Narrow Results

The stability in stock markets is the theme of this work. It has been demonstrated that the random walk theory alone is insufficient to explain the dynamic behavior of asset or stock prices. Deviations from the random walk theory reveal collective behaviors that produce waves and patterns. Research has shown that the Fibonacci sequence and the golden ratio emerge in such dynamic systems, representing states of minimal stability. Their sustained stability is ensured by the presence of Landau damping within the system. The complex dynamics of the stock market can be analyzed by considering the exchanged shares as fluctuating and the unexchanged shares as nonfluctuating entities. The traders exhibit a kind of group oscillations that resemble the waves in physical plasma. At steady state, the waves can be expressed by a cosine term, and at the least stable state, the dynamics involves the golden ratio, such that the cosine of $36^{\circ }$ is equal to half of the golden ratio. Using the trigonometric cosine formula, it is possible to obtain other angles which are the multiples of $9^{\circ }$. They can be expressed in terms of the golden ratio, and they stand as Fibonacci angles. The stabilization is achieved by a mechanism so-called Landau damping, and the waves thus created are called Elliott waves, and they keep the system near the instability border. It was found that these angles appear quite often in the motive and corrective Elliott waves in the weekly price change of crude oil between January 2001 and June 2023. The percent occurrence of these angles increases through oscillations in motive waves with peaks at 18°, $45^{\circ }$ and 72°. The corrective wave has a maximum peak at 36°, and the percent occurrence decreases through oscillations having smaller peak values at 54° and 72°. The highest values are such that the motive waves appear at 50% in the bull market, and the corrective waves at 27.8% in the bear market.

This paper adopts the visibility graph (VG) methodology to analyze the dynamic behavior of West Texas Intermediate (WTI), Brent and Shanghai (SC) crude oil futures during the COVID-19 pandemic and Russia–Ukraine conflict. Utilizing daily and high-frequency data, our study reveals a clear power-law decay in VG degree distributions and highlights pronounced clustering tendencies within crude oil futures VGs. We also uncover an inverse correlation between clustering coefficients and node degrees, further identifying that all VGs adhere not only to the small-world property but also exhibit intricate assortative mixing. Through the time-varying characteristics of VGs, we observe that WTI and Brent demonstrate aligned behaviors, while the SC market, with its unique trading mechanisms, deviates. Notably, the five-minute assortativity coefficient provides deep insights into the markets reactions to these global challenges, underscoring the distinct sensitivity of each market.

Oil and natural gas are indispensable energy commodities. Investigating the evolution and transformation of energy market dynamics represented by oil and natural gas holds significant implications for global energy governance, as well as political and economic development. We have employed the visibility graph algorithm to transform the most intuitive and readily available time series data of oil and natural gas prices into complex networks. Then, three network embedding algorithms based on machine learning are utilized to embed the network into multidimensional vector spaces, enabling us to identify market state changes in both energy products through the sequential clustering method. We find that the visibility graph algorithm and network embedding methods effectively preserve internal structural characteristics of data, capture similarities between price change rate nodes across different trading days in the oil and gas markets, while also identifying the memorability of price volatility trends. Beyond simple price trends, critical market fluctuations such as those induced by events like the COVID-19 or Russia–Ukraine conflict can be discerned from similarity matrix partitions of network node representation vectors. Furthermore, the sequential clustering algorithm accurately identifies transition points in the oil and gas markets’ states. Unlike conventional time series analysis methods, this innovative combination of visibility graph and network embedding algorithms allows for a multi-faceted exploration of market state changes at various levels; thereby facilitating deeper insights into underlying logic behind price time series.

In the recent decade, engineering and technology have been developed rapidly, and new requirements are rising for engineering education. So, new and more focused departments are rising in the engineering faculty. The Turkish economy has been developed, and it is necessary to develop new technologies in industry based on the new investments. The scientific models are required to decide which engineering departments are necessary based on the socio-economic development of the economy. For this aim, we present a strategic analysis of which department can be established to meet the requirements in Turkey in light of the latest developments in the world. In the analysis stage, we listed engineering departments in the world universities and compared them with Turkish universities. We determined the selection criteria for the alternative departments, following these analyses and their related data collected from the Turkish Statistical Institute’s website. We used the new impulse and momentum principle-based weight assignment procedure integrated Technique for Order Preferences by Similarity to the Ideal Solution (IMP-TOPSIS) method to rank alternative departments using different scenarios. We concluded that Artificial Intelligence Engineering is the most suitable alternative. In addition, Aerospace Engineering has the second importance, and Materials Science and Nanotechnology Engineering have the third importance, according to the obtained results.

On 1 January 1999, the European Union introduced a common currency Euro (EUR), to become the legal currency in all eleven countries which form the EUR. In order to test the EUR behavior and understand various features, the EUR exchange rate is artificially extrapolated back to 1993 by a linear superposition of the exchange rates of the 11 currencies composing EUR with respect to several currencies not belonging to the EUR, i.e., Swiss Franc (CHF), Danish Kroner (DKK), British Pound (GBP), Japanese Yen (JPY) and U.S. Dollar (USD) of interest for reasons given in the text. The distribution of fluctuations of the exchange rates is shown to be Gaussian for the central part of the distribution, and having fat tails for the large size fluctuations. Within the Detrended Fluctuation Analysis (DFA) statistical method, we have obtained the power law behavior describing the root-mean-square deviation of the exchange rate fluctuations as a function of time. For the period between January 1995 and January 1999, we have compared the time-dependent exponent of these exchange rate fluctuations for EUR and that of the 11 currencies which form the EUR. The German Mark (DEM) and the French Franc (FRF) have been the currencies primarily leading the fluctuations of the exchange rates, while Italian Lira (ITL) and Portuguese Escudo (PTE) are the less relevant currencies from this point of view. Technical considerations for the EUR implementation are given as conclusions. The cases of exchange rates with DKK appear quite different from the other four major currencies.

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0 < α ≤ 2). In this paper, we illustrate that widely used tail index estimates (log–log linear regression and Hill) can give exponents well above the asymptotic limit for α close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent α around 3 may very well indicate a Levy-stable distribution with α ≈ 1.8.

A simple spin model is studied, motivated by the dynamics of traders in a market, where expectation bubbles and crashes occur. The dynamics is governed by interactions, which are frustrated across different scales: while ferromagnetic couplings connect each spin to its local neighborhood, an additional coupling relates each spin to the global magnetization. This new coupling is allowed to be anti-ferromagnetic. The resulting frustration causes a metastable dynamics with intermittency and phases of chaotic dynamics. The model reproduces main observations of real economic markets as power-law distributed returns and clustered volatility.

We study a variant of the Cont–Bouchaud model, which utilizes the percolation approach of multi-agent simulations of the stock market fluctuations. Here, instead of considering the relative price change as the difference of the total demand and total supply, we consider the relative price change to be proportional to the "relative" difference of demand and supply (the ratio of the difference in total demand and total supply to the sum of the total demand and total supply). We then study the probability distribution of the price changes.

A simple Ising spin model, which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.

A generalization of the Cont–Bouchaud market model to three markets agrees with the correlations between New York, Tokyo, and Frankfurt as observed by Vandewalle et al.

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financial market. We recognize the power law distribution of contagion sizes in 3d- and 4d-networks as an indicator of SOC behavior. The SOC dynamics was not detected in 2d-lattices. The difference between 2d- and 3d- or 4d-systems is explained due to the percolation theory.

We empirically investigate distributions of individual consumption expenditure for four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. We use graphical techniques to test for normality and lognormality of these distributions. While prevailing economic theory does not predict any structure for these distributions, we find that in at least three commodity categories individual consumption expenditure conditional on a fixed income level is lognormally distributed.

A nonlinear differential equation of Sornette–Ide type with noise, for a complex variable, yields endogenous crashes, preceded by roughly log-periodic oscillations in the real part, and a strong increase in the imaginary part. The latter is interpreted as the trader expectation.

A new model for stock markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how the behavior of the noise and fundamentalists traders can be taken into account simultaneously in the time evolution of each stock price. The simulated time series generated by the model is analyzed in different ways order to compare parameters with those of real markets.

We consider a variant of the so-called Bornholdt spin model of a market dynamics, in which the random couplings with neighbors are incorporated. We observe that the occurrence of high returns decreases with a power law as the number of market participants becomes large up to three dimension.

We assume the market price to diffuse in a hierarchical comb of barriers, the heights of which represent the importance of new information entering the market. We find fat tails with the desired exponent for the price change distribution, and effective multifractality for intermediate times.

We study the distributions of money in a simple closed economic system for different types of monetary transactions. We know that for arbitrary and random sharing with locally conserving money transactions, the money distribution goes to the Gibb's distribution of statistical mechanics. We then consider the effects of savings, etc. and see how the distribution changes. We also propose a new model where the agents invest equal amounts of money in each transaction. We find that for short time-period, the money distribution obeys a power-law with an exponent very close to unity, and has an exponential tail; after a very long time, this distribution collapses and the entire amount of money goes to a tiny fraction of the population.

We simulate the interplay between productive and financial activity using a model that considers equal opportunities among individuals of a society. As the simulation evolves in time, three qualitative wealth distribution profiles are generated according to the flux of productive capital. We relate these curves to different socioeconomic structures: a primitive equalitarian society; a medieval society having a distribution of wealth with castes and discontinuities; and a modern society where this distribution is roughly exponential.

The traditional Sznajd model, as well as its Ochrombel simplification for opinion spreading, is applied to marketing with the help of advertising. The larger the lattice, the smaller the amount of advertising is needed to convince the whole market.

This note explores the consequences of nonlinear price impact functions on price dynamics within the chartist–fundamentalist framework. Price impact functions may be nonlinear with respect to trading volume. As indicated by recent empirical studies, a given transaction may cause a large (small) price change if market depth is low (high). Simulations reveal that such a relationship may create endogenous complex price fluctuations even if the trading behavior of chartists and fundamentalists is linear.