Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality

This paper presents a mean‐reverting jump diffusion model for the electricity spot price and derives the corresponding forward price in closed‐form. Based on historical spot data and forward data from England and Wales the model is calibrated and months, quarters, and seasons–ahead forward surfaces are presented.     

Multivariate dynamic modeling for Bayesian forecasting of business revenue

Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi-scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context-relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi-scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross-category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.     

The power‐of‐pull of economic sectors: A complex network analysis

To compare the relative power of individual sectors to pull the entire economy, i.e., the power‐of‐pull, this article utilizes a complex system perspective to model the economy as a network of economic sectors connected by trade flows. A sector's power‐of‐pull is defined and calculated as a function of the powers‐of‐pull of those sectors that it pulls through network linkages, and their powers‐of‐pull are, in turn, functions of those sectors that they further pull ad infinitum throughout the network. Theoretically, boosting activities in sectors with a higher power‐of‐pull will generate greater network effects while stimulating the entire economy, especially during recessions. This method is applied to the United States in the years before and after the 2008 financial crisis. The results provide a fresh look at the U.S. government's economic revival policies and reveal fundamental changes in the economic structure of the U.S. This work advocates a network‐based analysis of the economy as a complex system. © 2013 Wiley Periodicals, Inc. Complexity 18: 37–47, 2013     

Eigen‐frequencies in thin elastic 3‐D domains and Reissner–Mindlin plate models

The eigen‐frequencies of elastic three‐dimensional thin plates are addressed and compared to the eigen‐frequencies of two‐dimensional Reissner–Mindlin plate models obtained by dimension reduction. The qualitative mathematical analysis is supported by quantitative numerical data obtained by the p‐version finite element method. The mathematical analysis establishes an asymptotic expansion for the eigen‐frequencies in power series of the thickness parameter. Such results are new for orthotropic materials and for the Reissner–Mindlin model. The 3‐D and R–M asymptotics have a common first term but differ in their second terms. Numerical experiments for clamped plates show that for isotropic materials and relatively thin plates the Reissner–Mindlin eigen‐frequencies provide a good approximation to the three‐dimensional eigen‐frequencies. However, for some anisotropic materials this is no longer the case, and relative errors of the order of 30 per cent are obtained even for relatively thin plates. Moreover, we showed that no shear correction factor is known to be optimal in the sense that it provides the best approximation of the R–M eigen‐frequencies to their 3‐D counterparts uniformly (for all relevant thicknesses range). Copyright © 2002 John Wiley & Sons, Ltd.     

Convergence analysis for parallel‐in‐time solution of hyperbolic systems

Parallel‐in‐time algorithms have been successfully employed for reducing time‐to‐solution of a variety of partial differential equations, especially for diffusive (parabolic‐type) equations. A major failing of parallel‐in‐time approaches to date, however, is that most methods show instabilities or poor convergence for hyperbolic problems. This paper focuses on the analysis of the convergence behavior of multigrid methods for the parallel‐in‐time solution of hyperbolic problems. Three analysis tools are considered that differ, in particular, in the treatment of the time dimension: (a) space–time local Fourier analysis, using a Fourier ansatz in space and time; (b) semi‐algebraic mode analysis, coupling standard local Fourier analysis approaches in space with algebraic computation in time; and (c) a two‐level reduction analysis, considering error propagation only on the coarse time grid. In this paper, we show how insights from reduction analysis can be used to improve feasibility of the semi‐algebraic mode analysis, resulting in a tool that offers the best features of both analysis techniques. Following validating numerical results, we investigate what insights the combined analysis framework can offer for two model hyperbolic problems, the linear advection equation in one space dimension and linear elasticity in two space dimensions.     

Asymptotic dynamics of the one‐dimensional attraction–repulsion Keller–Segel model

The asymptotic behavior of the attraction–repulsion Keller–Segel model in one dimension is studied in this paper. The global existence of classical solutions and nonconstant stationary solutions of the attraction–repulsion Keller–Segel model in one dimension were previously established by Liu and Wang (2012), which, however, only provided a time‐dependent bound for solutions. In this paper, we improve the results of Liu and Wang (2012) by deriving a uniform‐in‐time bound for solutions and furthermore prove that the model possesses a global attractor. For a special case where the attractive and repulsive chemical signals have the same degradation rate, we show that the solution converges to a stationary solution algebraically as time tends to infinity if the attraction dominates. Copyright © 2014 John Wiley & Sons, Ltd.     

Simultaneity and non‐linear variability in financial markets: simulation and forecasting

Non‐linear variability in financial markets can emerge from several mechanisms, including simultaneity and time‐varying coefficients. In simultaneous equation systems, the reduced‐form coefficients that determine the behaviour of jointly dependent variables are products and ratios of the original structural coefficients. If the coefficients are stochastic, the resulting multiplicative interactions will result in high degrees of non‐linearity. Processes generated in this way will scale as fractals: they will exhibit intermittent outliers and scaling symmetries, i.e. proportionality relationships between fluctuations at different separation distances. A model is specified in which both the exchange rate itself and the exchange rate residual exhibit simultaneity. The exchange rate depends on other exchange rates, while the residual depends on the other residuals. The model is then simulated using embedding noise from a t‐distribution. The simulations replicate the observed properties of exchange rates, heavy‐tailed distributions and long memory in the variance. A forecasting algorithm is specified in two stages. The first stage is a model for the actual process. In the second stage the residuals are modelled as a function of the predicted rate of change. The first and second stage models are then combined. This algorithm exploits the scaling symmetry: the residual is proportional to the predicted rate of change at separation distances corresponding to the forecast horizon. The procedure is tested empirically on three exchange rates. At a daily frequency and a 1‐day forecast horizon, two‐stage models reduce the forecast error by one fourth. At a 5‐day horizon, the improvement is 10–15 percent. At a weekly frequency, the improvement at the 1‐week horizon is on the order of 30–40 percent. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian tail‐risk forecasting using realized GARCH

A realized generalized autoregressive conditional heteroskedastic (GARCH) model is developed within a Bayesian framework for the purpose of forecasting value at risk and conditional value at risk. Student‐t and skewed‐t return distributions are combined with Gaussian and student‐t distributions in the measurement equation to forecast tail risk in eight international equity index markets over a 4‐year period. Three realized measures are considered within this framework. A Bayesian estimator is developed that compares favourably, in simulations, with maximum likelihood, both in estimation and forecasting. The realized GARCH models show a marked improvement compared with ordinary GARCH for both value‐at‐risk and conditional value‐at‐risk forecasting. This improvement is consistent across a variety of data and choice of distributions. Realized GARCH models incorporating a skewed student‐t distribution for returns are favoured overall, with the choice of measurement equation error distribution and realized measure being of lesser importance. Copyright © 2017 John Wiley & Sons, Ltd.     

多机制半参数平滑转换回归模型——兼论我国宏观经济运行周期

本文结合多机制平滑转换回归模型和半参数平滑转换回归模型,提出多机制半参数平滑转换回归模型。对模型转换函数中的未知光滑有界函数采用级数估计,并给出了结合Back-fitting算法和非线性最小二乘法估计模型参数的具体执行步骤,随机模拟结果说明了本文模型和估计算法的可行性和灵活性。应用本文模型和估计算法对我国宏观经济运行周期的实证研究表明,我国经济增长的非线性结构可以分为四个显著不同的增长机制:扩张阶段、衰退阶段、收缩阶段、恢复阶段,并且宏观经济政策的作用有三到四个季度的迟滞效应。     

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Increasingly large volumes of space–time data are collected everywhere by mobile computing applications, and in many of these cases, temporal data are obtained by registering events, for example, telecommunication or Web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space–time autoregressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method is extended to include autoregressive terms of latent space–time processes. Specifically, a space–time autoregressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space–time process. The resulting model is specified within a hierarchical Bayesian framework, and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8‐h average ground level ozone concentration data from 1997 to 2006 from a large study region in the Eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of noncompliance with respect to the standard, are obtained and illustrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Capacity expansion with interrupted demand growth

In most long-range planning problems accurate forecasting of demand growth is often difficult. Sometimes unexpected shocks in the economy occur and disrupt the predicted growth rate of demand. For example, growth can unexpectedly cease for and indeterminate length of time due to crucial occurrnces such as wars, economic recessions or oil price shocks.In this paper, we examine the effects of unforeseen demand plateaus on the capacity expansion problem of sizing and timing production facilities. We assume that demand for capacity follows a stochastic process. That is, we allow for plateaus to happen at random future times and to continue for an uncertain duration. When the demand process is generated by an alternating renewal process, we show that demand plateaus result in a modified discounting rate and a modified import cost.     

Message‐Passing Algorithms for Synchronization Problems over Compact Groups

Various alignment problems arising in cryo‐electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as ℤ/L, U(1), or SO(3). The goal in such problems is to estimate an unknown vector of group elements given noisy relative observations. We present an efficient iterative algorithm to solve a large class of these problems, allowing for any compact group, with measurements on multiple “frequency channels” (Fourier modes, or more generally, irreducible representations of the group). Our algorithm is a highly efficient iterative method following the blueprint of approximate message passing (AMP), which has recently arisen as a central technique for inference problems such as structured low‐rank estimation and compressed sensing. We augment the standard ideas of AMP with ideas from representation theory so that the algorithm can work with distributions over general compact groups. Using standard but nonrigorous methods from statistical physics, we analyze the behavior of our algorithm on a Gaussian noise model, identifying phases where we believe the problem is easy, (computationally) hard, and (statistically) impossible. In particular, such evidence predicts that our algorithm is information‐theoretically optimal in many cases, and that the remaining cases exhibit statistical‐to‐computational gaps. © 2018 Wiley Periodicals, Inc.     

Model‐based quantification of the volatility of options at transaction level with extended count regression models

In this paper, we elaborate how Poisson regression models of different complexity can be used in order to model absolute transaction price changes of an exchange‐traded security. When combined with an adequate autoregressive conditional duration model, our modelling approach can be used to construct a complete modelling framework for a security's absolute returns at transaction level, and thus for a model‐based quantification of intraday volatility and risk. We apply our approach to absolute price changes of an option on the XETRA DAX index based on quote‐by‐quote data from the EUREX exchange and find that within our Bayesian framework a Poisson generalized linear model (GLM) with a latent AR(1) process in the mean is the best model for our data according to the deviance information criterion (DIC). While, according to our modelling results, the price development of the underlying, the intrinsic value of the option at the time of the trade, the number of new quotations between two price changes, the time between two price changes and the Bid–Ask spread have significant effects on the size of the price changes, this is not the case for the remaining time to maturity of the option. Copyright © 2006 John Wiley & Sons, Ltd.     

Organizational dynamic embeddedness and external shocks: The impact of financial and recession crises in strategic networks of the global pharmaceutical industry

We analyze the global pharmaceutical industry network using a unique database that covers strategic transactions (i.e., alliance, financing and acquisition collaborations) for the top 90 global pharmaceutical firms and their ego‐network partnerships totaling 4735 members during 1991–2012. The article explores insights on dynamic embeddedness analysis under network perturbations by exploring core and full networks' behavior during the global financial crisis of 2007–2008 and the subsequent global and Eurozone recessions of 2009–2012. We introduce and test literature grounded hypotheses as well as report network visualizations and nonparametric tests that reveal important discrepancies in both network types before and after the financial crisis offset. We observe that firms in core and full networks behave differently, with smaller top pharmaceutical firms of core networks particularly being affected by the crises, potentially due to a collaboration reduction with bigger top pharmaceuticals. On the other hand, big pharmaceuticals in full networks maintain their centrality position as a possible consequence of their strategic collaborations not only with other similarly sized firms but also due to their connections with subsidiaries and other private entities present in the total sample. Our results confirm the significant dynamicity reduction during financial crisis and recession periods for core and full networks, and highlight the importance that exogenous factors as well as network types play in centrality‐based dynamic longitudinal network analysis. © 2016 Wiley Periodicals, Inc. Complexity 21: 602–621, 2016     

Bayesian forecasting with the Holt–Winters model

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.     

基于贝叶斯向量自回归的区域经济预测模型:以青海为例

由于缺乏足够的观测数据等原因,常规的区域经济预测模型在我国难以获得预期的预测效果,而贝叶斯向量自回归(BVAR)模型将变量的统计性质作为参数的先验分布引入到传统的VAR模型中,能够克服自由度过少的问题,以青海为例,本文建立了一个BVAR模型,并引入了全国GDP和中央政府转移支付作为外生变量以描述国民经济与区域经济的联系...     

An efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations

In this paper, we propose an efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations. Firstly, we carry out a truncation from a three‐dimensional unbounded domain to a bounded spherical domain. By using spherical coordinate transformation and spherical harmonic expansion, we transform the original problem into a series of one‐dimensional eigenvalue problem that can be solved effectively. Secondly, we introduce a weighted Sobolev space to treat the singularity in the effective potential. Using the property of orthogonal polynomials in weighted Sobolev space, the error estimate for the approximate eigenvalues and corresponding eigenfunctions are proved. Error estimates show that our numerical method can achieve spectral accuracy for approximate eigenvalues and eigenfunctions. Finally, we give some numerical examples to demonstrate the efficiency of our algorithms and the correctness of the theoretical results.     

Forecasting seasonal time series data: a Bayesian model averaging approach

A flexible Bayesian periodic autoregressive model is used for the prediction of quarterly and monthly time series data. As the unknown autoregressive lag order, the occurrence of structural breaks and their respective break dates are common sources of uncertainty these are treated as random quantities within the Bayesian framework. Since no analytical expressions for the corresponding marginal posterior predictive distributions exist a Markov Chain Monte Carlo approach based on data augmentation is proposed. Its performance is demonstrated in Monte Carlo experiments. Instead of resorting to a model selection approach by choosing a particular candidate model for prediction, a forecasting approach based on Bayesian model averaging is used in order to account for model uncertainty and to improve forecasting accuracy. For model diagnosis a Bayesian sign test is introduced to compare the predictive accuracy of different forecasting models in terms of statistical significance. In an empirical application, using monthly unemployment rates of Germany, the performance of the model averaging prediction approach is compared to those of model selected Bayesian and classical (non)periodic time series models.     

Modeling first bid in retail secondary market online auctions: A Bayesian approach

We propose a Bayesian framework to model bid placement time in retail secondary market online business‐to‐business auctions. In doing so, we propose a Bayesian beta regression model to predict the first bidder and time to first bid, and a dynamic probit model to analyze participation. In our development, we consider both auction‐specific and bidder‐specific explanatory variables. While we primarily focus on the predictive performance of the models, we also discuss how auction features and bidders' heterogeneity could affect the bid timings, as well as auction participation. We illustrate the implementation of our models by applying to actual auction data and discuss additional insights provided by the Bayesian approach, which can benefit auctioneers.     

Forecasting tender price index under incomplete information

Tender price index (TPI) is essential for estimating the likely tender price of a given project. Due to incomplete information on future market conditions, it is difficult to accurately forecast the TPI. Most traditional statistical forecasting models require a certain number of historical data, which may not be completely available in many practical situations. In order to overcome this problem, the grey model is proposed for forecasting TPIs because it only requires a small number of input data. For this study, the data source was based on the TPIs produced by the Government's Architectural Services Department. On the basis of four input data, the grey model forecasted TPIs from 1981Q1 to 2011Q4. The mean absolute percentage errors of forecast TPIs in one quarter and two quarters ahead were 3.62 and 7.04%, respectively. In order to assess the accuracy and reliability of the grey model further, the same research method was used to forecast other three TPIs in Hong Kong. The forecasting results of all four TPIs were found to be very good. It was thus concluded that the grey model could be able to produce accurate TPI forecasts for a one-quarter to two-quarter forecast horizon.