Editorial - Constraints: From physical principles to molecular simulations and beyond

The two articles in this issue of the European Physical Journal Special Topics cover topics in Econophysics and GPU computing in the last years. In the first article [1], the formation of market prices for financial assets is described which can be understood as superposition of individual actions of market participants, in which they provide cumulative supply and demand. This concept of macroscopic properties emerging from microscopic interactions among the various subcomponents of the overall system is also well-known in statistical physics. The distribution of price changes in financial markets is clearly non-Gaussian leading to distinct features of the price process, such as scaling behavior, non-trivial correlation functions and clustered volatility. This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

GPU-computing in econophysics and statistical physics

This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

Neural Networks for Financial Time Series Forecasting

Financial and economic time series forecasting has never been an easy task due to its sensibility to political, economic and social factors. For this reason, people who invest in financial markets and currency exchange are usually looking for robust models that can ensure them to maximize their profile and minimize their losses as much as possible. Fortunately, recently, various studies have speculated that a special type of Artificial Neural Networks (ANNs) called Recurrent Neural Networks (RNNs) could improve the predictive accuracy of the behavior of the financial data over time. This paper aims to forecast: (i) the closing price of eight stock market indexes; and (ii) the closing price of six currency exchange rates related to the USD, using the RNNs model and its variants: the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The results show that the GRU gives the overall best results, especially for the univariate out-of-sample forecasting for the currency exchange rates and multivariate out-of-sample forecasting for the stock market indexes.     

Bubbles,crashes and intermittency in agent based market models

We define and study a rather complex market model, inspired from the Santa Fe artificial market and the Minority Game. Agents have different strategies among which they can choose, according to their relative profitability, with the possibility of not participating to the market. The price is updated according to the excess demand, and the wealth of the agents is properly accounted for. Only two parameters play a significant role: one describes the impact of trading on the price, and the other describes the propensity of agents to be trend following or contrarian. We observe three different regimes, depending on the value of these two parameters: an oscillating phase with bubbles and crashes, an intermittent phase and a stable `rational' market phase. The statistics of price changes in the intermittent phase resembles that of real price changes, with small linear correlations, fat tails and long range volatility clustering. We discuss how the time dependence of these two parameters spontaneously drives the system in the intermittent region. We analyze quantitatively the temporal correlation of activity in the intermittent phase, and show that the `random time strategy shift' mechanism that we proposed earlier allows one to understand the observed long ranged correlations. Other mechanisms leading to long ranged correlations are also reviewed. We discuss several other issues, such as the formation of bubbles and crashes, the influence of transaction costs and the distribution of agents wealth. Received 5 July 2002 / Received in final form 9 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: irene.giardina@roma1.infn.it     

Kernel methods and flexible inference for complex stochastic dynamics

Approximation theory suggests that series expansions and projections represent standard tools for random process applications from both numerical and statistical standpoints. Such instruments emphasize the role of both sparsity and smoothness for compression purposes, the decorrelation power achieved in the expansion coefficients space compared to the signal space, and the reproducing kernel property when some special conditions are met. We consider these three aspects central to the discussion in this paper, and attempt to analyze the characteristics of some known approximation instruments employed in a complex application domain such as financial market time series. Volatility models are often built ad hoc, parametrically and through very sophisticated methodologies. But they can hardly deal with stochastic processes with regard to non-Gaussianity, covariance non-stationarity or complex dependence without paying a big price in terms of either model mis-specification or computational efficiency. It is thus a good idea to look at other more flexible inference tools; hence the strategy of combining greedy approximation and space dimensionality reduction techniques, which are less dependent on distributional assumptions and more targeted to achieve computationally efficient performances. Advantages and limitations of their use will be evaluated by looking at algorithmic and model building strategies, and by reporting statistical diagnostics.     

Bidding strategy with forecast technology based on support vector machine in the electricity market

The participants in the electricity market are concerned very much with the market price evolution. Various technologies have been developed for price forecasting. The SVM (Support Vector Machine) has shown its good performance in market price forecasting. Two approaches for forming the market bidding strategies based on SVM are proposed. One is based on the price forecasting accuracy, with which the rejection risk is defined. The other takes into account the impact of the producer’s own bid. The risks associated with the bidding are controlled by the parameter settings. The proposed approaches have been tested on a numerical example.     

Multivariate Count Data Models for Time Series Forecasting

Count data appears in many research fields and exhibits certain features that make modeling difficult. Most popular approaches to modeling count data can be classified into observation and parameter-driven models. In this paper, we review two models from these classes: the log-linear multivariate conditional intensity model (also referred to as an integer-valued generalized autoregressive conditional heteroskedastic model) and the non-linear state-space model for count data. We compare these models in terms of forecasting performance on simulated data and two real datasets. In simulations, we consider the case of model misspecification. We find that both models have advantages in different situations, and we discuss the pros and cons of inference for both models in detail.     

Multi-scale correlations in different futures markets

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.     

Time series analysis and long range correlations of Nordic spot electricity market data

The electricity system price of the Nord Pool spot market is analysed. Different time scale analysis tools are assessed with focus on the Hurst exponent and long range correlations. Daily and weekly periodicities of the spot market are identified. Even though space time separation plots suggest more stationary behaviour than other financial time series, we find large fluctuations of the spot price market which suggest time-dependent scaling parameters.     

Jump point detection for real estate investment success

In the literature, studies on real estate market were mainly concentrating on the relation between property price and some key factors. The trend of the real estate market is a major concern. It is believed that changes in trend are signified by some jump points in the property price series. Identifying such jump points reveals important findings that enable policy-makers to look forward. However, not all jump points are observable from the plot of the series. This paper looks into the trend and introduces a new approach to the framework for real estate investment success.The main purpose of this paper is to detect jump points in the time series of some housing price indices and stock price index in Hong Kong by applying the wavelet analysis. The detected jump points reflect to some significant political issues and economic collapse. Moreover, the relations among properties of different classes and between stocks and properties are examined. It can be shown from the empirical result that a lead-lag effect happened between the prices of large-size property and those of small/medium-size property. However, there is no apparent relation or consistent lead in terms of change point measure between property price and stock price. This may be due to the fact that globalization effect has more impact on the stock price than the property price.     

Modeling natural gas market volatility using GARCH with different distributions

In this paper, we model natural gas market volatility using GARCH-class models with long memory and fat-tail distributions. First, we forecast price volatilities of spot and futures prices. Our evidence shows that none of the models can consistently outperform others across different criteria of loss functions. We can obtain greater forecasting accuracy by taking the stylized fact of fat-tail distributions into account. Second, we forecast volatility of basis defined as the price differential between spot and futures. Our evidence shows that nonlinear GARCH-class models with asymmetric effects have the greatest forecasting accuracy. Finally, we investigate the source of forecasting loss of models. Our findings based on a detrending moving average indicate that GARCH models cannot capture multifractality in natural gas markets. This may be the plausible explanation for the source of model forecasting losses.     

Multifractal detrended fluctuation analysis of the Chinese stock index futures market

Based on the multifractal detrended fluctuation analysis (MF-DFA) and multifractal spectrum analysis, this paper empirically studies the multifractal properties of the Chinese stock index futures market. Using a total of 2942 ten-minute closing prices, we find that the Chinese stock index futures returns exhibit long-range correlations and multifractality, making the single-scale index insufficient to describe the futures price fluctuations. Further, by comparing the original time series with the transformed time series through shuffling procedure and phase randomization procedure, we show the existence of two different sources of the multifractality for the Chinese stock index futures market. Our results suggest that the multifractality is mainly due to long-range correlations, although the fat-tailed probability distributions also contribute to such multifractal behaviour.     

Minimum Message Length in Hybrid ARMA and LSTM Model Forecasting

Modeling and analysis of time series are important in applications including economics, engineering, environmental science and social science. Selecting the best time series model with accurate parameters in forecasting is a challenging objective for scientists and academic researchers. Hybrid models combining neural networks and traditional Autoregressive Moving Average (ARMA) models are being used to improve the accuracy of modeling and forecasting time series. Most of the existing time series models are selected by information-theoretic approaches, such as AIC, BIC, and HQ. This paper revisits a model selection technique based on Minimum Message Length (MML) and investigates its use in hybrid time series analysis. MML is a Bayesian information-theoretic approach and has been used in selecting the best ARMA model. We utilize the long short-term memory (LSTM) approach to construct a hybrid ARMA-LSTM model and show that MML performs better than AIC, BIC, and HQ in selecting the model—both in the traditional ARMA models (without LSTM) and with hybrid ARMA-LSTM models. These results held on simulated data and both real-world datasets that we considered.We also develop a simple MML ARIMA model.     

Radical Complexity

This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.     

Herding and zero-intelligence agents in the order book dynamics of an artificial double auction market

Effects of herding on the order book dynamics of a double auction market is studied by an agent-based model. This is done by comparing results from a zero-intelligence model and a model in which herding effect is implemented by aggregation of agents who take market orders into opinion groups. The number of opinion groups in a simulation step is determined from previous volatilities of the market as different agents compare the price change over different time intervals. Besides confirming that when herding is included the tail of the distribution of volatility is enhanced, we found several new results. First, the autocorrelation time of volatility is much shorter than the memory of most of the agents because limit orders have strong influence on the location of best bid and best ask. Second, from the relation between bid-ask imbalance and price return we find that herding reduces the chance for a small imbalance to produce a large price change. Furthermore, herding tends to decrease spread. This is because herding decreases the chance that a market order changes the size of the spread. Finally, we find that the relation between spread and volatility in our models does not agree with empirical data, this indicates a difference between agents with no strategies and agents in real financial markets.     

Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents

We introduce a stochastic heterogeneous interacting-agent model for the short-time non-equilibrium evolution of excess demand and price in a stylized asset market. We consider a combination of social interaction within peer groups and individually heterogeneous fundamentalist trading decisions which take into account the market price and the perceived fundamental value of the asset. The resulting excess demand is coupled to the market price. Rigorous analysis reveals that this feedback may lead to price oscillations, a single bounce, or monotonic price behaviour. The model is a rare example of an analytically tractable interacting-agent model which allows us to deduce in detail the origin of these different collective patterns. For a natural choice of initial distribution, the results are independent of the graph structure that models the peer network of agents whose decisions influence each other.     

A Systematic Review of Statistical and Machine Learning Methods for Electrical Power Forecasting with Reported MAPE Score

Electric power forecasting plays a substantial role in the administration and balance of current power systems. For this reason, accurate predictions of service demands are needed to develop better programming for the generation and distribution of power and to reduce the risk of vulnerabilities in the integration of an electric power system. For the purposes of the current study, a systematic literature review was applied to identify the type of model that has the highest propensity to show precision in the context of electric power forecasting. The state-of-the-art model in accurate electric power forecasting was determined from the results reported in 257 accuracy tests from five geographic regions. Two classes of forecasting models were compared: classical statistical or mathematical (MSC) and machine learning (ML) models. Furthermore, the use of hybrid models that have made significant contributions to electric power forecasting is identified, and a case of study is applied to demonstrate its good performance when compared with traditional models. Among our main findings, we conclude that forecasting errors are minimized by reducing the time horizon, that ML models that consider various sources of exogenous variability tend to have better forecast accuracy, and finally, that the accuracy of the forecasting models has significantly increased over the last five years.     

Spin models as microfoundation of macroscopic market models

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thus bear the chance for better models for market regulation. However microscopic models and macroscopic models are commonly studied separately. Here, we exemplify a unified view of a microscopic and a macroscopic market model in a case study, deducing a macroscopic Langevin equation from a microscopic spin market model closely related to the Ising model. The interplay of the microscopic and the macroscopic view allows for a better understanding and adjustment of the microscopic model, as well, and may guide the construction of agent based market models as basis of macroscopic models.     

A mini-review on econophysics:Comparative study of Chinese and western financial markets

We present a review of our recent research in econophysics, and focus on the comparative study of Chinese and western financial markets. By virtue of concepts and methods in statistical physics, we investigate the time correlations and spatial structure of financial markets based on empirical high-frequency data. We discover that the Chinese stock market shares common basic properties with the western stock markets, such as the fat-tail probability distribution of price returns, the long-range auto-correlation of volatilities, and the persistence probability of volatilities, while it exhibits very different higher-order time correlations of price returns and volatilities, spatial correlations of individual stock prices, and large-fluctuation dynamic behaviors. Furthermore, multi-agent-based models are developed to simulate the microscopic interaction and dynamic evolution of the stock markets.