Apparent Multifractality in Financial Time Series

In the paper we show how L-FABS can be applied in a partial knowledge learning scenario or a full knowledge learning scenario to approximate financial time series. L-FABS combines agent-based simulation with machine learning to model the behavior of financial time series.We also discuss why Partial Knowledge and Full Knowledge learning scenario are relevant to the modeling of financial time series and how they can be used to assess the robustness of a modeling system for financial time series. In a Partial Knowledge learning setting usually only the initial conditions of the time series are provided, while in a Full Knowledge learning scenario any value of the financial time series is exploited as soon as it is available.An extensive experimental analysis of L-FABS is reported under a variety of financial time series and time frames.

GMRVV m–SVR model for financial time series forecasting

Financial time series data is a cornerstone of investment strategy development, providing critical insights into market trends, asset performance, and risk assessment. This research explores the application of advanced statistical and machine learning models for analyzing financial time series data to optimize investment strategies. The study examines various techniques, including autoregressive integrated moving average (ARIMA), GARCH models for volatility forecasting, and recurrent neural networks (RNNs) for capturing temporal dependencies in financial data. By leveraging these models, the research aims to enhance the prediction of market behavior and identify profitable investment opportunities. It also investigates the integration of feature engineering and real-time data processing to improve model accuracy and adaptability. Challenges such as overfitting, non-stationarity, and the unpredictability of financial markets are addressed, along with the importance of ethical considerations in data-driven decision-making. The findings provide actionable insights into the effective use of financial time series models, offering a robust framework for data-driven investment strategy optimization.

The log‐returns of most financial assets exhibit bursts of outlying observations that are characteristic of heavy tails. As such, models formulated for financial time series must capture heavy‐tailedness. Regular variation is a natural and often used concept to describe and model heavy‐tailed phenomena. This article first provides some evidence for heavy tails in log‐returns and then describes the basics of regular variation. It turns out that the two most commonly used models for financial time series, the GARCH and heavy‐tailed stochastic volatility (SV) processes, have finite‐dimensional distributions that are regularly varying. Regular variation is also a powerful tool for deriving large sample properties of important statistics of financial time series, from maxima to sample autocorrelations of functions of the process. These techniques show that although GARCH and SV processes share many common features, there can be a substantial difference in the large sample properties of the maxima and sample autocorrelations.

Financial time series forecasting using rough sets with time-weighted rule voting

The main aim of this paper is presentation and empirical analysis of the new approach which combines volatility models with Peaks over Threshold method. The standard volatility models better estimate medium size values of financial times series. The new approach is based on possibility, that extremes are estimated using POT method, and medium values are estimated using standard volatility models. The contribution of this paper is analysis of the value-atrisk and the expected shortfall for this new approach. Financial risk model evaluation of this risk measures is one of the key part of this paper. Conditional tail estimates are obtained by adjusting the unconditional extreme value theory procedure with the returns filtered by standard volatility models (McNeil, Frey, 2000). Additionally, risk measures estimates obtained from volatility models with application of EVT versus those computed, using standard volatility models for financial time series are compared.

In this paper, we present a parametric modelling of financial time series using long memory k-factor Gegenbauer processes suggested by Gray et al. (1989) and known in the statistical literature as generalized long memory processes. Using forecasting performances of this kind of processes and recent results on estimation theory we show how on an application to the monthly time series of exchange rates for the French franc against the US dollar, we can improve the efficiency of the long-term forecasting process.Key wordsFinancial seriesforecastinggeneralized long memory processes

Forecasting economic and financial time-series with non-linear models

This paper continues research within the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics of the faculty of Economics of PSU. Modeling and prediction of financial time series is quite a perspective area of research, because it allows participants of financial processes to reduce risks and make effective decisions. For example, we could research financial processes with the help of fractal analysis. In the article there is studied and worked out in detail one of the methods of fractal analysis of financial time series – the box-counting method for assessment of the fractal dimension. This method is often used in studies conducted by domestic authors, but the authors do not delve into the characteristics and problems of using the box-counting method for analysis of time series, that means that the answers to the interested questions have not yet been given. The main problem is that, as a rule, the analyzed object in the tasks of applying the box-counting method to time series is a computer image of the plot of series. In the article there is proposed the procedure of adaptation of the box-counting method for assessment of the fractal dimension of time series, the procedure does not require the formation of a computer image of the plot. In the article there is considered following difficulties developed from this adaptation: 1) high sensitivity of the resulting estimation of the dimension to the input parameters of the method (the ratio of the sides of the covered by cells plane with the plot; the used range of lengths of the side of the cell; the number of partitions of the plane into cells); 2) the non-obviousness of choosing the optimal values ​​of these parameters. In the article there are analyzed approaches to the selection of these parameters that were proposed by other authors, and there are determined the most suitable approaches for the adapted box-counting method. Also there are developed unique methods for determining the ratio of the sides of the plane with the plot. In the paper there is written the computer program that implements the developed method, and this program is tested on the generated data. The study obtained the following results. The fact of sensitivity of the adapted box-counting method to input parameters is confirmed, that indicates the high importance of the correct choice of these parameters. According to the study, there is found out inability of the proposed methods of automatic determination the ratio of the sides of the plane in relation to artificial time series. There are obtained the most precise (in a statistical sense) estimates of fractal dimension, those found by means of the adapted box-counting method, with the fixed ratio of the sides 1:1. According to comparing the adapted box-counting method and R/S analysis, there are obtained the most precise estimates by the second method (R/S analysis). Finally in the paper there are formulated the possible directions for further research: 1) comparison of the accuracy of various methods for assessment of the fractal dimension on series of different lengths; 2) comparison of the methods of fractal analysis and p-adic analysis for modeling and prediction of financial time series; 3) determination of the conditions of applicability of various methods; 4) approbation of the developed methods for determining of the ratio of the sides of the plane with the plot on real economic data.

Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks

Volatility modelling of asset returns is an important aspect for many financial applications, e.g., option pricing and risk management. GARCH models are usually used to model the volatility processes of financial time series. However, multivariate GARCH modelling of volatilities is still a challenge due to the complexity of parameters estimation. To solve this problem, we suggest using Independent Component Analysis (ICA) for transforming the multivariate time series into statistically independent time series. Then, we propose the ICA-GARCH model which is computationally efficient to estimate the volatilities. The experimental results show that this method is more effective to model multivariate time series than existing methods, e.g., PCA-GARCH.KeywordsFinancial EngineeringGARCHICAMultivariate Time SeriesVolatility

Statistical tests of stochastic process models used in the financial theory of insurance companies

In this paper, based on the characteristics of real-time and time characteristics of financial data, time series is used as an entry point to mine financial data. Using the trigonometric polynomial graph method, the visualization of financial and economic cube data and the definition of clustering distance are carried out. Combined with wavelet analysis theory to decompose the periodic, trend and random terms of financial data time series, so as to predict the development of financial data with different scale components. In addition, BIRCH method is utilized to construct CF tree through data clustering features for micro-clustering of financial data. And K-meadiods method is chosen to fill the gap of BIRCH method in the application of large datasets to realize the macro-clustering of financial and economic data, and to establish BIRCH.K-meadiods clustering method. Compared with similar models, the prediction and clustering model of financial data based on time series has an overlap rate of >99.00% between the predicted and actual values of financial data and an error in the interval of (0,300), which can assist in the in-depth mining and clustering analysis of the value of financial data with high-precision prediction, and expand the level of decision-making considerations for the internal management of the enterprise and even for the external construction.

In this article, we conduct a statistical analysis of the autocorrelation functions (ACF) of multi-scale logarithmic returns computed over maximal monotonic uninterrupted trends (runs) in financial indices’ daily data. We analyze the Dow Jones Industrial Average (DJIA) and the Mexican IPC (Índice de Precios y Cotizaciones) over a period from 30 October 1978 to 19 May 2025. We examine how deterministic alternation of signs shapes the ACF of multi-scale returns, and we evaluate covariance stationarity via formal tests (e.g., Augmented Dickey–Fuller and Phillips–Perron). We conclude that, despite the persistent long-memory oscillations in the ACF, multi-scale return series pass the stationarity tests, an outcome with interesting implications for econometric modeling of financial time series.

We examine a variety of graphical models to construct optimal portfolios. Graphical models such as PCA-KMeans, autoencoders, dynamic clustering, and structural learning can capture the time varying patterns in the covariance matrix and allow the creation of an optimal and robust portfolio. We compared the resulting portfolios from the different models with baseline methods. In many cases our graphical strategies generated steadily increasing returns with low risk and outgrew the S&P 500 index. This work suggests that graphical models can effectively learn the temporal dependencies in time series data and are proved useful in asset management.