Multifractal Behaviors of Stock Indices and Their Ability to Improve Forecasting in a Volatility Clustering Period

The financial market is a complex system, which has become more complicated due to the sudden impact of the COVID-19 pandemic in 2020. As a result there may be much higher degree of uncertainty and volatility clustering in stock markets. How does this “black swan” event affect the fractal behaviors of the stock market? How to improve the forecasting accuracy after that? Here we study the multifractal behaviors of 5-min time series of CSI300 and S&P500, which represents the two stock markets of China and United States. Using the Overlapped Sliding Window-based Multifractal Detrended Fluctuation Analysis (OSW-MF-DFA) method, we found that the two markets always have multifractal characteristics, and the degree of fractal intensified during the first panic period of pandemic. Based on the long and short-term memory which are described by fractal test results, we use the Gated Recurrent Unit (GRU) neural network model to forecast these indices. We found that during the large volatility clustering period, the prediction accuracy of the time series can be significantly improved by adding the time-varying Hurst index to the GRU neural network.     

The relationships between Shanghai stock market and CNY/USD exchange rate: New evidence based on cross-correlation analysis,structural cointegration and nonlinear causality test

This paper explores the co-movement of Shanghai stock market and China Yuan (CNY) exchange rates. First, we find that stock price and exchange rate are significantly cross-correlated. Second, employing a cointegration test allowing for a structural break, we find that the Shanghai Composite Index (SCI) is not cointegrated with the exchange rate of CNY/USD. The so-called “cointegration” found in previous studies is just caused by the shock of the recent financial crisis. Third, using linear and nonlinear Granger causality tests, we find no causality between stock prices and exchange rates during the period before the recent financial crisis. After the financial crisis, a unidirectional causality behavior running from exchange rates to stock index is present.     

Empirical behavior of a world stock index from intra-day to monthly time scales

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Student t distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5min horizon they originate in the foreign exchange market. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock index.     

Estimating time-varying conditional correlations between stock and foreign exchange markets

This study explores the dynamic interaction between stock market returns and changes in nominal exchange rates. Many financial variables are known to exhibit fat tails and autoregressive variance structure. It is well-known that unconditional covariance and correlation coefficients also vary significantly over time and multivariate generalized autoregressive model (MGARCH) is able to capture the time-varying variance-covariance matrix for stock market returns and changes in exchange rates. The model is applied to daily Euro-Dollar exchange rates and two stock market indexes from the US economy: Dow-Jones Industrial Average Index and S&P500 Index. The news impact surfaces are also drawn based on the model estimates to see the effects of idiosyncratic shocks in respective markets.     

基于格兰杰因果网络的中美贸易战对上证行业冲击的研究

中美贸易战对行业冲击是普遍关注的问题,本文选取2016年8月—2019年10月的上证行业指数,构建了格兰杰因果关系网络,然后结合事件分析法对风险传播模型的参数进行估计,最后利用蒙特卡罗算法模拟行业受到贸易战冲击后金融风险传播情况,并计算贸易战发生前后的上证股市金融网络风险传播的基本再生数.研究发现:第一,贸易战明显改变了上证行业关系结构,行业指数之间联系变得更为紧密;第二,贸易战发生初期,受美国加征关税影响,上证股市感染节点数量迅速增加,并且感染规模会在第10—15个交易日内达到峰值,感染节点数量大约在第25个交易日后开始趋于平缓,市场逐渐恢复;第三,基本再生数计算结果表明,上证股市在贸易战发生初期金融风险传播较快,上证股市容易产生“同涨同跌”的现象.     

Data Rate Aware Reliable Transmission Mechanism in Wireless Sensor Networks using Bayesian Regularized Neural Network approach

Wireless Sensor Networks consists of interconnected nodes that exchange information wirelessly enabling its deployment in innovative application areas. Network reliability streamline this exchange of information and communication technology to improve the overall performance of the network. The network reliability is categorized as: node reliability and link reliability. In this article, the node reliability is quantified with the help of packet reliability. The packet reliability is enhanced by optimizing the data rate using Bayesian Regularized Neural Network approach, which thus makes the network more reliable and sustainable. The optimization is carried out in three phases: network designing, data rate prediction and reliability evaluation. The network design includes the deployment of sensor nodes for gathering the communication data using NS-2.35. In the next phase, data rate prediction is carried out to enhance the reliability of the network. The reliability of a network is directly influenced by the packet loss ratio. According to research and the network experts, the acceptable threshold limit for the packet loss ratio is 5 percent. The data rate prediction is carried out to minimize the packet loss using the Bayesian Regularized Neural Network algorithm. The packet reliability is measured in terms of packet loss across the wireless network. Finally, a novel framework is presented for evaluating the packet reliability of the wireless network.     

Neural Networks for Estimating Speculative Attacks Models

Currency crises have been analyzed and modeled over the last few decades. These currency crises develop mainly due to a balance of payments crisis, and in many cases, these crises lead to speculative attacks against the price of the currency. Despite the popularity of these models, they are currently shown as models with low estimation precision. In the present study, estimates are made with first- and second-generation speculative attack models using neural network methods. The results conclude that the Quantum-Inspired Neural Network and Deep Neural Decision Trees methodologies are shown to be the most accurate, with results around 90% accuracy. These results exceed the estimates made with Ordinary Least Squares, the usual estimation method for speculative attack models. In addition, the time required for the estimation is less for neural network methods than for Ordinary Least Squares. These results can be of great importance for public and financial institutions when anticipating speculative pressures on currencies that are in price crisis in the markets.     

Market efficiency in foreign exchange markets

We investigate the relative market efficiency in financial market data, using the approximate entropy(ApEn) method for a quantification of randomness in time series. We used the global foreign exchange market indices for 17 countries during two periods from 1984 to 1998 and from 1999 to 2004 in order to study the efficiency of various foreign exchange markets around the market crisis. We found that on average, the ApEn values for European and North American foreign exchange markets are larger than those for African and Asian ones except Japan. We also found that the ApEn for Asian markets increased significantly after the Asian currency crisis. Our results suggest that the markets with a larger liquidity such as European and North American foreign exchange markets have a higher market efficiency than those with a smaller liquidity such as the African and Asian markets except Japan.     

Financial Return Distributions: Past,Present, and COVID-19

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.     

Simultaneous Determination of Multicomponents in Air Toxic Organic Compounds Using Artificial Neural Networks in Ftir Spectroscopy

The application of Artificial Neural Networks (ANNs) for nonlinear multivariate calibration using simulated FTIR data was demonstrated in this paper. Neural networks consisting of three layers of nodes were trained by using the back-propagation learning rule. Since parameters affect the performance of the network greatly, simulated data were used to train the network in order to get a satisfactory combination of all parameters. The mixtures of four air toxic organic compounds whose FTIR spectra are overlapped were chosen to evaluate the calibration and prediction ability of the network. The relative standard error (RSD%), the percent standard error of prediction samples (%SEP) and the percent standard error of calibration samples (%SEC) are used for evaluating the ability of the neural network.     

Cross-sample entropy of foreign exchange time series

The correlation of foreign exchange rates in currency markets is investigated based on the empirical data of DKK/USD, NOK/USD, CAD/USD, JPY/USD, KRW/USD, SGD/USD, THB/USD and TWD/USD for a period from 1995 to 2002. Cross-SampEn (cross-sample entropy) method is used to compare the returns of every two exchange rate time series to assess their degree of asynchrony. The calculation method of confidence interval of SampEn is extended and applied to cross-SampEn. The cross-SampEn and its confidence interval for every two of the exchange rate time series in periods 1995-1998 (before the Asian currency crisis) and 1999-2002 (after the Asian currency crisis) are calculated. The results show that the cross-SampEn of every two of these exchange rates becomes higher after the Asian currency crisis, indicating a higher asynchrony between the exchange rates. Especially for Singapore, Thailand and Taiwan, the cross-SampEn values after the Asian currency crisis are significantly higher than those before the Asian currency crisis. Comparison with the correlation coefficient shows that cross-SampEn is superior to describe the correlation between time series.     

Tests of the random walk hypothesis for financial data

We propose a method from the viewpoint of deterministic dynamical systems to investigate whether observed data follow a random walk (RW) and apply the method to several financial data. Our method is based on the previously proposed small-shuffle surrogate method. Hence, our method does not depend on the specific data distribution, although previously proposed methods depend on properties of the data distribution. The data we use are stock market (Standard & Poor's 500 in US market and Nikkei225 in Japanese market), exchange rate (British Pound/US dollar and Japanese Yen/US dollar), and commodity market (gold price and crude oil price). We found that these financial data are RW whose first differences are independently distributed random variables or time-varying random variables.     

Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices

This investigation integrates a novel hybrid asymmetric volatility approach into an Artificial Neural Networks option-pricing model to upgrade the forecasting ability of the price of derivative securities. The use of the new hybrid asymmetric volatility method can simultaneously decrease the stochastic and nonlinearity of the error term sequence, and capture the asymmetric volatility. Therefore, analytical results of the ANNS option-pricing model reveal that Grey-EGARCH volatility provides greater predictability than other volatility approaches.     

Long term memory in extreme returns of financial time series

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R≥4. We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.     

Low q-moment multifractal analysis of Gold price, Dow Jones Industrial Average and BGL-USD exchange rate

An estimate of the low q-moment values of the assumed multifractal spectrum of Gold price, Dow Jones Industrial Average (DJIA) and Bulgarian Lev - USA Dollar (BGL-USD) exchange rate over a 6 1/2 year time span has been made. The findings can be compared to the analysis made on 23 foreign currency exchange rates by Vandewalle and Ausloos but there is a clear indication of some differences. Comparison to fractional Brownian motion is made. The analysis shows that these three financial data are not likely fractal but rather multifractal indeed. Received 17 October 1998 and Received in final form 2 November 1998     

A nonparametric method of multi-step ahead forecasting in diffusion processes

This paper provides a nonparametric model of multi-step ahead forecasting in diffusion processes. The model is constructed from the local linear model with the Gaussian kernel. The paper provides simulation studies to evaluate its performance of multi-step ahead forecasting by comparing with the global linear model, showing the better forecasting performance of the nonparametric model than the global linear model. The paper also conducts empirical analysis for forecasting using intraday data of the Japanese stock price index and the time series of heart rates. The result shows the performance of forecasting does not differ much in the Japanese stock price index, but that the nonparametric model shows significantly better performance in the analysis of the heart rates.     

High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets

Stock investors usually make their short-term investment decisions according to recent stock information such as the late market news, technical analysis reports, and price fluctuations. To reflect these short-term factors which impact stock price, this paper proposes a comprehensive fuzzy time-series, which factors linear relationships between recent periods of stock prices and fuzzy logical relationships (nonlinear relationships) mined from time-series into forecasting processes. In empirical analysis, the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) and HSI (Heng Seng Index) are employed as experimental datasets, and four recent fuzzy time-series models, Chen’s (1996), Yu’s (2005), Cheng’s (2006) and Chen’s (2007), are used as comparison models. Besides, to compare with conventional statistic method, the method of least squares is utilized to estimate the auto-regressive models of the testing periods within the databases. From analysis results, the performance comparisons indicate that the multi-period adaptation model, proposed in this paper, can effectively improve the forecasting performance of conventional fuzzy time-series models which only factor fuzzy logical relationships in forecasting processes. From the empirical study, the traditional statistic method and the proposed model both reveal that stock price patterns in the Taiwan stock and Hong Kong stock markets are short-term.     

Frequency analysis of tick quotes on the foreign exchange market and agent-based modeling: A spectral distance approach

High-frequency financial data of the foreign exchange market (EUR/CHF, EUR/GBP, EUR/JPY, EUR/NOK, EUR/SEK, EUR/USD, NZD/USD, USD/CAD, USD/CHF, USD/JPY, USD/NOK, and USD/SEK) are analyzed by utilizing the Kullback-Leibler divergence between two normalized spectrograms of the tick frequency and the generalized Jensen-Shannon divergence among them. The temporal structure variations of the similarity between currency pairs is detected and characterized. A simple agent-based model in which N market participants exchange M currency pairs is proposed. The equation for the tick frequency is approximately derived theoretically. Based on the analysis of this model, the spectral distance of the tick frequency is associated with the similarity of the behavior (perception and decision) of the market participants in exchanging these currency pairs.     

Correlation structures in short-term variabilities of stock indices and exchange rates

Financial data usually show irregular fluctuations and some trends. We investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) among financial data from the viewpoint of deterministic dynamical systems. Our method is based on the small-shuffle surrogate method. The data we use are daily closing price of Standard & Poor's 500 and the volume, and daily foreign exchange rates, Euro/US Dollar (USD), British Pound/USD and Japanese Yen/USD. We found that these data are not independent.     

Does implied volatility of currency futures option imply volatility of exchange rates?

By investigating currency futures options, this paper provides an alternative economic implication for the result reported by Stein [Overreactions in the options market, Journal of Finance 44 (1989) 1011–1023] that long-maturity options tend to overreact to changes in the implied volatility of short-maturity options. When a GARCH process is assumed for exchange rates, a continuous-time relationship is developed. We provide evidence that implied volatilities may not be the simple average of future expected volatilities. By comparing the term–structure relationship of implied volatilities with the process of the underlying exchange rates, we find that long-maturity options are more consistent with the exchange rates process. In sum, short-maturity options overreact to the dynamics of underlying assets rather than long-maturity options overreacting to short-maturity options.