series is central to many real-world applications. In this study, we introduce a novel approach to modeling financial time series using a deep learning model. We use a Long Short-Term Memory (LSTM) network equipped with the trainable initial hidden states. By learning to reconstruct time series, the proposed model can represent high-dimensional time series data with its parameters. An experiment with the Korean stock market data showed that the model was able to capture the relative similarity between a large number of stock prices…

Scaling and multiscaling in financial series: a simple model

We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments. Despite its few parameters, the model is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with a remarkable a…

金融时间序列的依赖性度量

Measure of Dependence for Financial Time-Series

本文针对金融时间序列机器学习中准确准备数据和评估预测能力的难题，回顾并奠定了全面分析时间序列数据塑造及评估各种依赖性度量的基础，并提出了一种方法、框架及具体示例来选择和评估合适的依赖性度量。

Techniques for multifractal spectrum estimation in financial time series

Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both theoretical and practical point of view. Particularly, we discuss the methods based on estimation of Rényi entropy, which provide a powerful tool especially in presence of heavy-tailed data. To put some flesh on bare bones, all methods are compared on various real financial datasets, including daily and high-frequency data.

通过金融时间序列聚类实现普惠金融信贷产品

Towards Financially Inclusive Credit Products Through Financial Time Series Clustering

提出一种新颖的时间序列聚类算法，通过分析消费者交易数据理解其金融行为，帮助金融机构在不依赖传统信用评分的情况下提供普惠信贷、储蓄和保险产品。

金融数据因果推断与机制聚类中的时间序列 K-means

Time-Series K-means in Causal Inference and Mechanism Clustering for Financial Data

本文提出将基于 DTW 的 TS-K-means 融入 ANM-MM 框架，以提升金融时间序列的因果推断与机制聚类性能，并通过模拟和真实数据验证其优势。

Assessing symmetry of financial returns series

Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic Tn are also calculated and a procedure f…

Modelling of dependence in high-dimensional financial time series by cluster-derived canonical vines

We extend existing models in the financial literature by introducing a cluster-derived canonical vine (CDCV) copula model for capturing high dimensional dependence between financial time series. This model utilises a simplified market-sector vine copula framework similar to those introduced by Heinen and Valdesogo (2008) and Brechmann and Czado (2013), which can be applied by conditioning asset time series on a market-sector hierarchy of indexes. While this has been shown by the aforementioned authors to control the excessive parameterisation of vine copulas in high dimensions, their models ha…

Financial Time Series Analysis and Forecasting with HHT Feature Generation and Machine Learning

We present the method of complementary ensemble empirical mode decomposition (CEEMD) and Hilbert-Huang transform (HHT) for analyzing nonstationary financial time series. This noise-assisted approach decomposes any time series into a number of intrinsic mode functions, along with the corresponding instantaneous amplitudes and instantaneous frequencies. Different combinations of modes allow us to reconstruct the time series using components of different timescales. We then apply Hilbert spectral analysis to define and compute the associated instantaneous energy-frequency spectrum to illustrate t…

面向金融数据科学竞赛的多元时间序列数据特征工程方法

Feature Engineering Methods on Multivariate Time-Series Data for Financial Data Science Competitions

本文研究面向金融数据科学竞赛的多元时间序列特征工程方法，在美国市场价格数据上应用多种特征工程技术，并以Numerai-Signals目标检验模型预测能力，同时寻求股票/期货市场数据集以扩展基准研究。

A proposal of a methodological framework with experimental guidelines to investigate clustering stability on financial time series

We present in this paper an empirical framework motivated by the practitioner point of view on stability. The goal is to both assess clustering validity and yield market insights by providing through the data perturbations we propose a multi-view of the assets' clustering behaviour. The perturbation framework is illustrated on an extensive credit default swap time series database available online at www.datagrapple.com.

DELPHYNE：一种面向通用与金融时间序列的预训练模型

DELPHYNE: A Pre-Trained Model for General and Financial Time Series

针对现有时间序列预训练模型因金融数据不足和跨域负迁移而难以超越简单金融基准的问题，本文提出 Delphyne，仅需少量微调即可在公开数据集和多种金融任务上取得竞争优势。

Scaling transformation and probability distributions for financial time series

The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between non-linear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a non-…

Best linear forecast of volatility in financial time series

The autocorrelation function of volatility in financial time series is fitted well by a superposition of several exponents. Such a case admits an explicit analytical solution of the problem of constructing the best linear forecast of a stationary stochastic process. We describe and apply the proposed analytical method for forecasting volatility. The leverage effect and volatility clustering are taken into account. Parameters of the predictor function are determined numerically for the Dow Jones 30 Industrial Average. Connection of the proposed method to the popular ARCH models is discussed.

Style Transfer with Time Series: Generating Synthetic Financial Data

Training deep learning models that generalize well to live deployment is a challenging problem in the financial markets. The challenge arises because of high dimensionality, limited observations, changing data distributions, and a low signal-to-noise ratio. High dimensionality can be dealt with using robust feature selection or dimensionality reduction, but limited observations often result in a model that overfits due to the large parameter space of most deep neural networks. We propose a generative model for financial time series, which allows us to train deep learning models on millions of …

A multiscale view on inverse statistics and gain/loss asymmetry in financial time series

Researchers have studied the first passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to illustrate that this is a long rather than short time scale phenomenon -- if enough low frequency content of the price process is removed, the asymmetry disappears. We also propose a new model, which explain the asymmetry by prolonged, correlated…