Modeling foreign exchange market activity around macroeconomic news: Hawkes-process approach

Modelling time-varying interactions in complex systems: the Score Driven Kinetic Ising Model

A common issue when analyzing real-world complex systems is that the interactions between their elements often change over time. Here we propose a new modeling approach for time-varying interactions generalising the well-known Kinetic Ising Model, a minimalistic pairwise constant interactions model which has found applications in several scientific disciplines. Keeping arbitrary choices of dynamics to a minimum and seeking information theoretical optimality, the Score-Driven methodology allows to extract from data and interpret the presence of temporal patterns describing time-varying interactions. We identify a parameter whose value at a given time can be directly associated with the local predictability of the dynamics and we introduce a method to dynamically learn its value from the data, without specifying parametrically the system's dynamics. We extend our framework to disentangle different sources (e.g. endogenous vs exogenous) of predictability in real time, and show how our methodology applies to a variety of complex systems such as financial markets, temporal (social) networks, and neuronal populations.

Analysis of Individual High-Frequency Traders’ Buy–Sell Order Strategy Based on Multivariate Hawkes Process

Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track the order history of individual HFTs in the USD/JPY forex market to reveal how individual HFTs interact with the order book and what strategies they use to place their limit orders. Specifically, we introduced an 8-dimensional multivariate Hawkes process that included the excitations due to the occurrence of limit orders, cancel orders, and executions in the order book change, and performed maximum likelihood estimations of the limit order processes for 134 HFTs. As a result, we found that the limit order generation processes of 104 of the 134 HFTs were modeled by a multivariate Hawkes process. In this analysis of the EBS market, the HFTs whose strategies were modeled by the Hawkes process were categorized into three groups according to their excitation mechanisms: (1) those excited by executions; (2) those that were excited by the occurrences or cancellations of limit orders; and (3) those that were excited by their own orders.

Quantifying the Endogeneity in Online Donations

Charitable crowdfunding provides a new channel for people and families suffering from unforeseen events, such as accidents, severe illness, and so on, to seek help from the public. Thus, finding the key determinants which drive the fundraising process of crowdfunding campaigns is of great importance, especially for those suffering. With a unique data set containing 210,907 crowdfunding projects covering a period from October 2015 to June 2020, from a famous charitable crowdfunding platform, specifically Qingsong Chou, we will reveal how many online donations are due to endogeneity, referring to the positive feedback process of attracting more people to donate through broadcasting campaigns in social networks by donors. For this aim, we calibrate three different Hawkes processes to the event data of online donations for each crowdfunding campaign on each day, which allows us to estimate the branching ratio, a measure of endogeneity. It is found that the online fundraising process works in a sub-critical state and nearly 70-90% of the online donations are endogenous. Furthermore, even though the fundraising amount, number of donations, and number of donors decrease rapidly after the crowdfunding project is created, the measure of endogeneity remains stable during the entire lifetime of crowdfunding projects. Our results not only deepen our understanding of online fundraising dynamics but also provide a quantitative framework to disentangle the endogenous and exogenous dynamics in complex systems.

Deep learning-based exchange rate prediction during the COVID-19 pandemic

This study proposes an ensemble deep learning approach that integrates Bagging Ridge (BR) regression with Bi-directional Long Short-Term Memory (Bi-LSTM) neural networks used as base regressors to become a Bi-LSTM BR approach. Bi-LSTM BR was used to predict the exchange rates of 21 currencies against the USD during the pre-COVID-19 and COVID-19 periods. To demonstrate the effectiveness of our proposed model, we compared the prediction performance with several more traditional machine learning algorithms, such as the regression tree, support vector regression, and random forest regression, and deep learning-based algorithms such as LSTM and Bi-LSTM. Our proposed ensemble deep learning approach outperformed the compared models in forecasting exchange rates in terms of prediction error. However, the performance of the model significantly varied during non-COVID-19 and COVID-19 periods across currencies, indicating the essential role of prediction models in periods of highly volatile foreign currency markets. By providing an improved prediction performance and identifying the most seriously affected currencies, this study is beneficial for foreign exchange traders and other stakeholders in that it offers opportunities for potential trading profitability and for reducing the impact of increased currency risk during the pandemic.

Detection of Mutual Exciting Structure in Stock Price Trend Dynamics

We investigated a comprehensive analysis of the mutual exciting mechanism for the dynamic of stock price trends. A multi-dimensional Hawkes-model-based approach was proposed to capture the mutual exciting activities, which take the form of point processes induced by dual moving average crossovers. We first performed statistical measurements for the crossover event sequence, introducing the distribution of the inter-event times of dual moving average crossovers and the correlations of local variation (LV), which is often used in spike train analysis. It was demonstrated that the crossover dynamics in most stock sectors are generally more regular than a standard Poisson process, and the correlation between variations is ubiquitous. In this sense, the proposed model allowed us to identify some asymmetric cross-excitations, and a mutually exciting structure of stock sectors could be characterized by mutual excitation correlations obtained from the kernel matrix of our model. Using simulations, we were able to substantiate that a burst of the dual moving average crossovers in one sector increases the intensity of burst both in the same sector (self-excitation) as well as in other sectors (cross-excitation), generating episodes of highly clustered burst across the market. Furthermore, based on our finding, an algorithmic pair trading strategy was developed and backtesting results on real market data showed that the mutual excitation mechanism might be profitable for stock trading.

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns

We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.

Quantifying uncertainty in a predictive model for popularity dynamics

The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here we present a fully tractable approach to analytically describe the distribution of the number of events in a Hawkes process, which, in contrast to purely empirical studies or simulation-based models, enables the effect of process parameters on cascade dynamics to be analyzed. We show that the presented theory also allows predictions regarding the future distribution of events after a given number of events have been observed during a time window. Our results are derived through a differential-equation approach to attain the governing equations of a general branching process. We confirm our theoretical findings through extensive simulations of such processes. This work provides the basis for more complete analyses of the self-exciting processes that govern the spreading of information through many communication platforms, including the potential to predict cascade dynamics within confidence limits.

Robust identification of controlled Hawkes processes

The identification of Hawkes-like processes can pose significant challenges. Despite substantial amounts of data, standard estimation methods show significant bias or fail to converge. To overcome these issues, we propose an alternative approach based on an expectation-maximization algorithm, which instrumentalizes the internal branching structure of the process, thus improving convergence behavior. Furthermore, we show that our method provides a tight lower bound for maximum-likelihood estimates. The approach is discussed in the context of a practical application, namely the collection of outstanding unsecured consumer debt.

Modeling aggressive market order placements with Hawkes factor models

Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-excitation respectively. We calibrate the model for a Shenzhen Stock Exchange stock. We find that the exponential kernel with a smooth cut-off (i.e. the subtraction of two exponentials) produces much better calibration than the monotonous exponential kernel (i.e. the sum of two exponentials). The exogenous baseline intensity explains the U-shaped intraday pattern. Our empirical results show that the endogenous submission clustering is mainly caused by self-excitation rather than cross-excitation.

Detection of intensity bursts using Hawkes processes: An application to high-frequency financial data

Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local nonstationarity or the presence of an external perturbation to the system. In this paper we propose a procedure for the detection of intensity bursts within the Hawkes process framework. By using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown. Moreover, the initial time of the burst can be determined with a precision given by the typical interevent time. We apply our methodology to the midprice change in foreign exchange (FX) markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival. We show lead-lag relations in intensity burst occurrence across different FX rates and we discuss their relation with price jumps.

Hawkes process model with a time-dependent background rate and its application to high-frequency financial data

A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of variable-width basis functions, and the parameters are estimated by a Bayesian method. Our model can capture not only the slow time variation, such as in the intraday seasonality, but also the rapid one, which follows a macroeconomic news announcement. By analyzing the tick data of the Nikkei 225 mini, we find that (i) our model is better fitted to the data than the Hawkes models with a constant background rate or a slowly varying background rate, which have been commonly used in the field of quantitative finance; (ii) the improvement in the goodness-of-fit to the data by our model is significant especially for sessions where considerable fluctuation of the background rate is present; and (iii) our model is statistically consistent with the data. The branching ratio, which quantifies the level of the endogeneity of markets, estimated by our model is 0.41, suggesting the relative importance of exogenous factors in the market dynamics. We also demonstrate that it is critically important to appropriately model the time-dependent background rate for the branching ratio estimation.

Social interactions among grazing reef fish drive material flux in a coral reef ecosystem

In human financial and social systems, exchanges of information among individuals cause speculative bubbles, behavioral cascades, and other correlated actions that profoundly influence system-level function. Exchanges of information are also widespread in ecological systems, but their effects on ecosystem-level processes are largely unknown. Herbivory is a critical ecological process in coral reefs, where diverse assemblages of fish maintain reef health by controlling the abundance of algae. Here, we show that social interactions have a major effect on fish grazing rates in a reef ecosystem. We combined a system for observing and manipulating large foraging areas in a coral reef with a class of dynamical decision-making models to reveal that reef fish use information about the density and actions of nearby fish to decide when to feed on algae and when to flee foraging areas. This "behavioral coupling" causes bursts of feeding activity that account for up to 68% of the fish community's consumption of algae. Moreover, correlations in fish behavior induce a feedback, whereby each fish spends less time feeding when fewer fish are present, suggesting that reducing fish stocks may not only reduce total algal consumption but could decrease the amount of algae each remaining fish consumes. Our results demonstrate that social interactions among consumers can have a dominant effect on the flux of energy and materials through ecosystems, and our methodology paves the way for rigorous in situ measurements of the behavioral rules that underlie ecological rates in other natural systems.

Markets, Herding and Response to External Information

We focus on the influence of external sources of information upon financial markets. In particular, we develop a stochastic agent-based market model characterized by a certain herding behavior as well as allowing traders to be influenced by an external dynamic signal of information. This signal can be interpreted as a time-varying advertising, public perception or rumor, in favor or against one of two possible trading behaviors, thus breaking the symmetry of the system and acting as a continuously varying exogenous shock. As an illustration, we use a well-known German Indicator of Economic Sentiment as information input and compare our results with Germany’s leading stock market index, the DAX, in order to calibrate some of the model parameters. We study the conditions for the ensemble of agents to more accurately follow the information input signal. The response of the system to the external information is maximal for an intermediate range of values of a market parameter, suggesting the existence of three different market regimes: amplification, precise assimilation and undervaluation of incoming information.