Mathematics

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12 pages, 1542 KiB

Open AccessArticle

Using Market News Sentiment Analysis for Stock Market Prediction

by Marian Pompiliu Cristescu, Raluca Andreea Nerisanu, Dumitru Alexandru Mara and Simona-Vasilica Oprea

Mathematics 2022, 10(22), 4255; https://doi.org/10.3390/math10224255 - 14 Nov 2022

Cited by 15 | Viewed by 11847

(1) Background: Since the current crises that has inevitably impacted the financial market, market prediction has become more crucial than ever. The question of how risk managers can more accurately predict the evolution of their portfolio, while taking into consideration systemic risks brought [...] Read more.

(1) Background: Since the current crises that has inevitably impacted the financial market, market prediction has become more crucial than ever. The question of how risk managers can more accurately predict the evolution of their portfolio, while taking into consideration systemic risks brought on by a systemic crisis, is raised by the low rate of success of portfolio risk-management models. Sentiment analysis on natural language sentences can increase the accuracy of market prediction because financial markets are influenced by investor sentiments. Many investors also base their decisions on information taken from newspapers or on their instincts. (2) Methods: In this paper, we aim to highlight how sentiment analysis can improve the accuracy of regression models when predicting the evolution of the opening prices of some selected stocks. We aim to accomplish this by comparing the results and accuracy of two cases of market prediction using regression models with and without market news sentiment analysis. (3) Results: It is shown that the nonlinear autoregression model improves its goodness of fit when sentiment analysis is used as an exogenous factor. Furthermore, the results show that the polynomial autoregressions fit better than the linear ones. (4) Conclusions: Using the sentiment score for market modelling, significant improvements in the performance of linear autoregressions are showcased. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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11 pages, 361 KiB

Open AccessArticle

Is Jump Robust Two Times Scaled Estimator Superior among Realized Volatility Competitors?

by Maria Čuljak, Josip Arnerić and Ante Žigman

Mathematics 2022, 10(12), 2124; https://doi.org/10.3390/math10122124 - 18 Jun 2022

Cited by 1 | Viewed by 2055

Abstract

This paper compares the empirical performance of the realized volatility estimators on an extensive high-frequency dataset of stock indices from four developed European markets with thick trading and intensive intraday activity. Even though the proposed estimators have distinctive properties, it is not clear [...] Read more.

This paper compares the empirical performance of the realized volatility estimators on an extensive high-frequency dataset of stock indices from four developed European markets with thick trading and intensive intraday activity. Even though the proposed estimators have distinctive properties, it is not clear which one has a better performance in terms of unbiasedness and consistency. Some of them are robust to microstructure noise only, and others are robust solely to price jumps, whereas a few of them are robust to both. Therefore, the main purpose is finding a benchmark estimator among alternative competitors, as the best proxy of integrated variance, and empirical demonstration of its superiority. The vast majority of the existing studies largely rely on developed US data or simulation data, but inferences obtained on such data might deviate from European developed markets. This study aims to fill in that niche. In particular, the optimal sampling frequency of proposed benchmark estimator is determined with respect to the trade-off between its bias and the variance of each stock index individually. Afterwards, probability integral transformation, Mincer–Zarnowitz regression and upper tail correlation from appropriate copula function are considered as an adequate pairwise comparison methods. Notable contributions of this paper include unambiguously proven superiority of robust two times scaled estimator for selected European developed markets within the range of optimal slow time frequency from 10 to 30 s. Finally, recommendations for research and practitioners regarding the usage of jump robust two times scaled estimator are given. In fact, asset managers, institutional investors as well as market regulators could benefit from proposed realized volatility benchmark in making long-term investment decisions, leading to sustainable finance. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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20 pages, 624 KiB

Open AccessArticle

Mathematical Modeling and Methodology for Assessing the Pace of Socio-Economic Development of the Russian Federation

by Victor Orlov, Tatyana Ivanova, Tatyana Ladykova and Galina Sokolova

Mathematics 2022, 10(11), 1869; https://doi.org/10.3390/math10111869 - 30 May 2022

Cited by 3 | Viewed by 1813

Abstract

The article develops the author’s methodology for assessing the rates of socio-economic development and their forecasting in the Russian Federation, which makes it possible to consider factors with heterogeneous metrics. For this, an index analysis of thirty-two indicators divided into seven macro-regional blocks [...] Read more.

The article develops the author’s methodology for assessing the rates of socio-economic development and their forecasting in the Russian Federation, which makes it possible to consider factors with heterogeneous metrics. For this, an index analysis of thirty-two indicators divided into seven macro-regional blocks (income, labor, business, ecology, society, prospects, finance) was carried out, integral indicators were calculated that characterize their changes and the pace of socio-economic development of the Russian Federation was determined. Further, using the means of mathematical modeling, a multifactorial mathematical model was built and tested in real-time, which makes it possible to obtain a high-quality predicted result. Based on the forecasts obtained, it can be stated that it is necessary to adjust certain indicators that actively influence the pace of development, which is a mathematical justification for making managerial decisions when developing strategies and programs related to socio-economic progress in the Russian Federation. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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23 pages, 5508 KiB

Open AccessArticle

Geometric Brownian Motion (GBM) of Stock Indexes and Financial Market Uncertainty in the Context of Non-Crisis and Financial Crisis Scenarios

by Vasile Brătian, Ana-Maria Acu, Diana Marieta Mihaiu and Radu-Alexandru Șerban

Mathematics 2022, 10(3), 309; https://doi.org/10.3390/math10030309 - 19 Jan 2022

Cited by 8 | Viewed by 6049

Abstract

The present article proposes a methodology for modeling the evolution of stock market indexes for 2020 using geometric Brownian motion (GBM), but in which drift and diffusion are determined considering two states of economic conjunctures (states of the economy), i.e., non-crisis and financial [...] Read more.

The present article proposes a methodology for modeling the evolution of stock market indexes for 2020 using geometric Brownian motion (GBM), but in which drift and diffusion are determined considering two states of economic conjunctures (states of the economy), i.e., non-crisis and financial crisis. Based on this approach, we have found that the GBM proved to be a suitable model for making forecasts of stock market index values, as it describes quite well their future evolution. However, the model proposed by us, modified geometric Brownian motion (mGBM), brings some contributions that better describe the future evolution of stock indexes. Evidence in this regard was provided by analyzing the DAX, S&P 500, and SHANGHAI Composite stock indexes. Throughout the research, it was also found that the entropy of these markets, analyzed in the periods of non-crisis and financial crisis, does not differ significantly for DAX—German Stock Exchange (EU) and S&P 500—New York Stock Exchange (US), and insignificant differences for SHANGHAI Composite—Shanghai Stock Exchange (Asia). Given the fact that there is a direct link between market efficiency and their entropy (high entropy—high efficiency; low entropy—low efficiency), it can be deduced that the analyzed markets are information-efficient in both economic conjunctures, and, in this case, the use of GBM for forecasting is justified, as the prices have a random evolution (random walk). Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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20 pages, 33261 KiB

Open AccessArticle

Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

by Vasile Brătian, Ana-Maria Acu, Camelia Oprean-Stan, Emil Dinga and Gabriela-Mariana Ionescu

Mathematics 2021, 9(22), 2983; https://doi.org/10.3390/math9222983 - 22 Nov 2021

Cited by 6 | Viewed by 4258

Abstract

In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes [...] Read more.

In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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18 pages, 335 KiB

Open AccessArticle

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

by Ivan Arraut, João Alexandre Lobo Marques and Sergio Gomes

Mathematics 2021, 9(21), 2777; https://doi.org/10.3390/math9212777 - 2 Nov 2021

Cited by 3 | Viewed by 2038

Abstract

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the [...] Read more.

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

19 pages, 4680 KiB

Open AccessArticle

Analysing the Stock Market as an Economic Lever, Using a Qualitative and a Quantitative Model

by Marian-Pompiliu Cristescu, Raluca-Andreea Nerișanu, Maria Flori, Florin Stoica and Florentina Laura Stoica

Mathematics 2021, 9(19), 2369; https://doi.org/10.3390/math9192369 - 24 Sep 2021

Cited by 2 | Viewed by 3017

Abstract

The article aims to provide a perspective on economic growth by relying on the influence and use of the stock market as an economic lever. Two methods will be used: a quantitative one, determined by a multiple linear regression model, and a qualitative [...] Read more.

The article aims to provide a perspective on economic growth by relying on the influence and use of the stock market as an economic lever. Two methods will be used: a quantitative one, determined by a multiple linear regression model, and a qualitative one that encumbers a sustainable vector model for generating economic growth. The data panel covers 36 states, for a period of 21 years. The paper manages to identify the main control functions that the stock exchange has over the macroeconomic context, through the quantitative and qualitative method, and to highlight the most important positive and negative attributes of using qualitative methods, in contrast to quantitative ones. The results show a predominant probabilistic characteristic of quantitative methods, in contrast to the flexibility and complexity of the qualitative method, which has been used. Additionally, the quantitative method offers a strictly cartesian perspective for determining future scenarios, while the sustainable vector model, based on a fractalized vision of reality, manages to capture a plurality of perspectives, as well as the interrelationships between the determining parameters, thus being a complex system of simple equations, as opposed to the quantitative method which is defined as a simple system of complex equations. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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13 pages, 488 KiB

Open AccessEditor’s ChoiceArticle

Nonlinearities and Chaos: A New Analysis of CEE Stock Markets

by Claudiu Tiberiu Albulescu, Aviral Kumar Tiwari and Phouphet Kyophilavong

Mathematics 2021, 9(7), 707; https://doi.org/10.3390/math9070707 - 25 Mar 2021

Cited by 15 | Viewed by 2766

Abstract

After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for [...] Read more.

After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for nonlinear and chaotic behavior, we look for the presence of nonlinearities and chaos in five CEE stock markets. We document, in general, the presence of nonlinearities and chaos which questions the efficient market hypothesis. However, if all tests highlight a chaotic behavior for the analyzed index returns, there are noteworthy differences between the analyzed stock markets underlined by nonlinearity tests, which question, thus, their level of significance. Moreover, the results of nonlinearity tests partially contrast the previous findings reported in the literature on the same group of stock markets, showing, thus, a change in their recent behavior, compared with the 1990s. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)

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