An alternative method for forecasting price volatility by combining models

In this article, we study the volatility in the monthly price series of edible oils in domestic and international markets using the two popular family of nonlinear time-series models, viz, Generalized autoregressive conditional heteroscedastic (GARCH) models and Stochastic volatility (SV) models. To improve the forecasts of the volatility process, we also propose a new method of combining the volatility of these two competing models using the powerful technique of Kalman filter. The individual models as well as the combined models are assessed on their ability to predict the correct directional change (CDC) in future values as well as other goodness-of-fit statistics. Further, forecasting performance are also evaluated by computing various measures to validate the proposed methodology.     

Using compositional and Dirichlet models for market share regression

When the aim is to model market shares, the marketing literature proposes some regression models which can be qualified as attraction models. They are generally derived from an aggregated version of the multinomial logit model. But aggregated multinomial logit models (MNL) and the so-called generalized multiplicative competitive interaction models (GMCI) present some limitations: in their simpler version they do not specify brand-specific and cross effect parameters. In this paper, we consider alternative models: the Dirichlet model (DIR) and the compositional model (CODA). DIR allows to introduce brand-specific parameters and CODA allows additionally to consider cross effect parameters. We show that these two models can be written in a similar fashion, called attraction form, as the MNL and the GMCI models. As market share models are usually interpreted in terms of elasticities, we also use this notion to interpret the DIR and CODA models. We compare the properties of the models in order to explain why CODA and DIR models can outperform traditional market share models. An application to the automobile market is presented where we model brands market shares as a function of media investments, controlling for the brands price and scrapping incentive. We compare the quality of the models using measures adapted to shares.     

Semiparametric Regression Models with Applications to Scoring: A Review

Semiparametric regression models have been proposed in the econometric literature as a trade-off between the simple but easily implementable and interpretable parametric models and the flexible but structure free smoothing techniques. Some semiparametric models for binary response with possible application to scoring data are reviewed: single-index models, generalized partially linear models, generalized partially linear single-index models, and multiple-index models. All these models are extensions of the classical logistic regression.     

INFLUENCE DIAGNOSTICS IN PROPER DISPERSION MODELS

This paper discusses the application of influence diagnostic methods in univariate proper dispersion models. This class includes, in particular, continuous generalized linear models as well as other subclasses of continuous regression models. We emphasize the study of the local influence on the likelihood displacement and predictions from the models. Some of the diagnostics are illustrated by an example on directional data.     

广义Gamma分布簇广义线性混合模型的构建

 本文在广义Gamma分布簇基础上引入异质性来构建广义线性混合模型。本文构建的广义Gamma分布簇广义线性混合模型在广义线性混合模型的框架下分析,通过参数重整技术把广义Gamma分布簇变量的建模问题与指数分布簇变量的建模问题联系起来,模型推断可以方便地利用广义线性混合模型和广义线性模型的研究成果,同时也可以方便地推广到其他模型。三参数广义Gamma分布可以收缩到两参数的Gamma分布、Weibull分布或指数分布,能降低模型误设的风险,还能便利地分析误差结构。     

Multistate recapture models: Modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.     

Systematic Effects of Capital Service Price Definition on Perceptions of Input Substitution

Earlier attempts at reconciling disparate substitution elasticity estimates examined differences in separability hypotheses, data bases, and estimation techniques, as well as methods employed to construct capital service prices. Although these studies showed that differences in elasticity estimates between two or three studies may be attributable to the aforementioned features of the econometric models, they have been unable to demonstrate this link statistically and establish the existence of systematic relationships between features of the econometric models and the perception of production technologies generated by those models. Using sectoral data covering the entire production side of the U.S. economy, we estimate 34 production models for alternative definitions of the capital service price. We employ substitution elasticities calculated from these models as dependent variables in the statistical search for systematic relationships between features of the econometric models and perceptions of the sectoral technology as characterized by the elasticities. Statistically significant systematic effects are found between the monotonicity and concavity properties of the cost functions and service price–technical change specifications as well as between substitution elasticities.     

Random field models in image analysis

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures, and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon, and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but a better mathematical understanding of these issues is needed as well as efficient algorithms for applications. These issues need to be resolved before random field models will be widely accepted as general tools in the image processing community.     

Bivariate location–scale models for regression analysis, with applications to lifetime data

Summary.  The literature on multivariate linear regression includes multivariate normal models, models that are used in survival analysis and a variety of models that are used in other areas such as econometrics. The paper considers the class of location–scale models, which includes a large proportion of the preceding models. It is shown that, for complete data, the maximum likelihood estimators for regression coefficients in a linear location–scale framework are consistent even when the joint distribution is misspecified. In addition, gains in efficiency arising from the use of a bivariate model, as opposed to separate univariate models, are studied. A major area of application for multivariate regression models is to clustered, 'parallel' lifetime data, so we also study the case of censored responses. Estimators of regression coefficients are no longer consistent under model misspecification, but we give simulation results that show that the bias is small in many practical situations. Gains in efficiency from bivariate models are also examined in the censored data setting. The methodology in the paper is illustrated by using lifetime data from the Diabetic Retinopathy Study.     

Random field models in image analysis*

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but a better mathematical understanding of these issues is needed as well as efficient algorithms for applications. These issues need to be resolved before random field models will be widely accepted as general tools in the image-processing community.     

Multistate recapture models: modelling incomplete individual histories

Multistate capture-recapture models are a natural generalization of the usual one-site recapture models. Similarly, individuals are sampled on discrete occasions, at which they may be captured or not. However, contrary to the one-site case, the individuals can move within a finite set of states between occasions. The growing interest in spatial aspects of population dynamics presently contributes to making multistate models a very promising tool for population biology. We review first the interest and the potential of multistate models, in particular when they are used with individual states as well as geographical sites. Multistate models indeed constitute canonical capture-recapture models for individual categorical covariates changing over time, and can be linked to longitudinal studies with missing data and models such as hidden Markov chains. Multistate models also provide a promising tool for handling heterogeneity of capture, provided states related to capturability can be defined and used. Such an approach could be relevant for population size estimation in closed populations. Multistate models also constitute a natural framework for mixtures of information in individual history data. Presently, most models can be fit using program MARK. As an example, we present a canonical model for multisite accession to reproduction, which fully generalizes a classical one-site model. In the generalization proposed, one can estimate simultaneously age-dependent rates of accession to reproduction, natal and breeding dispersal. Finally, we discuss further generalizations - such as a multistate generalization of growth rate models and models for data where the state in which an individual is detected is known with uncertainty - and prospects for software development.     

Empirical Performance and Asset Pricing in Hidden Markov Models

Abstract

To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address leptokurtic feature, volatility smile, and volatility clustering effects of the asset return distributions. However, analytical tractability remains a problem for most alternative models. In this article, we study a class of hidden Markov models including Markov switching models and stochastic volatility models, that can incorporate leptokurtic feature, volatility clustering effects, as well as provide analytical solutions to option pricing. We show that these models can generate long memory phenomena when the transition probabilities depend on the time scale. We also provide an explicit analytic formula for the arbitrage-free price of the European options under these models. The issues of statistical estimation and errors in option pricing are also discussed in the Markov switching models.     

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.     

Outlier detection and accommodation in general spatial models

This paper studies outlier detection and accommodation in general spatial models including spatial autoregressive models and spatial error model as special cases. Using mean-shift and variance-weight models respectively, test statistics for multiple outliers are derived and the detecting procedures are proposed. In addition, several key diagnostic measures such as standardized residuals and leverage measure are defined in general spatial models. Outlier modified models are proposed to accommodate outliers in the data set. The performance of test statistics, including size and power, are examined via simulation studies. Three real examples are analyzed and the results show that the proposed methodology is useful for identifying and accommodating outliers in general spatial models.     

Partially Linear Additive Models with Unknown Link Functions

In this paper, we consider partially linear additive models with an unknown link function, which include single‐index models and additive models as special cases. We use polynomial spline method for estimating the unknown link function as well as the component functions in the additive part. We establish that convergence rates for all nonparametric functions are the same as in one‐dimensional nonparametric regression. For a faster rate of the parametric part, we need to define appropriate ‘projection’ that is more complicated than that defined previously for partially linear additive models. Compared to previous approaches, a distinct advantage of our estimation approach in implementation is that estimation directly reduces estimation in the single‐index model and can thus deal with much larger dimensional problems than previous approaches for additive models with unknown link functions. Simulations and a real dataset are used to illustrate the proposed model.     

Chi-Squared Goodness-of-Fit Tests for Parametric Accelerated Failure Time Models

We give chi-squared goodness-of fit tests for parametric regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, and models with cross-effects of survival functions. Random right censored data are used. Choice of random grouping intervals as data functions is considered.     

Modelling lifetimes by quantile functions using Parzen's score function

The present paper introduces methods of constructing quantile functions as models of lifetimes with monotone and nonmonotone hazard functions. This is accomplished on the basis of the relationships the hazard quantile function has with the score function introduced by Parzen in connection with the tail heaviness of probability distributions. Three models illustrated here contain several existing models as particular cases. The appropriateness of the models in real situations is also demonstrated.     

未决赔款准备金评估模型的比较研究

近10多年来,关于未决赔款准备金评估模型的研究取得了较大进展,其中虽然也包含对各种评估模型相互关系的探讨,如关于各种随机模型的比较、以及基于B-F法对各种准备金评估模型的比较等,但仍然不够全面和系统。在对准备金评估模型从不同角度进行了较为系统的分类和综述的同时,首次以最基本的链梯模型为基础,建立了一个统一的框架,并对常见的一些准备金评估模型进行了综合比较和分析,揭示了它们之间的一些重要关系,给出了在实务中选择准备金评估模型的一些建议。     

Markov chain Monte Carlo with the Integrated Nested Laplace Approximation

The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on producing an accurate approximation to the posterior marginal distributions of the parameters in the model and some other quantities of interest by using repeated approximations to intermediate distributions and integrals that appear in the computation of the posterior marginals. INLA focuses on models whose latent effects are a Gaussian Markov random field. For this reason, we have explored alternative ways of expanding the number of possible models that can be fitted using the INLA methodology. In this paper, we present a novel approach that combines INLA and Markov chain Monte Carlo (MCMC). The aim is to consider a wider range of models that can be fitted with INLA only when some of the parameters of the model have been fixed. We show how new values of these parameters can be drawn from their posterior by using conditional models fitted with INLA and standard MCMC algorithms, such as Metropolis–Hastings. Hence, this will extend the use of INLA to fit models that can be expressed as a conditional LGM. Also, this new approach can be used to build simpler MCMC samplers for complex models as it allows sampling only on a limited number of parameters in the model. We will demonstrate how our approach can extend the class of models that could benefit from INLA, and how the R-INLA package will ease its implementation. We will go through simple examples of this new approach before we discuss more advanced applications with datasets taken from the relevant literature. In particular, INLA within MCMC will be used to fit models with Laplace priors in a Bayesian Lasso model, imputation of missing covariates in linear models, fitting spatial econometrics models with complex nonlinear terms in the linear predictor and classification of data with mixture models. Furthermore, in some of the examples we could exploit INLA within MCMC to make joint inference on an ensemble of model parameters.     

Moving average models—time series in m-dimensions

Stochastic models for discrete time series in the time domain are well known but such models lack consideration of spatial dependency I We expand on their work by constructing spatially dependent moving average models. Definitions of order, stationarity, invertibility, autocorrelation function, and spectrum are made as natural extensions of those in zero dimensions and are implemented in the one and two-space dimensional models.