Multivariate Hawkes process analysis of posts on a web service about uncomfortable gender experiences

The occurrence patterns of important words found in six texts (one historical pamphlet and five renowned academic books) are analyzed using both univariate and multivariate Hawkes processes. By treating the occurrence patterns as binary time-series data along the texts, we investigate how effectively univariate and multivariate Hawkes processes capture the characteristics of these word occurrence signals. Through maximum likelihood estimation and subsequent simulations, we found that the multivariate Hawkes process clearly outperforms the univariate Hawkes process in modeling word occurrence signals. Moreover, we found that the multivariate Hawkes process can provide a Hawkes graph, which serves as an intuitive representation of the relationships between concepts appearing in the analyzed text. Furthermore, our study demonstrates that the importance of concepts within a given text can be quantitatively estimated based on the optimized parameter values of the multivariate Hawkes process.

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator encompassed the projected estimator (PE) as a special case. We provide the convergence rates and asymptotic distributions of the Q-MLE estimators under mild conditions. Extensive numerical experiments demonstrate that the Q-MLE method performs better, especially when heteroscedasticity exists. Furthermore, two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincide with financial, economic, or geographical interpretations.

ABSTRACTThis paper proposes a noisy GARCH model with two volatility sequences (an unobserved and an observed/predictive one) and a stochastic time‐varying conditional kurtosis. The unobserved volatility equation, equipped with random coefficients, is a linear function of the past squared observations and of the past predictive volatility. The predictive volatility is the conditional mean of the unobserved volatility, thus following the standard GARCH specification, where its coefficients are equal to the means of the random coefficients. The means and the variances of the random coefficients, as well as the unobserved volatilities, are estimated using a three‐stage procedure. First, we estimate the means of the random coefficients using the Gaussian quasi‐maximum likelihood estimator (QMLE), then the variances of the random coefficients, using a weighted least squares estimator (WLSE), and finally the latent volatilities through a volatility filtering process under the assumption that the random parameters follow an Inverse Gaussian distribution, with the innovation being normally distributed. Hence, the conditional distribution of the model is the Normal Inverse Gaussian (NIG), which entails a closed form expression for the posterior mean of the unobserved volatility and of the random coefficients. Consistency and asymptotic normality of the QMLE and WLSE are established under quite tractable assumptions. The proposed methodology is illustrated with various simulated and real examples. It is shown that the filtered volatility can improve both in‐sample and out‐of‐sample forecasts of the predictive volatility, even when the future observations are unknown and are replaced by their predictions.

Quasi-likelihood estimation of structure-changed threshold double autoregressive models

As an extension of self-exciting Hawkes process, the multivariate Hawkes process models counting processes of different types of random events with mutual excitement. In this paper, we present a perfect sampling algorithm that can generate i.i.d. stationary sample paths of multivariate Hawkes process without any transient bias. In addition, we provide an explicit expression of algorithm complexity in model and algorithm parameters and provide numerical schemes to find the optimal parameter set that minimizes the complexity of the perfect sampling algorithm.

Some limit theorems for Hawkes processes and application to financial statistics

How Can Our Tweets Go Viral? Point-Process Modelling of Brand Content

doi:10.1093/comnet/cnab010 “Figure 4 was erroneously published without any text. This error has now been corrected online.”

Composite partial likelihood estimation for length-biased and right-censored data with competing risks

This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

Web services form a new distributed computing paradigm. Collaborative verification and validation are important when Web services from different vendors are integrated together to carry out a coherent task. This paper presents a new approach to verify Web services by model checking the process model of OWL-S (Web ontology language for Web services) and to validate them by the test cases automatically generated in the model checking process. We extend the BLAST, a model checker that handles control flow model naturally, to handle the concurrency in OWL-S. We also propose enhancement in OWL-S and PDDL (Planning Domain Definition Language) to facilitate the automated test case generation. Experiments on realistic examples are provided to illustrate the process.

Apart from quick detection of abnormal changes in a multivariate process, it is also critical to accurately identify the factors of abnormal changes after an out-of-control signal in multivariate statistical process control. Some diagnostic methods for fault identification were proposed by scholars on which one of the basic assumptions is that the process data are independent. The independent assumption is reasonable for many applications. However, with the development of industrial automation, the process data usually meet the phenomenon of autocorrelation. As it is well known, the autocorrelation affects detection ability of control chart. It is a natural question that is whether the autocorrelation affects the diagnostic performance of the diagnostic procedures. In the article, we propose the method adopted the analogy residual sequences and compare it with the performance of existing diagnostic methods for different shift sizes and various autocorrelation and cross-correlation structures. To limit the complexity, our discussion employs a first-order vector autoregressive process and focuses mainly on bivariate data in this article. The results of the simulation show the performances of diagnostic procedures were affected by autocorrelation and the impacts become greater as autocorrelation increases. On the other hand, the proposed method in the article can be free from the impacts of autocorrelation. Finally, a real example is also presented to demonstrate the implementation of the proposed method.

A multilayer distributed structure based on web service is put forward. The layer structure of power marketing business is described, based on the layer structure. The paper deduces that every business can be encapsulated by web service and each of them can communicate easily. The connection between the power marketing management information system and other systems is analyzed, and then the use of web service is presented to realize the integration between this system and the related systems. In the end, with the real example of a power marketing management information system, the solution for web service and the corresponding codes are presented.

A Point Process Framework for Predicting Popularity of Content in Online Social Networks

Dynamic Asset Correlations Based on Vines