The purpose of this article is to present the issue of algorithms of the change detection model for the political business cycle. Political business cycle issue is interesting in the context of the current political situation in Europe, ie, the progressive integration of the European Union countries and the wave of financial problems that affected the state, which has been regarded so far as economically stable. Monitoring of this phenomenon is characterized by the fact that we do not usually have full information about the behavior of business indexes before and after the change. It is assumed that we are observing a stochastic sequence whose mathematical model predicts a sudden change. The process is Markovian when the change moment is given. The initial problem of disorder detection is transformed to the optimal stopping of the observed sequence. In order to construct an algorithm for estimating the moment of change, we transform the task into an equivalent problem of optimal stopping based on the observed magnitude and some statistics. The analysis obtained from the transformation of the problem is the source of the change point estimation algorithms. The formula for the optimal decision functions is derived.

European options are a significant financial product. Barrier options, in turn, are European options with a barrier constraint. The investor may pay less buying the barrier option obtaining the same result as that of the European option whenever the barrier is not breached. Otherwise, the option's payoff cancels. In this paper, we obtain closed-form expressions of the exact no-arbitrage prices, delta hedges, and gammas of a call option with a moving barrier that tracks the prices of the risk-free asset. Besides the interest in its own right, this class of options constitutes the core element to obtain, via an original and simple technique, the closed-form expressions for the estimates of the prices of call options with barriers of arbitrary shape. Equally important is the fact that a bound for the worst associated error is provided, so the investor can evaluate beforehand if the accuracy provided is according to his/her needs or not. Discrete monitored barrier provisions are also allowed in the estimates. Simulations are performed illustrating the accuracy of the estimates. A quality of the aforementioned procedures is that the time consumed in computations is very small. In turn, we observe that the approximate prices, delta hedges, and gammas of the barrier option associated to the risk-free asset, obtained via a PDE approach in conjunction with a good finite difference method, converge to the closed-form expressions of the prices, hedges, and gammas of the option. This attests the correctness of the analytical results.

The binomial model is a standard framework used to introduce risk neutral pricing of financial assets. Martingale representation, backward stochastic differential equations, and the Malliavin calculus are difficult concepts in a continuous-time setting. This paper presents these ideas in the simple, discrete-time binomial model.

A novel method for offline detection of multiple change points in multidimensional time series is proposed. It is based on the notion of *ε*-complexity of continuous vector functions. The proposed methodology does not use any prior information on data-generating mechanisms; therefore, it can be applied to multidimensional time series of arbitrary nature. Its performance is demonstrated in simulations and an application to high-frequency financial data.

In this paper, we take financial crisis into consideration for American call options and put options pricing problems by using a jump diffusion model. Under no-arbitrage pricing principle, we obtain a PDE (partial differential equation), which is different from the PDE derived from the classical Black-Scholes model, it adds a postcrash market index to the primary equation. Then, we introduce the penalty method for solving the nonlinear PDE. Numerical results suggest that the option value will be affected by the crash.

Recent researches on Generalized Regression Neural Networks show that this technique could be a promising option for modeling nonlinear time series, in general, and for financial series, in particular. Different types of artificial neural networks have been extensively studied, but the relationship between the statistical properties of the input data series and the models' accuracy was not emphasized. Therefore, our aim is to provide such an analysis. We study the Bucharest Exchange Trading series registered during the period from October 2000 to September 2014. Firstly, we test the series randomness, the existence of an increasing or nonlinear trend, its stationarity around a deterministic trend, and the breakpoints existence. Then, using the series decomposition, we define the detrended series and the deseasonalized series. Secondly, we build Generalized Regression Neural Network models for the original series, the subseries detected after the segmentation, the detrended, and deseasonalized ones. Comparing the modeling results, we conclude that some “regularity” properties (as normality and homoskedasticity) do not influence the models' quality (as expected).

]]>This study investigates two random threshold shock models for a repairable deteriorating system with nonnegligible maintenance times, with and without a spare via a phase-type geometric process. The system fails whenever the intershock arrival time is less than a random threshold. The provision of stochastic lead time is incorporated in Model II so that an ordering policy *N*−1 and a replacement policy *N* based on the number of failures of the system are also considered. An explicit expression of the average cost rate is derived for both models and the optimal replacement policy *N** is obtained by minimizing the long-run average cost rate analytically. The numerical illustrations and sensitivity analysis provided therein conform to the observations made in the study.

In this paper, the problem of nonlinearity recovery in Hammerstein systems is considered. Two algorithms are presented: the first is a standard orthogonal series algorithm, whereas the other, ie, the aggregative one, exploits the convex programming approach. The finite sample size properties of both approaches are examined, compared, and illustrated in a numerical experiment. The aggregative algorithm performs better when the number of measurements is comparable to the number of parameters; however, it also imposes additional smoothness restrictions on the recovered nonlinearities.

Accurately charting the progress of oil production is a problem of great current interest. Oil production is widely known to be cyclical: in any given system, after it reaches its peak, a decline will begin. With this in mind, Marion King Hubbert developed his peak theory in 1956 based on the bell-shaped curve that bears his name. In the present work, we consider a stochastic model based on the theory of diffusion processes and associated with the Hubbert curve. The problem of the maximum likelihood estimation of the parameters for this process is also considered. Since a complex system of equations appears, with a solution that cannot be guaranteed by classical numerical procedures, we suggest the use of metaheuristic optimization algorithms such as simulated annealing and variable neighborhood search. Some strategies are suggested for bounding the space of solutions, and a description is provided for the application of the algorithms selected. In the case of the variable neighborhood search algorithm, a hybrid method is proposed in which it is combined with simulated annealing. In order to validate the theory developed here, we also carry out some studies based on simulated data and consider 2 real crude oil production scenarios from Norway and Kazakhstan.

]]>Discrete-time stochastic volatility models play a key role in the analysis of financial time series. However, the parametric assumption of conditional distribution for asset returns, given the volatility, has been questioned. When the conditional distribution is unknown and unspecified, in this paper, a maximum-likelihood estimation approach for the semiparametric stochastic volatility models is proposed based on kernel density estimation and hidden Markov models. Several numerical studies are conducted to evaluate the finite sample performance of the proposed estimation method. Implementation on empirical studies also illustrates the validity of the proposed method in practice.

]]>A coherent system that consists of *n* independent components and equipped with *r* cold standby components is considered. A generalized mixture representation for the survival function of such a system is obtained, and it is used to examine reliability properties of the system. In particular, the effect of adding *r* standby components to a given set of original components is measured by computing mean time to failure of the system. The limiting behavior of the failure rate of the system is also examined using the mixture representation. The results are illustrated for a bridge system. A case study that is concerned with an oil pipeline system is also presented.

This paper first empirically measured the investment efficiency and the influence of equity incentive on investment efficiency of listed companies in China within supply-side structural reform based on the two-tier stochastic frontier approach. The two-tier stochastic frontier model was combined with the traditional *Richardson Model* and the data of empirical test were based on the nonfinancial companies, which is listed on Shanghai and Shenzhen A-Share Markets in the period 2009 to 2015. On the aspect of investment efficiency, the different results were obtained from the overall empirical test, and further tests grouped by property rights, scales, and regions, and the corresponding reasons were analyzed. On the other aspect of influence of equity incentive on investment efficiency, the results showed that the implementation of equity incentive contributed to improve the overinvestment and underinvestment but the effects were not considerable in Chinese listed companies studied in this paper. Last, some suggestions on the problems found during the research were put forward.

Kriging (or a Gaussian process) provides metamodels for deterministic and random simulation models. Actually, there are several types of Kriging; the classic type is the so-called universal Kriging, which includes ordinary Kriging. These classic types require estimation of the trend in the input-output data of the underlying simulation model; this estimation weakens the Kriging metamodel. We therefore consider the so-called intrinsic Kriging (IK), which originated in geostatistics, and derive IK types for deterministic simulations and random simulations, respectively. Moreover, for random simulations, we derive experimental designs that specify the number of replications that varies with the input combination of the simulation model. To compare the performance of IK and classic Kriging, we use several numerical experiments with deterministic simulations and random simulations, respectively. These experiments show that IK gives better metamodels, in most experiments.

]]>The mathematical concept of multiplier robust control is applied to a dam operation problem, which is an urgent issue on river water environment, as a new industrial application of stochastic optimal control. The goal of the problem is to find a fit-for-purpose and environmentally sound operation policy of the flow discharge from a dam so that overgrowth of the harmful algae *Cladophora glomerata* *Kützing* in its downstream river is effectively suppressed. A minimal stochastic differential equation for the algae growth dynamics with uncertain growth rate is first presented. The performance index to be maximized by the operator of the dam while minimized by nature is formulated within the framework of differential games. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs equation whose solution determines the worst-case optimal operation policy of the dam, ie, the policy that the operator wants to find. Application of the model to overgrowth suppression of *Cladophora glomerata* *Kützing* just downstream of a dam in a Japanese river is then carried out. Values of the model parameters are identified with which the model successfully reproduces the observed population dynamics. A series of numerical experiments are performed to find the most effective operation policy of the dam based on a relaxation of the current policy.

We propose a rule-based method of spike detection and suppression method. This method is an extension of the jump detector that was proposed by the second author, M. Pawlak and A. Steland. Its elementary properties are established, and the example of application for a laser power control in a 3-dimensional additive manufacturing process is discussed.

]]>The use of definitive screening designs (DSDs) has been increasing since their introduction in 2011. These designs are used to screen factors and to make predictions. We assert that the choice of analysis method for these designs depends on the goal of the experiment, screening, or prediction. In this work, we present simulation results to address the explanatory (screening) use and the predictive use of DSDs. To address the predictive ability of DSDs, we use two 5-factor DSDs and simultaneously run central composite designs case studies on which we will compare several common analysis methods. Overall, we find that for screening purposes, the Dantzig selector using the Bayesian Information Criterion statistic is a good analysis choice; however, when the goal of analysis is prediction forward selection using the Bayesian Information Criterion statistic produces models with a lower mean squared prediction error.

]]>In accelerated life tests (ALTs), test units are often tested in multiple test chambers along with different stress conditions. The nonhomogeneity of test chambers precludes the complete randomized experiment and may affect the life-stress relationship of the test product. The chamber-to-chamber variation should be taken into account for ALT planning so as to obtain more accurate test results. In this paper, planning ALTs under a nested experimental design structure with random test chamber effects is studied. First, by a 2-phase approach, we illustrate to what extent different test chamber assignments to stress conditions may impact the estimation of unknown parameters. Then, *D*-optimal test plans with 2 test chambers are considered. To construct the optimal design, we establish the generalized linear mixed model for failure-time data and apply a quasi-likelihood method, where test chamber assignments, as well as other decision variables that are required for planning ALTs, are simultaneously determined.

The stochastic behaviour of lifetimes of a two component system is often primarily influenced by the system structure and by the covariates shared by the components. Any meaningful attempt to model the lifetimes must take into consideration the factors affecting their stochastic behaviour. In particular, for a load share system, we describe a reliability model incorporating both the load share dependence and the effect of observed and unobserved covariates. The model includes a bivariate Weibull to characterize load share, a positive stable distribution to describe frailty, and also incorporates effects of observed covariates. We investigate various interesting reliability properties of this model using cross ratio functions and conditional survivor functions. We implement maximum likelihood estimation of the model parameters and discuss model adequacy and selection. We illustrate our approach using a simulation study. For a real data situation, we demonstrate the superiority of the proposed model that incorporates both load share and frailty effects over competing models that incorporate just one of these effects. An attractive and computationally simple cross-validation technique is introduced to reconfirm the claim. We conclude with a summary and discussion.

]]>The computation of the reliability function of a (complex) coherent system is a difficult task. Hence, sometimes, we should simply work with some bounds (approximations). The computation of these bounds has been widely studied in the case of coherent systems with independent and identically distributed (IID) components. However, few results have been obtained in the case of heterogeneous (non ID) components. In this paper, we derive explicit bounds for systems with heterogeneous (independent or dependent) components. Also some stochastic comparisons are obtained. Some illustrative examples are included where we compare the different bounds proposed in the paper.

]]>We construct an arbitrage-free scenario tree reduction model, from which some arbitrage-free scenario tree reduction algorithms are designed. They ensure that the reduced scenario trees are arbitrage free. Numerical results show the practicality and efficiency of the proposed algorithms. Results for multistage portfolio selection problems demonstrate the necessity and importance for guaranteeing that the reduced scenario trees are arbitrage free, as well as the practicality of the proposed arbitrage-free scenario tree reduction algorithms for financial optimization.

]]>A discrete-time mover-stayer (MS) model is an extension of a discrete-time Markov chain, which assumes a simple form of population heterogeneity. The individuals in the population are either stayers, who never leave their initial states or movers who move according to a Markov chain. We, in turn, propose an extension of the MS model by specifying the stayer's probability as a logistic function of an individual's covariates. Such extension has been recently discussed for a continuous time MS but has not been considered before for a discrete time one. This extension allows for an in-sample classification of subjects who never left their initial states into stayers or movers. The parameters of an extended MS model are estimated using the expectation-maximization algorithm. A novel bootstrap procedure is proposed for out of sample validation of the in-sample classification. The bootstrap procedure is also applied to validate the in-sample classification with respect to a more general dichotomy than the MS one. The developed methods are illustrated with the data set on installment loans. But they can be applied more broadly in credit risk area, where prediction of creditworthiness of a loan borrower or lessee is of major interest.

]]>Relational event data, which consist of events involving pairs of actors over time, are now commonly available at the finest of temporal resolutions. Existing continuous-time methods for modeling such data are based on point processes and directly model interaction “contagion,” whereby one interaction increases the propensity of future interactions among actors, often as dictated by some latent variable structure. In this article, we present an alternative approach to using temporal-relational point process models for continuous-time event data. We characterize interactions between a pair of actors as either spurious or as resulting from an underlying, persistent connection in a latent social network. We argue that consistent deviations from expected behavior, rather than solely high frequency counts, are crucial for identifying well-established underlying social relationships. This study aims to explore these latent network structures in two contexts: one comprising of college students and another involving barn swallows.

]]>This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out-of-sample performance. A mixed-integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out-of-sample time period. As mixed-integer program is a well-known NP-hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental results show that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.

]]>One of the major challenges associated with the measurement of customer lifetime value is selecting an appropriate model for predicting customer future transactions. Among such models, the Pareto/negative binomial distribution (Pareto/NBD) is the most prevalent in noncontractual relationships characterized by latent customer defections; ie, defections are not observed by the firm when they happen. However, this model and its applications have some shortcomings. Firstly, a methodological shortcoming is that the Pareto/NBD, like all lifetime transaction models based on statistical distributions, assumes that the number of transactions by a customer follows a Poisson distribution. However, many applications have an empirical distribution that does not fit a Poisson model. Secondly, a computational concern is that the implementation of Pareto/NBD model presents some estimation challenges specifically related to the numerous evaluation of the Gaussian hypergeometric function. Finally, the model provides 4 parameters as output, which is insufficient to link the individual purchasing behavior to socio-demographic information and to predict the behavior of new customers. In this paper, we model a customer's lifetime transactions using the Conway-Maxwell-Poisson distribution, which is a generalization of the Poisson distribution, offering more flexibility and a better fit to real-world discrete data. To estimate parameters, we propose a Markov chain Monte Carlo algorithm, which is easy to implement. Use of this Bayesian paradigm provides individual customer estimates, which help link purchase behavior to socio-demographic characteristics and an opportunity to target individual customers.

]]>We propose a methodology based on partial least squares (PLS) regression models using the beta distribution, which is useful for describing data measured between zero and one. The beta PLS model parameters are estimated with the maximum likelihood method, whereas a randomized quantile residual and the generalized Cook and Mahalanobis distances are considered as diagnostic methods. A simulation study is provided for evaluating the performance of these diagnostic methods. We illustrate the methodology with real-world mining data. The results obtained in this study based on the beta PLS model and its diagnostics may be of interest for the mining industry.

]]>This paper considers information properties of coherent systems when component lifetimes are independent and identically distributed. Some results on the entropy of coherent systems in terms of ordering properties of component distributions are proposed. Moreover, various sufficient conditions are given under which the entropy order among systems as well as the corresponding dual systems hold. Specifically, it is proved that under some conditions, the entropy order among component lifetimes is preserved under coherent system formations. The findings are based on system signatures as a useful measure from comparison purposes. Furthermore, some results on the system's entropy are derived when lifetimes of components are dependent and identically distributed. Several illustrative examples are also given.

]]>Microseismic sensing networks are important tools for the assessment and control of geomechanical hazards in underground mining operations. In such a setting, the maintenance of a healthy network, that is, one that accurately registers all microseisms above some minimum energy level with acceptable levels of noise, is crucially relevant.

In this paper, we develop a nondisruptive method to monitor the health of such a network, by associating with each sensor a set of performance indexes, inspired from reliability engineering, which are estimated from the set of registered signals. Our method addresses 2 relevant features of each of the sensors' behavior, namely, what type of noise is or might be affecting the registering process, and how effective at registering microseisms the sensor is.

The method is evaluated through a case study with microseismic data registered at the Chilean underground mine El Teniente. This study illustrates our method's capability to discriminate and rank sensors with satisfactory, poor, or defective sensing performances, as well as to characterize their failure profile or type, an information that can be used to plan or optimize the network maintenance procedures.

In recent years, there has been an increasing incidence of failure of rock bolts due to stress corrosion cracking and localized corrosion attack in Australian underground coal mines. Unfortunately, prediction of the risk of failure from results obtained from laboratory testing is not necessarily reliable because it is difficult to properly simulate the mine environment. An alternative way of predicting failure is to apply machine learning methods to data obtained from underground mines. In this paper, support vector machines are built to predict failure of bolts in complex mine environments. Feature transformation and feature selection methods are applied to extract useful information from the original data. A dataset, which had continuous features and spatial data, was used to test the proposed model. The results showed that principal component analysis-based feature transformation provides reliable risk prediction.

]]>In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance-gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off-line Markov Chain Monte Carlo in synthetic and real data applications.

]]>No abstract is available for this article.

]]>This paper proposes a dynamic system, with an associated fusion learning inference procedure, to perform real-time detection and localization of nuclear sources using a network of mobile sensors. This is motivated by the need for a reliable detection system in order to prevent nuclear attacks in major cities such as New York City. The approach advocated here installs a large number of relatively inexpensive (and perhaps relatively less accurate) nuclear source detection sensors and GPS devices in taxis and police vehicles moving in the city. Sensor readings and GPS information are sent to a control center at a high frequency, where the information is immediately processed and fused with the earlier signals. We develop a real-time detection and localization method aimed at detecting the presence of a nuclear source and estimating its location and power. We adopt a Bayesian framework to perform the fusion learning and use a sequential Monte Carlo algorithm to estimate the parameters of the model and to perform real-time localization. A simulation study is provided to assess the performance of the method for both stationary and moving sources. The results provide guidance and recommendations for an actual implementation of such a surveillance system. Copyright © 2017 John Wiley & Sons, Ltd.

]]>A commonly occurring problem in reliability testing is how to combine pass/fail test data that is collected from disparate environments. We have worked with colleagues in aerospace engineering for a number of years where two types of test environments in use are ground tests and flight tests. Ground tests are less expensive and consequently more numerous. Flight tests are much less frequent, but directly reflect the actual usage environment. We discuss a relatively simple combining approach that realizes the benefit of a larger sample size by using ground test data, but at the same time accounts for the difference between the two environments. We compare our solution with what look like more sophisticated approaches to the problem in order to calibrate its limitations. Overall, we find that our proposed solution is robust to its inherent assumptions, which explains its usefulness in practice. Copyright © 2017 John Wiley & Sons, Ltd.

]]>Model fusion methods, or more generally ensemble methods, are a useful tool for prediction. Combining predictions from a set of models smooths out biases and reduces variances of predictions from individual models, and hence, the combined predictions typically outperform those from individual models. In many algorithms, individual predictions are arithmetically averaged with equal weights. However, in the presence of correlated models, the fusion process is required to account for association between models; otherwise, the naively averaged predictions will be suboptimal. This article describes optimal model fusion principles and illustrates the potential pitfalls of naive fusion in the presence of correlated models for binary data. An efficient algorithm for correlated model fusion is detailed and applied to algorithms mining social media information to predict civil unrest. Copyright © 2017 John Wiley & Sons, Ltd.

]]>Missing data are prevalent issue in analyses involving data collection. The problem of missing data is exacerbated for multisource analysis, where data from multiple sensors are combined to arrive at a single conclusion. In this scenario, it is more likely to occur and can lead to discarding a large amount of data collected; however, the information from observed sensors can be leveraged to estimate those values not observed. We propose two methods for imputation of multisource data, both of which take advantage of potential correlation between data from different sensors, through ridge regression and a state-space model. These methods, as well as the common median imputation, are applied to data collected from a variety of sensors monitoring an experimental facility. Performance of imputation methods is *compared* with the mean absolute deviation; however, rather than using this metric to solely rank the methods, we also propose an approach to identify significant differences. Imputation techniques will also be *assessed* by their ability to produce appropriate confidence intervals, through coverage and length, around the imputed values. Finally, performance of imputed datasets is compared with a marginalized dataset through a weighted k-means clustering. In general, we found that imputation through a dynamic linear model tended to be the most accurate and to produce the most precise confidence intervals, and that imputing the missing values and down weighting them with respect to observed values in the analysis led to the most accurate performance. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

This article describes statistical analyses pertaining to marketing data from a large multinational pharmaceutical firm. We describe models for monthly new prescription counts that are written by physicians for the firm's focal drug and for competing drugs, as functions of physician-specific and time-varying predictors. Modeling patterns in discrete-valued time series, and specifically time series of counts, based on large datasets, is the focus of much recent research attention. We first provide a brief overview of Bayesian approaches we have employed for modeling multivariate count time series using Markov Chain Monte Carlo methods. We then discuss a flexible level correlated model framework, which enables us to combine different marginal count distributions and to build a hierarchical model for the vector time series of counts, while accounting for the association among the components of the response vector, as well as possible overdispersion. We employ the integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling using the R-INLA package (r-inla.org). To enhance computational speed, we first build a model for each physician, use features of the estimated trends in the time-varying parameters in order to cluster the physicians into groups, and fit aggregate models for all physicians within each cluster. Our three-stage analysis can provide useful guidance to the pharmaceutical firm on their marketing actions. Copyright © 2017 John Wiley & Sons, Ltd.

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