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This study endeavors to introduce a method for measuring stock market investment risk, leveraging data mining techniques alongside decision trees (DTs). By harnessing extensive stock market data and integrating steps such as data cleaning, feature selection, and model construction within data mining technology, an effective risk measurement model is formulated. Specifically, DTs serve as the primary modeling tool, adept at capturing intricate relationships and nonlinear characteristics prevalent within the stock market, thereby facilitating precise measurement of investment risks. Through empirical analysis, the efficacy and viability of the proposed method in risk measurement are substantiated, furnishing investors with a pivotal decision-making reference. Overall, this study contributes to the ongoing discourse on stock market risk assessment by integrating advanced data mining methodologies, thereby enhancing the accuracy and reliability of risk evaluation in investment decision-making processes.

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.

Artificial Neural Networks (ANNs) has been used as a powerful modeling technique for forecasting. In this study, the relationship between multiples and stock prices has been investigated on the Pakistan Stock Exchange 100 Index by incorporating financial modeling through neural network. The aim is to develop multiple-based valuation model to check whether multiples are viable factor in predicting stock movements. Forecasting model has been developed by using neural network. Prediction accuracy of the developed forecasting model has been evaluated. Findings reveal that neural network outperforms in comparison to linear regression and forecasts stock prices with 98% accuracy.

This study explores the return and volatility spillovers between S&P 500 and cryptocurrencies [Litecoin (LTC), Bitcoin (BTC) and Ethereum (ETH)] during the pre-COVID-19 period and COVID-19 period using the VAR–BEKK–AGARCH model on hourly data. Furthermore, this study also quantifies the optimal portfolio weights and hedge ratios during both sample periods. The findings of study show that the return and volatility spillovers between the US stock and cryptocurrency markets are not significant during the pre-COVID-19 period. However, the study finds unidirectional return transmission from S&P 500 to all the cryptocurrencies during the COVID-19 period. During the COVID-19 period, the volatility spillover is unidirectional from S&P 500 to Litecoin, whereas the volatility transmissions are not significant for the pairs of S&P 500–Bitcoin and S&P 500–Ethereum. Based on optimal weights, the portfolio managers are recommended to slightly decrease their investments in S&P 500 for the portfolios of S&P 500/BTC, S&P 500/ETH and S&P 500/LTC during the COVID-19 period. Finally, during the COVID-19 period, all hedge ratios were found to be higher, implying higher hedging costs during the COVID-19 period compared to the pre-COVID-19 period. Our research offers valuable insights to the fund managers, investors and policymakers regarding diversification opportunities, hedging, optimal asset allocation and risk management.

This paper estimates the smooth transition autoregressive model with exogenous variables to evaluate the effects of stock market returns on the exchange-traded funds’ (ETFs) returns in China with reserve requirement ratio (RRR) from monetary policy as a transition variable. The sample used in this study lasts from March 4, 2005 to June 30, 2017. The empirical result points out that there is the effect of RRR value on the relationship between stock market returns and ETF return. Moreover, these effects are variable depending on the conversion and its changes over time in different variations of threshold intervals. Lastly, the larger the change of China’s stock market variables’ lag period, the smaller the impacts on Chinese ETF return.

We analyze the connectedness between the sentiment index and the return and volatility of the crude oil, stock and gold markets by employing the time-varying parameter vector autoregression model vis-à-vis the coronavirus disease (COVID-19) epidemic. Our sentiment index is constructed via text mining technology. We also employ a network to visualize and better understand the structure of the connectedness. The results confirm that the sentiment index is the net pairwise directional connectedness receiver, while the infectious disease equity market volatility tracker is the transmitter. Furthermore, the impact of the COVID-19 pandemic on the total connectedness of volatility is unprecedented.

This paper explores the return connectedness among energy and financial markets in China and the US pre and during the COVID-19 pandemic. We find that the spillovers during COVID-19 were obviously higher than normal period, and before COVID-19, the total spillover effects of Chinese markets are larger than that of the US, while during the COVID-19, the situation is just the opposite. Second, before COVID-19, crude oil, fuel oil, gold, and silver are the main net contributors, gasoline, natural gas, platinum, equities, and exchange rate are the main receivers. However, in the context of the COVID-19 pandemic, the roles of crude oil, gold, gasoline, and platinum as net contributors or net recipients experienced a reversal. Third, during the COVID-19, in the US, the strongest net contributor shifts from gold to fuel oil. In China, silver always be the strongest net contributor. The above findings suggest that policymakers are advised to promptly adjust regulatory policies, and investors should adopt a discerning approach to asset allocation.

This work explores the use of the Higuchi fractal dimension (HFD) to characterize the complexity of the Standard and Poor’s (S&P) Index for the period from 1928 to 2023. It is found that the fractal dimension is not constant but exhibits large time fluctuations. In line with adaptive market hypothesis notions, such a feature can be seen as the response of the stock market to a complex and changing environment formed by a diversity of participants and exogenous shocks. The concept of fractal dimension was extended to consider scale dependence and multifractality. It is shown that the fractality dimension approaches an integer value when the time scale increases, which reflects smoother price fluctuation profiles. It was also shown that the multifractal HFD exhibits large fluctuations for scales of weeks, months, and quarters, which can be linked to the seasonal periods of the operation of the stock market. The impact of salient events was also assessed. It was found that the 1987 and 2008 market crashes had the highest effect on the multifractal HFD, suggesting that these events involved multiple factors. Overall, the results in the present work showed that the fractal dimension tools and notions provide a useful and complementary framework for characterizing the behavior of financial indices.

We formulate a microscopic model of the stock market and study the resulting macroscopic phenomena via simulation. In a market of homogeneous investors periodic booms and crashes in stock price are obtained, When there are two types of investors in the market, differing only in their memory spans, we observe sharp irregular transitions between eras where one population dominates the market and eras where the other population dominates. When the number of investor subgroups is three the market undergoes a dramatic qualitative change — it becomes complex. We show that complexity is an intrinsic property of the stock market. This suggests an alternative to the widely accepted but empirically questionable random walk hypothesis.

In this empirical paper we show that in the months following a crash there is a distinct connection between the fall of stock prices and the increase in the range of interest rates for a sample of bonds. This variable, which is often referred to as the interest rate spread variable, can be considered as a statistical measure for the disparity in lenders' opinions about the future; in other words, it provides an operational definition of the uncertainty faced by economic agents. The observation that there is a strong negative correlation between stock prices and the spread variable relies on the examination of eight major crashes in the United States between 1857 and 1987. That relationship which has remained valid for one and a half century in spite of important changes in the organization of financial markets can be of interest in the perspective of Monte Carlo simulations of stock markets.

In January 1999, the authors published a quantitative prediction that the Nikkei index should recover from its 14-year low in January 1999 and reach ≈20 500 a year later. The purpose of the present paper is to evaluate the performance of this specific prediction as well as the underlying model: the forecast, performed at a time when the Nikkei was at its lowest (as we can now judge in hindsight), has correctly captured the change of trend as well as the quantitative evolution of the Nikkei index since its inception. As the change of trend from sluggish to recovery was estimated quite unlikely by many observers at that time, a Bayesian analysis shows that a skeptical (resp. neutral) Bayesian sees prior belief in our model amplified into a posterior belief 19 times larger (resp. reach the 95% level).

We present a simple and general result that the sign of the variations or increments of uncorrelated times series are predictable with a remarkably high success probability of 75% for symmetric sign distributions. The origin of this paradoxical result is explained in details. We also present some tests on synthetic, financial and global temperature time series.

Price changes of the primary index of the Australian Stock Market are analyzed over a period of about 20 years. The probability distribution of the relative changes in the index (returns) satisfies a distribution which is almost independent of the time interval chosen to measure the change. The distribution is consistent with the analysis of New York and other stock exchanges and also seems to satisfy a power law with exponent consistent with an inverse cubic law. If the data are separated into positive and negative returns this conclusion is not justified, particularly for the rising market. Thus there seems to be a significant asymmetry in the distribution.

We use econophysics techniques to investigate the characteristics of the distribution of returns from the All Ordinaries Index and from optimal portfolios constructed from individual stocks on the Australian Stock Exchange. We find in general that the tails of the distributions are asymmetric and that the negative tail favours a power-law behaviour while the positive tail is more Gaussian.

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stock prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.

This paper discusses the initial value sensitivity (IVS) of Chinese stock market, including the single stock market and the Chinese A-share stock market, with respect to real markets and evolving models. The aim is to explore the relationship between IVS of the Chinese A-share stock market and the investment psychology based on the evolving model of genetic cellular automaton (GCA). We find: (1) The Chinese stock market is sensitively dependent on the initial conditions. (2) The GCA model provides a considerable reliability in complexity simulation (e.g. the IVS). (3) The IVS of stock market is positively correlated with the imitation probability when the intensity of the imitation psychology reaches a certain threshold. The paper suggests that the government should seek to keep the imitation psychology under a certain level, otherwise it may induce severe fluctuation to the market.

In this study, we utilize the coherence spectrum and structure-function methods to examine the multi-scale coherence and multifractal characteristics of financial time series. The phase spectrum reveals the temporal shift between two indices, indicating whether one leads or lags by several days within a region of high correlation that is scale-dependent. This information can serve as a predictive model for quantitative analysis. The Fourier power spectrum and scaling exponents, derived from the structure-function method, exhibit universal patterns across indices from various countries. Our findings suggest that stock market indices display behavior akin to turbulence, as demonstrated by the structure-function, power-law scaling and multifractal movements. Our results suggest that the fluctuations of indices could be accurately represented by a multifractal random walk model, offering a complex and insightful view of the financial market.

The stock market model of Levy, Persky, Solomon is simulated for much larger numbers of investors. While small markets can lead to realistically looking prices, the resulting prices of large markets oscillate smoothly in a semi-regular fashion.

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

We propose that the herding behavior of traders leads not only to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to "anti-bubbles" with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price characterized by decelerating log-periodic oscillations. We document this behavior of the Japanese Nikkei stock index from 1990 to present and of the gold future prices after 1980, both after their all-time highs. We perform simultaneously parametric and nonparametric analyses that are fully consistent with each other. We extend the parametric approach to the next order of perturbation, comparing the log-periodic fits with one, two and three log-frequencies, the latter providing a prediction for the general trend in the coming years. The nonparametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a preferred scale ratio of λ≈3.5 for the Nikkei index and λ≈1.9 for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.