Multivariate Stochastic Model Research Articles

A flexible multivariate model for high-dimensional correlated count data

We propose a flexible multivariate stochastic model for over-dispersed count data. Our methodology is built upon mixed Poisson random vectors (Y1,…,Yd), where the {Yi} are conditionally independent Poisson random variables. The stochastic rates of the {Yi} are multivariate distributions with arbitrary non-negative margins linked by a copula function. We present basic properties of these mixed Poisson multivariate distributions and provide several examples. A particular case with geometric and negative binomial marginal distributions is studied in detail. We illustrate an application of our model by conducting a high-dimensional simulation motivated by RNA-sequencing data.

Non-Gaussianity Detection of EEG Signals Based on a Multivariate Scale Mixture Model for Diagnosis of Epileptic Seizures.

The detection of epileptic seizures from scalp electroencephalogram (EEG) signals can facilitate early diagnosis and treatment. Previous studies suggested that the Gaussianity of EEG distributions changes depending on the presence or absence of seizures; however, no general EEG signal models can explain such changes in distributions within a unified scheme. This article describes the formulation of a stochastic EEG model based on a multivariate scale mixture distribution that can represent changes in non-Gaussianity caused by stochastic fluctuations in EEG. In addition, we propose an EEG analysis method by combining the model with a filter bank and introduce a feature representing the non-Gaussianity latent in each EEG frequency band. We applied the proposed method to multichannel EEG data from twenty patients with focal epilepsy. The results showed a significant increase in the proposed feature during epileptic seizures, particularly in the high-frequency band. The feature calculated in the high-frequency band allowed highly accurate classification of seizure and non-seizure segments [area under the receiver operating characteristic curve (AUC) = 0.881] using only a simple threshold. This article proposed a multivariate scale mixture distribution-based stochastic EEG model capable of representing non-Gaussianity associated with epileptic seizures. Experiments using simulated and real EEG data demonstrated the validity of the model and its applicability to epileptic seizure detection. The stochastic fluctuations of EEG quantified by the proposed model can help detect epileptic seizures with high accuracy.

A note on nonlinear least squares estimation of multivariate stochastic unit root models

A note on nonlinear least squares estimation of multivariate stochastic unit root models

A theory of multivariate stress testing

We present a theoretical framework for stressing multivariate stochastic models. We consider a stress to be a change of measure, placing a higher weight on multivariate scenarios of interest. In particular, a stressing mechanism is a mapping from random vectors to RadonNikodym densities. We postulate desirable properties for stressing mechanisms addressing alternative objectives. Consistently with our focus on dependence, we require throughout invariance to monotonic transformations of risk factors. We study in detail the properties of two families of stressing mechanisms, based respectively on mixtures of univariate stresses and on transformations of statistics we call Spearman and Kendall’s cores. Furthermore, we characterize the aggregation properties of those stressing mechanisms, which motivate their use in deriving new capital allocation methods, with properties different to those typically found in the literature. The proposed methods are applied to stress testing and capital allocation, using the simulation model of a UK-based non-life insurer.

A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics

The growth and yield modeling of a forest stand has progressed rapidly, starting from the generalized nonlinear regression models of uneven/even-aged stands, and continuing to stochastic differential equation (SDE) models. We focus on the adaptation of the SDEs for the modeling of forest stand dynamics, and relate the tree and stand size variables to the age dimension (time). Two different types of diffusion processes are incorporated into a hybrid model in which the shortcomings of each variable types can be overcome to some extent. This paper presents the hybrid multivariate SDE regarding stand basal area and volume models in a forest stand. We estimate the fixed- and mixed-effect parameters for the multivariate hybrid stochastic differential equation using a maximum likelihood procedure. The results are illustrated using a dataset of measurements from Mountain pine tree (Pinus mugo Turra).

Stochastic modeling of chlorophyll-a for probabilistic assessment and monitoring of algae blooms in the Lower Nakdong River, South Korea

Eutrophication is one of the critical water quality issues in the world nowadays. Various studies have been conducted to explore the contributing factors related to eutrophication symptoms. However, in the field of eutrophication modeling, the stochastic nature associated with the eutrophication process has not been sufficiently explored, especially in a multivariate stochastic modeling framework. In this study, a multivariate hidden Markov model (MHMM) that can consider the spatio-temporal dependence in chlorophyll-a concentration over the Nakdong River of South Korea was proposed. The MHMM can effectively cluster the intra-seasonal and inter-annual variability of chlorophyll-a, thereby enabling us to understand the spatio-temporal evolutions of algal blooms. The relationships between hydro-climatic conditions (e.g., temperature and river flow) and chlorophyll-a concentrations were evident, whereas a relatively weak relationship with water quality parameters was observed. The MHMM enables us to effectively infer the conditional probability of the eutrophication state for the following month. The self-transition likelihood of staying in the current state is substantially higher than the likelihood of moving to other states. Moreover, the proposed modeling approach can effectively offer a probabilistic decision-support framework for constructing an alert classification of the eutrophication. The potential use of the proposed modeling framework was also provided.

Two-Scale Network Dynamic Model for Energy Commodity Processes

In this work, we examine the relationship between different energy commodity spot prices. To do this, multivariate stochastic models with and without external random interventions describing the price of energy commodities are developed. Random intervention process is described by a continuous jump process. The developed mathematical model is utilized to examine the relationship between energy commodity prices. The time-varying parameters in the stochastic model are estimated using the recently developed parameter identification technique called local lagged adapted generalized method of moment (LLGMM). The LLGMM method provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. The usefulness of the LLGMM approach is illustrated by applying to energy commodity data sets for state and parameter estimation problems. Moreover, the forecasting and confidence interval problems are also investigated (U.S. Patent Pending for the LLGMM method described in this manuscript).

Common‐factor stochastic volatility modelling with observable proxy

AbstractMulti‐asset modelling is of fundamental importance to financial applications such as risk management and portfolio selection. In this article, we propose a multivariate stochastic volatility modelling framework with a parsimonious and interpretable correlation structure. Building on well‐established evidence of common volatility factors among individual assets, we consider a multivariate diffusion process with a common‐factor structure in the volatility innovations. Upon substituting an observable market proxy for the common volatility factor, we markedly improve the estimation of several model parameters and latent volatilities. The model is applied to a portfolio of several important constituents of the S&P500 in the financial sector, with the VIX index as the common‐factor proxy. We find that the prediction intervals for asset forecasts are comparable to those of more complex dependence models, but that option‐pricing uncertainty can be greatly reduced by adopting a common‐volatility structure. The Canadian Journal of Statistics 48: 36–61; 2020 © 2020 Statistical Society of Canada

Wind speed estimation based on a novel multivariate Weibull distribution

Good practice in smart grids is networked sensors topologies which give the ability to fuse sensors to obtain a new feature based on sensors’ complementarity. Moreover, to get a prediction based on other sensors, possibly in other areas, in case of sensor failure. This ability may be achieved by correlating sensor data based on their historical observations. This study addresses the problem of stochastic multivariate modelling within the framework of cyber-physical systems. Weibull distribution function (WDF) was found to be the best probability distribution function to fit wind variations. The main idea of this study is to propose a generalised multivariate stochastic model to describe the joint probability between multi-stochastic variables. A novel multivariate WDF for wind modelling is proposed to estimate wind speed in one location based on wind speed data on other location(s). The suggested approach is applied to three cases to demonstrate the efficacy of the developed technique. It is pointed out that this approach could be generalised for the multivariate WDF of wind modelling situations. Finally, it is shown that there are existing structures resemblances between the wind Weibull versus normal distribution models arising from the fact WDF reflects a natural phenomenon with some restrictions.

Stochastic dynamical systems always undergo trending mechanisms of transition to criticality

We study diverse mechanisms of the transition of stochastic dynamical systems to critical states. We begin from employing two independent quantitative methods of time series analysis, first-order detrended fluctuation analysis and multivariate canonical coherence analysis, and investigate GPS data of land surface displacements. We find out that there are two different mechanisms of the transition to criticality: the first mechanism is consistent with that observed in some biological dynamical systems and associated with a growth of the energies at low frequencies in the power spectrum, whereas the second mechanism is new and governed by a decay of the energies at high frequencies. Despite this difference, we show that both mechanisms lead to a loss of chaoticity in the system’s behavior and result in a more deterministic evolution of the system as a whole. Basing on these findings, we develop a multivariate stochastic model that qualitatively explains both empirically observed mechanisms. The obtained results allow to pose a hypothesis that, in spite of the spread understanding, in stochastic dynamical systems of any nature the transition to a critical state is always realized through a trending nonlinear process that has nothing to do with purely random dynamics.

On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes

In reliability and survival analysis, the shot-noise processes have been intensively employed as a useful tool for modeling the impact of a dynamic environment (in the form of the point process of stresses) on survival characteristics of systems and organisms. However, the studies on the shot-noise processes have been mostly focused on the univariate analysis. In this paper, we develop a class of multivariate stochastic failure models based on a dynamic shock model induced by multiple shot-noise processes and study its properties. Explicit parametric forms for the multivariate survival functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well.

A Theory of Scenario Generation

We show how to reduce financial asset prices to low-dimensional scenario trees. Applied to time series, the scenarios and their probabilities become time-varying factors. From S&P 500 options, two or three time-varying scenarios suffice to forecast returns, implied variance or skewness on par, or better, than extant multivariate stochastic volatility jump-diffusion models, while reducing the computational effort to fractions of a second.

Forecasting mortality rates: multivariate or univariate models?

It is well known that accurate forecasts of mortality rates are essential to various demographic research topics, such as population projections and the pricing of insurance products such as pensions and annuities. In this study, we argue that including the lagged rates of neighbouring ages cannot further improve mortality forecasting after allowing for autocorrelations. This is because the sample cross-correlation function cannot exhibit meaningful and statistically significant correlations. In other words, rates of neighbouring ages are usually not leading indicators in mortality forecasting. Therefore, multivariate stochastic mortality models like the classic Lee–Carter may not necessarily lead to more accurate forecasts, compared with sophisticated univariate models. Using Australian mortality data, simulation and empirical studies employing the Lee–Carter, Functional Data, Vector Autoregression, Autoregression-Autoregressive Conditional Heteroskedasticity and exponential smoothing (ETS) state space models are performed. Results suggest that ETS models consistently outperform the others in terms of forecasting accuracy. This conclusion holds for both female and male mortality data with different empirical features across various forecasting error measurements. Hence, ETS can be a widely useful tool to model and forecast mortality rates in actuarial practice.

A multivariate stochastic unit root model with an application to derivative pricing

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model’s parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black–Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black–Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option is obtained and shown to extend the existing option price formula in a manner that embodies the effect of a stochastic departure from a unit root. An empirical application reveals that the new model substantially reduces the average percentage pricing error of the Black–Scholes and Heston’s (1993) stochastic volatility (with zero volatility risk premium) pricing schemes in most moneyness-maturity categories considered.

Multivariate Stochastic Process Models for Correlated Responses of Mixed Type

We propose a new model for correlated outputs of mixed type, such as continuous and binary outputs, with a particular focus on joint regression and classification, motivated by an application in constrained optimization for com- puter simulation modeling. Our framework is based upon multivariate stochastic processes, extending Gaussian process methodology for modeling of continuous multivariate spatial outputs by adding a latent process structure that allows for joint modeling of a variety of types of correlated outputs. In addition, we imple- ment fully Bayesian inference using particle learning, which allows us to conduct fast sequential inference. We demonstrate the effectiveness of our proposed meth- ods on both synthetic examples and a real world hydrology computer experiment optimization problem where it is helpful to model the black box objective function as correlated with satisfaction of the constraint.

Protection motivation theory and cigarette smoking among vocational high school students in China: a cusp catastrophe modeling analysis.

BackgroundTobacco use is one of the greatest public health problems worldwide and the hazards of cigarette smoking to public health call for better recognition of cigarette smoking behaviors to guide evidence-based policy. Protection motivation theory (PMT) provides a conceptual framework to investigate tobacco use. Evidence from diverse sources implies that the dynamics of smoking behavior may be quantum in nature, consisting of an intuition and an analytical process, challenging the traditional linear continuous analytical approach. In this study, we used cusp catastrophe, a nonlinear analytical approach to test the dual-process hypothesis of cigarette smoking.MethodsData were collected from a random sample of vocational high school students in China (n = 528). The multivariate stochastic cusp modeling was used and executed with the Cusp Package in R. The PMT-based Threat Appraisal and Coping Appraisal were used as the two control variables and the frequency of cigarette smoking (daily, weekly, occasional, and never) in the past month was used as the outcome variable.ResultsConsistent with PMT, the Threat Appraisal (asymmetry, α1 = 0.1987, p < 0.001) and Coping Appraisal (bifurcation, β2 = 0.1760, p < 0.05) significantly predicted the smoking behavior after controlling for covariates. Furthermore, the cusp model performed better than the alternative linear and logistic regression models with regard to higher R 2 (0.82 for cusp, but 0.21 for linear and 0.25 for logistic) and smaller AIC and BIC.ConclusionStudy findings support the conclusion that cigarette smoking in adolescents is a quantum process and PMT is relevant to guide studies to understand smoking behavior for smoking prevention and cessation.

Multivariate stochastic modeling of washing machine loads profile in Iran

The present paper, investigates the stochastic modeling of the domestic electrical load profile in a residential area. The Domestic Load Modeling (DLM) methodologies are more complicated compared to the industrial, commercial and agricultural load modeling. Domestic loads contain a wide diversity of loads that exist in every household consuming a remarkable portion of the overall domestic consumption. Diversity of domestic loads has created different consumption patterns with variable usage timing and duration caused by miscellaneous factors. The intuitive uncertainty in DLM is the main motivation to apply Domestic Loads Stochastic Modeling (DLSM) in the present paper. This study uses multivariable probability distribution function. Additionally, simultaneous correlation between different weekdays and different hours of a day has been performed. Monte Carlo technique is applied in order to generate different samples for domestic electrical load profile. As a result, the behavior of domestic electrical load profile for all residents in a region was estimated based on a limited number of questionnaires using DLSM. The study was performed for the Ekbatan residential complex in Tehran, Iran.

Multistage performance modelling in digital marketing management

IntroductionInteractive media, apart from one-to-one communication, allow for detailed tracking of the performance of online campaigns and improving it with the use of dedicated technologies (Hoffman and Novak, 1995). Several interdisciplinary research directions can be observed with the main goal of increasing outcomes from online advertising and identification of new challenges (Guha et al., 2010). Campaign execution is usually based on media plans, which are prepared at strategical level with conventional planning methods (Cannon, 2001) or dedicated models dealing with a multi-objective approach in the online environment (Hengbo and Yanfeng, 2012; Du and Xu, 2012). While campaign planning takes place periodically, the online advertising systems require tuning and optimization in real time. In the online environment, methods based on multivariate testing or stochastic models or contextual selection (Tang et al., 2013) are used. Apart from optimization, improvement is performed with the use of behavioral targeting systems (Yan et al., 2009), retargeting customers with revealed interest in specific products (Lambrecht and Tucker, 2013) or real time bidding systems (Yuan et al., 2013). Intensive online advertising can affect websites and makes information seeking more difficult and causes an increased cognitive load, frustration and other negative emotions (Brajnik and Gabrielli, 2010). Due to factors related to cognitive avoidance, the dropping performance of online advertising is observed over time (Kelly et al., 2010). With connected characteristics related to audience, changes of the performance over the time, campaign planning requires the use of past data with the ability of taking into an account uncertain information. Earlier approaches based on stochastic or fuzzy models use same importance for data from past periods and from recent results.Due to searching for a more realistic approach, the presented research is based on the use of past data with a forgetting function and weighted importance of data from past periods. The work is presented as follows: after the literature review and the problem statement, the conceptual framework of a multistage performance modelling is presented. In the next stage, the proposed framework is used in an empirical study for dynamic evaluation of data from experimental advertising campaign. Finally, conclusions are presented.1. Literature ReviewInteractive media created the ability to measure different results from online marketing campaigns and use them in the decision process related to planning at both strategy and tactical levels. New metrics are used in this field for media planning for the evaluation of online campaigns and are based on the direct response and interactions or longer term influence on brand awareness (Novak and Hoffman, 1996; Pavlou and Stewart, 2000) with an essential quantitative approach to media planning (Hoffman and Novak, 2000). New approaches dedicated to online media use its specifics, but conventional media planning based on earlier approaches is still applicable in that area (Cannon, 2001). The basis for online campaign execution within the portal selling advertising space is the scheduling at different slots the use of different creations. Estimations of potential audiences and the ability to serve advertisements use the analysis based on the planned behaviors and site pre-visit intentions (Wu, 2007). At the operational level other areas deal with the real time campaign optimization and searching for the best method of resource exploitation with the use of stochastic models (Chakrabarti et al., 2009). Even when a banner selection is performed at the operational level and the selection is used with the different parameter scheduling, the execution is based on plans from a strategical level (Amiri and Menon, 2003). Scheduling is used within advertising server applications to select specific content as an answer to a request coming from a web browser. …

Applying Copulas Functions for Wind and Hydro Complementarity Evaluation: A Brazilian Case

Wind energy has been expanding in many countries typically hydro electricity producers in the last decades and some investments take advantage from the complementarity among hydro and wind productions as a strategy to increase profits and minimize risks. In this paper, our focus is applying copulas functions to evaluate a complementarity between wind and hydro production in different regions in Brazil. The goal is evaluate which regions are most suitable for development of wind energy considering the existing hydro electricity production. Copulas functions can capture the dependence structure among random variables offering a great flexibility in building multivariate stochastic models while statistic correlation does not capture nonlinear effects sufficiently. For this reason, we apply nine different copulas functions in our study finding those that best capture the complementarity.

A multivariate stochastic model to assess research performance

There is a worldwide trend towards application of bibliometric research evaluation, in support of the needs of policy makers and research administrators. However the assumptions and limitations of bibliometric measurements suggest a probabilistic rather than the traditional deterministic approach to the assessment of research performance. The aim of this work is to propose a multivariate stochastic model for measuring the performance of individual scientists and to compare the results of its application with those arising from a deterministic approach. The dataset of the analysis covers the scientific production indexed in Web of Science for the 2006–2010 period, of over 900 Italian academic scientists working in two distinct fields of the life sciences.