Empirical likelihood intervals for conditional Value‐at‐Risk in ARCH/GARCH models

Value‐at‐Risk (VaR) is a simple, but useful measure in risk management. When some volatility model is employed, conditional VaR is of importance. As autoregressive conditional heteroscedastic (ARCH) and generalized ARCH (GARCH) models are widely used in modelling volatilities, in this article, we propose empirical likelihood methods to obtain an interval estimation for the conditional VaR with the volatility model being an ARCH/GARCH model.     

Modeling and optimization of product design and portfolio management interface

The paper presents modeling and analysis of product design and product portfolio management (PD-PM) domains interaction using an integrated simulation-optimization model. To represent the interactions, the product design phase is modeled as a discrete-scenario static system. The goal of this work is to develop a decision support framework that relies on product design-product portfolio management integration in order to aid product design planning and design execution. We utilize dependency matrix approach to illustrate domain relation between the product design and product portfolio management domains, and to facilitate their integration. Hence, the process integration model utilizes iterative effects, and their attendant processing duration and costs, to pattern domain interaction. An industrial case study is used to illustrate the application and utility of the proposed approach.     

Multi-variate t Autoregressions: Innovations, Prediction Variances and Exact Likelihood Equations

Abstract.  The multi-variate t distribution provides a viable framework for modelling volatile time-series data; it includes the multi-variate Cauchy and normal distributions as special cases. For multi-variate t autoregressive models, we study the nature of the innovation distribution and the prediction error variance; the latter is nonconstant and satisfies a kind of generalized autoregressive conditionally heteroscedastic model. We derive the exact likelihood equations for the model parameters, they are related to the Yule–Walker equations and involve simple functions of the data, the model parameters and the autocovariances up to the order of the model. The maximum likelihood estimators are obtained by alternately solving two linear systems and illustrated using the lynx data. The simplicity of these equations contributes greatly to our theoretical understanding of the likelihood function and the ensuing estimators. Their range of applications are not limited to the parameters of autoregressive models; in fact, they are applicable to the parameters of ARMA models and covariance matrices of stochastic processes whose finite-dimensional distributions are multi-variate t .     

Maximum‐likelihood maximum‐entropy constrained probability density function estimation for prediction of rare events

This work addresses the problem of estimating complete probability density functions (PDFs) from historical process data that are incomplete (lack information on rare events), in the framework of Bayesian networks. In particular, this article presents a method of estimating the probabilities of events for which historical process data have no record. The rare‐event prediction problem becomes more difficult and interesting, when an accurate first‐principles model of the process is not available. To address this problem, a novel method of estimating complete multivariate PDFs is proposed. This method uses the maximum entropy and maximum likelihood principles. It is tested on mathematical and process examples, and the application and satisfactory performance of the method in risk assessment and fault detection are shown. Also, the proposed method is compared with a few copula methods and a nonparametric kernel method, in terms of performance, flexibility, interpretability, and rate of convergence. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1013–1026, 2014     

Bayesian sequential joint detection and estimation

Abstract

Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.     

Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions

In this article, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well known that the group lasso estimator is not simultaneously estimation consistent and model selection consistent in structural break settings. Hence, we use a first step group lasso estimation of a diverging number of breakpoint candidates to produce weights for a second adaptive group lasso estimation. We prove that parameter changes are estimated consistently by group lasso and show that the number of estimated breaks is greater than the true number but still sufficiently close to it. Then, we use these results and prove that the adaptive group lasso has oracle properties if weights are obtained from our first step estimation. Simulation results show that the proposed estimator delivers the expected results. An economic application to the long-run US money demand function demonstrates the practical importance of this methodology.     

DYNAMIC STATE-SPACE MODELS

Abstract. In many cases, multiple time series can be viewed as realizations of the same underlying process and such data usually accumulate in time. The historic time-series data provide important information for our current prediction. In this paper, we extend the traditional state-space model to a general dynamic scheme, in which estimation and prediction across time series and within a time series are handled by a unified O ( N ) sequential procedure. Under this framework, the information from historic data serves as the prior for the current time series and the estimation and prediction of a time series can incorporate the information from other time series as well as its own history. The solution is to construct sequentially a new state-space model for the next time series conditional on the past time series. Because we achieve the general dynamic estimation and prediction through constructing new conditional state-space models, existing estimation procedures for state-space models can be adapted into this framework with minimal modifications. An application to infant growth curves is used as illustration.     

Integrated approach to improving the value potential of biopharmaceutical R&D portfolios while mitigating risk

Effective prioritisation of R&D portfolios under resource constraints is critical for biopharmaceutical companies to gain competitive advantage. This paper presents an application of a prototype software tool to assess the reward and risk associated with different drug portfolios in development. The tool adopts a hierarchical framework to incorporate the interactions between drug development activities, the available resources and databases. The valuation approach highlights the cash flow implications of diverse portfolios under uncertainty and uses efficient frontier analysis to prioritise portfolios for given constraints. A case study is presented to illustrate the application of this method where Monte Carlo simulations are used to capture the inherent uncertainties in drug development. The example addresses the portfolio management question of which antibody drug candidates to select for clinical development given finite levels of resources. The analysis highlighted the impact of different drug combinations on the expected portfolio profitability and risk. The simulation studies were used to generate efficient frontiers so as to identify the optimal portfolios at different levels of risk and budgetary constraint. This valuation method helps decision‐makers to identify clearly where a company portfolio is positioned with regard to the risk‐return characteristics of alternative product portfolios and hence facilitates investment decisions. Copyright © 2006 Society of Chemical Industry     

Partition-based distributed extended Kalman filter for large-scale nonlinear processes with application to chemical and wastewater treatment processes

In this article, we address a partition-based distributed state estimation problem for large-scale general nonlinear processes by proposing a Kalman-based approach. First, we formulate a linear full-information estimation design within a distributed framework as the basis for developing our approach. Second, the analytical solution to the local optimization problems associated with the formulated distributed full-information design is established, in the form of a recursive distributed Kalman filter algorithm. Then, the linear distributed Kalman filter is extended to the nonlinear context by incorporating successive linearization of nonlinear subsystem models, and the proposed distributed extended Kalman filter approach is formulated. We conduct rigorous analysis and prove the stability of the estimation error dynamics provided by the proposed method for general nonlinear processes consisting of interconnected subsystems. A chemical process example is used to illustrate the effectiveness of the proposed method and to justify the validity of the theoretical findings. In addition, the proposed method is applied to a wastewater treatment process for estimating the full-state of the process with 145 state variables.     

回填土壤Cd、Pb、Cu、As现状调查及生态风险评价

某高校回填工程是该校基础建设的重要内容之一,该回填工程大、时间长、回填土壤来源广泛,校园人口较为密集,因此对该回填工程所用土壤进行生态风险评估极为必要。本研究在对回填工程土壤重金属总量分析的基础上,采用单项潜在生态风险指数法和综合潜在生态风险指数法进行了生态风险评价。重金属总量分析结果表明:土壤中Cd、As和Cu含量的平均值分别超标26.33、4.35和2.23倍。生态风险评价结果表明:Cd和As分别属强度和中等风险,对生态危害的潜在风险很大;Cu和Pb属轻微风险,对生态危害性小。且采样点区域风险值由高至低依次排序为:9#3#1#7#6#10#4#12#11#5#8#2#13#,总体上看,整个回填工程区域存在较强的生态风险。     

CONTRIBUTIONS TO EVOLUTIONARY SPECTRAL THEORY

Abstract. The purpose of this paper is to discuss several fundamental issues in the theory of time-dependent spectra for univariate and multivariate non-stationary processes. The general framework is provided by Priestley's evolutionary spectral theory which is based on a family of stochastic integral representations. A particular spectral density function can be obtained from the Wold—Cramér decomposition, as illustrated by several examples. It is shown why the coherence is time invariant in the evolutionary theory and how the theory can be generalized so that the coherence becomes time dependent. Statistical estimation of the spectrum is also considered. An improved upper bound for the bias due to non-stationarity is obtained which does not rely on the characteristic width of the process. The results obtained in the paper are illustrated using time series simulated from an evolving bivariate autoregressive moving-average process of order (1, 1) with a highly time-varying coherence.     

ESTIMATION FOR NON-LINEAR TIME SERIES MODELS USING ESTIMATING EQUATIONS

Godambe's (1985) theorem on optimal estimating equations for stochastic processes is applied to non-linear time series estimation problems. Examples are considered from the usual classes of non-linear time series models. A recursive estimation procedure based on optimal estimating equations is provided. It is also shown that pre-filtered estimates can be used to obtain the optimal estimate from a non-linear state-space model.     

FAST LINEAR ESTIMATION METHODS FOR VECTOR AUTOREGRESSIVE MOVING-AVERAGE MODELS

Abstract. Three linear methods for estimating parameter values of vector auto-regressive moving-average (VARMA) models which are in general at least an order of magnitude faster than maximum likelihood estimation are developed in this paper. Simulation results for different model structures with varying numbers of component series and observations suggest that the accuracy of these procedures is in most cases comparable with maximum likelihood estimation. Procedures for estimating parameter standard error are also discussed and used for identification of nonzero elements in the VARMA polynomial structures. These methods can also be used to establish the order of the VARMA structure. We note, however, that the primary purpose of these estimates is to generate initial estimates for the nonzero parameters in order to reduce subsequent computational time of more efficient estimation procedures such as exact maximum likelihood.     

Estimation of rheological parameters using velocity measurements

In the present investigation, we develop a method for estimating rheological parameters of viscoelastic fluids using velocity measurement in a square straight channel. It is believed that a somewhat complicated patterns of secondary flows due to the non-zero second normal stress difference are more useful than the simple viscometric flows traditionally adopted in the determination of rheological parameters. The inverse problem of determining the rheological parameters from a set of velocity measurements is solved using a conjugate gradient method. When applied to a general constitutive equation encompassing the UCM model, the Oldroyd-B model and the PTT model, the present method is found to yield a reasonably accurate estimation of five rheological parameters simultaneously even with noisy velocity measurements.     

Multistage Estimation Procedures with Bounded Risk for the Normal Mean Under LINEX Loss Function

Abstract

This paper considers multistage estimation procedures to achieve a bounded risk when estimating the mean of a normal distribution under a LINEX loss function. Two-stage and three-stage estimation procedures are introduced and their second-order asymptotics are examined. Moderate-sample-size performances are compared between multistage and purely sequential procedures.     

Quasi‐Bayesian Estimation of Time‐Varying Volatility in DSGE Models

We propose a novel quasi‐Bayesian Metropolis‐within‐Gibbs algorithm that can be used to estimate drifts in the shock volatilities of a linearized dynamic stochastic general equilibrium (DSGE) model. The resulting volatility estimates differ from the existing approaches in two ways. First, the time variation enters non‐parametrically, so that our approach ensures consistent estimation in a wide class of processes, thereby eliminating the need to specify the volatility law of motion and alleviating the risk of invalid inference due to mis‐specification. Second, the conditional quasi‐posterior of the drifting volatilities is available in closed form, which makes inference straightforward and simplifies existing algorithms. We apply our estimation procedure to a standard DSGE model and find that the estimated volatility paths are smoother compared to alternative stochastic volatility estimates. Moreover, we demonstrate that our procedure can deliver statistically significant improvements to the density forecasts of the DSGE model compared to alternative methods.     

Bounded risk estimation of a finite population mean optimal strategies

Bounded risk estimation of the mean of a finite population is considered under three simple random sampling strategies: (i) with replacement, mean per unit estimation, (ii) with replacement, mean per distinct unit estimation, and (iii) without replacement, mean per unit estimation. It is well known that in the fixed sample size scheme, (iii) fares better than (ii) and (ii) better than (i). However, in the current context, the sample sizes are dictated by (possibly, degenerate) stopping times, and visualizing the cost (due to measurements/recording, etc.) as a function of the number of distinct units in the sample, it is shown that the second strategy still fares better than the first, although the third strategy may not perform better than the second one. Actually, in the case of known population variance, it is shown that in the light of the number of distinct units, the difference of ASN for the second and third strategies can never be greater than two or less than minus one. A similar relationship also holds in the case of unknown population variance when we define the stopping rules in a coherent manner. The theoretical results are backed up by numerical examples too. Also, dominance of strategy (ii) over (i) in a general sequential setup constitutes an important task of the current study. Finally, to reconcile strategies (ii) and (iii) in a general sequential setup, the coherence of the associated stopping times has also been discussed thoroughly.     

Composition and molecular-weight dependence of the glass transition in polystyrene-poly(2,6-dimethylphenylene ether) blends

The glass transition behaviours of a series of poly(2,6-dimethylphenylene ethers) with various molecular weights and their blends with polystyrene have been studied. The data are analysed according to the Fox-Flory equation (M_n dependence) and the Gordon-Taylor equation (composition dependence). A more rigorous treatment according to the theory developed by Kanig is presented and data of polystyrene-poly(vinyl methyl ether) blends, as well as polystyrene-poly(methyl vinylether) blends which do not obey the Gordon-Taylor equation, are discussed in the framework of this theory. The theory allows the estimation of the energy required to separateA-B contacts.     

Time‐Dependent Dual‐Frequency Coherence in Multivariate Non‐Stationary Time Series

Coherence is one common metric for cross‐dependence in multichannel signals. However, standard coherence does not sufficiently model many biological signals with complex dependence structures such as cross‐oscillatory interactions between a low‐frequency component in one signal and a high‐frequency component in another. The notion of cross‐dependence between low‐ and high‐frequency components, as defined in classical harmonizable processes, is still inadequate because it assumes time invariance and thus cannot capture cross‐frequency interactions that evolve over time. We construct a novel framework for modeling and estimating these dependencies under the replicated time series setting. Under this framework, we establish the novel concept of evolutionary dual‐frequency coherence and develop time‐localized estimators based on dual‐frequency local periodograms. The proposed nonparametric estimation procedure does not suffer from model misspecification. It uses the localized fast Fourier transform and hence is able to handle massive data. When applied to electroencephalogram data recorded in a motor intention experiment, the proposed method uncovers new and interesting cross‐oscillatory interactions that have been overlooked by the standard approaches.     

On sequential R estimation of location in the general behrens fisher model

For a general Behrens-Fisher model (relating to a shift in location between two symmetric distributions with possibly different shapes), asymptotic theory of sequential R-estimation is studied. Sequential versions of the usual two sample R-estimators and some alternative ones (based on the difference of one sample R-estimators) are considered and asymptotic risk efficiency results for these estimators are presented. In this context, under the general Behrens-Fisher model, for R-estimators, uniform integrability and moment convergence results are established.