Benchmark priors for Bayesian model averaging

In contrast to a posterior analysis given a particular sampling model, posterior model probabilities in the context of model uncertainty are typically rather sensitive to the specification of the prior. In particular, ‘diffuse’ priors on model-specific parameters can lead to quite unexpected consequences. Here we focus on the practically relevant situation where we need to entertain a (large) number of sampling models and we have (or wish to use) little or no subjective prior information. We aim at providing an ‘automatic’ or ‘benchmark’ prior structure that can be used in such cases. We focus on the normal linear regression model with uncertainty in the choice of regressors. We propose a partly non-informative prior structure related to a natural conjugate g-prior specification, where the amount of subjective information requested from the user is limited to the choice of a single scalar hyperparameter g_0j. The consequences of different choices for g_0j are examined. We investigate theoretical properties, such as consistency of the implied Bayesian procedure. Links with classical information criteria are provided. More importantly, we examine the finite sample implications of several choices of g_0j in a simulation study. The use of the MC³ algorithm of Madigan and York (Int. Stat. Rev. 63 (1995) 215), combined with efficient coding in Fortran, makes it feasible to conduct large simulations. In addition to posterior criteria, we shall also compare the predictive performance of different priors. A classic example concerning the economics of crime will also be provided and contrasted with results in the literature. The main findings of the paper will lead us to propose a ‘benchmark’ prior specification in a linear regression context with model uncertainty.     

Latent Markov Modelling of Recidivism Data

This article discusses the application of latent Markov modelling for the analysis of recidivism data. We briefly examine the relations of Markov modelling with log–linear analysis, pointing out pertinent differences as well. We show how the restrictive Markov model may be more easily applicable by adding latent variables to the model, in which case the latent Markov model is a dynamic version of the latent class model. As an illustration, we apply latent Markov analysis on an empirical data set of juvenile prosecution careers, showing how the Markov analyses producing well-fitting and interpretable solutions. We end by comparing the possible contributions of Markov modelling in recidivism research, outlining its drawbacks as well. Recommendations and directions for future research conclude the article.     

平滑转换自回归模型的平稳性问题研究

根据时间序列宽平稳的定义,本文认为,平滑转换自回归模型的序列不是宽平稳序列,利用ADF统计量检验其平稳性是没有意义的;其次,依据马尔科夫链的遍历性,我们认为,STAR模型的序列是严平稳序列,且通过对模型系数的联合取值的限制保证了模型的平稳性。以一阶对数平滑转换自回归模型为例,其平稳的条件是,β与r符号相反,且|β+r|<1,β可以等于1,也可以绝对值小于1。     

A New Regime Switching Model with State–Varying Endogeneity

In this paper, we propose a state-varying endogenous regime switching model (the SERS model), which includes the endogenous regime switching model by Chang et al., the CCP model, as a special case. To estimate the unknown parameters in the SERS model, we propose a maximum likelihood estimation method. Monte Carlo simulation results show that in the absence of state-varying endogeneity, the SERS model and the CCP model perform similarly, while in the presence of state-varying endogeneity, the SERS model performs much better than the CCP model. Finally, we use the SERS model to analyze Chinese stock market returns, and our empirical results show that there exists strongly state-varying endogeneity in volatility switching for the Shanghai Composite Index returns. Moreover, the SERS model can indeed produce a much more realistic assessment for the regime switching process than the one obtained by the CCP model.     

基于Markov模型的中国高端卷烟产品销量预测研究

本文通过对全国调拨价每条100元以上的卷烟销量进行分析,预测出未来几年内其销量增长的趋势。笔者依据历年销量的增长率不同将其划分为不同的状态,计算出状态之间的转移概率矩阵,并构造出销量增长率的马尔可夫模型,求出其销量增长率的期望值,通过对比近两年的实际销量值计算出其预测销量的误差,为未来几年卷烟销量的预测提供参考,同时此模型适用于中国中低端卷烟的销量预测,研究结果对于全国烟草行业的营销实践具有参考价值。     

Transition matrix models of consumer credit ratings

Although the corporate credit risk literature includes many studies modelling the change in the credit risk of corporate bonds over time, there has been far less analysis of the credit risk for portfolios of consumer loans. However, behavioural scores, which are calculated on a monthly basis by most consumer lenders, are the analogues of ratings in corporate credit risk. Motivated by studies of corporate credit risk, we develop a Markov chain model based on behavioural scores for establishing the credit risk of portfolios of consumer loans. Although such models have been used by lenders to develop models for the Basel Accord, nothing has been published in the literature on them. The model which we suggest differs in many respects from the corporate credit ones based on Markov chains — such as the need for a second order Markov chain, the inclusion of economic variables and the age of the loan. The model is applied using data on a credit card portfolio from a major UK bank.     

Estimating Transition Probabilities from a Time Series of Independent Cross Sections

This paper considers the implementation of a nonstationary, heterogeneous Markov model for the analysis of a binary dependent variable in a time series of independent cross sections. The model, previously considered by M offitt (1993), offers the opportunity to estimate entry and exit transition probabilities and to examine the effects of time-constant and time-varying covariates on the hazards. We show how ML estimates of the parameters can be obtained by Fisher's method-of-scoring and how to estimate both fixed and time-varying covariate effects. The model is exemplified with an analysis of the labor force participation decision of Dutch women using data from the Socio-economic Panel (SEP) study conducted in the Netherlands between 1986 and 1995. We treat the panel data as independent cross sections and compare the employment status sequences predicted by the model with the observed sequences in the panel. Some open problems concerning the application of the model are also discussed.     

Validating an agent-based model of the Zipf׳s Law: A discrete Markov-chain approach

This study discusses the validation of an agent-based model of emergent city systems with heterogeneous agents. To this end, it proposes a simplified version of the original agent-based model and subjects it to mathematical analysis. The proposed model is transformed into an analytically tractable discrete Markov model, and its city size distribution is examined. Its discrete nature allows the Markov model to be used to validate the algorithms of computational agent-based models. We show that the Markov chains lead to a power-law distribution when the ranges of migration options are randomly distributed across the agent population. We also identify sufficient conditions under which the Markov chains produce the Zipf׳s Law, which has never been done within a discrete framework. The conditions under which our simplified model yields the Zipf׳s Law are in agreement with, and thus validate, the configurations of the original heterogeneous agent-based model.     

Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting,incorporating realized measures

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.     

A threshold stochastic volatility model with explanatory variables

In this paper, we introduce a threshold stochastic volatility model with explanatory variables. The Bayesian method is considered in estimating the parameters of the proposed model via the Markov chain Monte Carlo (MCMC) algorithm. Gibbs sampling and Metropolis–Hastings sampling methods are used for drawing the posterior samples of the parameters and the latent variables. In the simulation study, the accuracy of the MCMC algorithm, the sensitivity of the algorithm for model assumptions, and the robustness of the posterior distribution under different priors are considered. Simulation results indicate that our MCMC algorithm converges fast and that the posterior distribution is robust under different priors and model assumptions. A real data example was analyzed to explain the asymmetric behavior of stock markets.     

Use of a Markov decision process model for treatment selection in an asymptomatic disease with consideration of risk sensitivity

Some potentially dangerous diseases are completely asymptomatic. Their diagnosis as incidental findings of ever-more-sensitive medical imaging can leave patients and physicians in something of a quandary. The patient feels well, and potential interventions to stave off long-term deterioration or death bring with them immediate risks. We discuss the use of a Markov Decision Process (MDP) model (rather than Monte Carlo simulation of a Markov Model) to create a tool for analyzing individual treatment decisions for asymptomatic chronic diseases where a patient’s condition cannot improve. We formulate a finite-horizon MDP model to determine optimal treatment plans and discuss three distinct optimality criteria: (a) maximizing expected quality-adjusted-life years with and without discounting, (b) maximizing the expected number of life years in good health, and (c) maximizing the expected utility for number of years in good health. In (c) we assume exponential utility and consider different risk aversion factors reported in the medical literature. We illustrate the model’s use by considering asymptomatic intracranial aneurysm. Our model builds on a simulation model [19] created to examine treatment recommendations based on cost-effectiveness. We demonstrate that incorporating risk aversion leads to “no treatment” recommendations for some types of aneurysm. Furthermore, the use of alternate patient-selected criteria leads to recommendations that vary from [19] in several scenarios. We also discuss the use of the software as a decision support tool to help make individualized treatment recommendations and demonstrate that the computational performance of the algorithm makes its use feasible during a short office visit.     

中国贸易产品多样性的测度及动态分析

本文调整了传统测算多样性指数的方法,对我国HS6位编码的进出口产品多样性进行了测度,并使用马尔可夫链模型对其发展趋势进行动态分析。研究表明,我国贸易产品波动尤其是出口产品的波动还将维持在一个较高的水平,劳动密集型产品作为我国贸易优势产品,对我国贸易进一步向竞争更为激烈的资本技术密集型产品领域扩展起到降低风险、稳定发展的作用。进口贸易也将通过调整进口产品结构,促进资本、技术等引进加快我国贸易结构的转型升级。本文的研究拟为评价我国贸易质量、制定贸易转型政策提供有效参考。     

Time varying VARs with inequality restrictions

In many applications involving time-varying parameter VARs, it is desirable to restrict the VAR coefficients at each point in time to be non-explosive. This is an example of a problem where inequality restrictions are imposed on states in a state space model. In this paper, we describe how existing MCMC algorithms for imposing such inequality restrictions can work poorly (or not at all) and suggest alternative algorithms which exhibit better performance. Furthermore, we show that previous algorithms involve an approximation relating to a key prior integrating constant. Our algorithms are exact, not involving this approximation. In an application involving a commonly used U.S. data set, we present evidence that the algorithms proposed in this paper work well.     

Approximate Bayesian Computation for a Class of Time Series Models

In the following article, we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which we mean that one cannot evaluate the likelihood even up to a non‐negative unbiased estimate. This paper reviews and develops a class of approximation procedures based upon the idea of ABC, but specifically maintains the probabilistic structure of the original statistical model. This latter idea is useful, in that one can adopt or adapt established computational methods for statistical inference. Several existing results in the literature are surveyed, and novel developments with regards to computation are given.     

Spillover shifts in the FX market: Implication for the behavior of a safe haven currency

This paper explores the behavior of safe haven currencies by analyzing shock transmission among major currencies. To capture state-dependent directional spillovers, we incorporate Markov regime-switching parameters into the spillover model and estimate them using a Bayesian MCMC algorithm. By considering weekly data from September 2000 to March 2020, we find that the Japanese yen and the Swiss franc, both of which yield relatively high excess returns in times of crisis, exhibit larger reductions of shock transmission and reception during periods of high-volatility than during periods of low-volatility. This implies that the safe haven currencies insulate themselves from shocks from other currencies by reducing interdependence across the FX market in crisis.     

基于状态转移模型的我国股指期货走势预测方法

文章应用马尔科夫状态转移模型,假定股指期货收益服从正态分布,将中国内地股指期货品种IF1103收益分为三个状态,发现80%的收益都很平稳,波动不大,且持续时间长,少数收益波动很大,持续时间很短,这与实际基本符合。     

On the waiting time distribution in a GI/G/1 queue with a Coxian–2 service time distribution

The purpose of this paper is to derive in an alternative way the result that the complementary waiting–time distribution function in the Gl/G/I queue is the sum of two exponential functions when the service time has a Coxian–2 distribution. The idea is to interpret this type of service–time distribution as the sum of a stochastic number of exponentially distributed phases. In this way the model can be seen as a special G/^x/W/1 batch–arrival queue where the batch–size distribution is deduced from the Coxian service–time distribution. For the latter model we give an embedded Markov–chain approach. Because of the special form of the batch–size distribution the steady–state distribution of this Markov chain can be represented as the sum of two geometric terms of which the coefficients can be explicitly given. From this result the waiting–time distribution can be deduced immediately. Apart from its didactic interest the result can be useful to obtain simple approximations for more general GI/G/1 models.     

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump-diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.     

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.     

Non‐parametric regression in clustered multistate current status data with informative cluster size

Datasets examining periodontal disease records current (disease) status information of tooth‐sites, whose stochastic behavior can be attributed to a multistate system with state occupation determined at a single inspection time. In addition, the tooth‐sites remain clustered within a subject, and the number of available tooth‐sites may be representative of the true periodontal disease status of that subject, leading to an ‘informative cluster size’ scenario. To provide insulation against incorrect model assumptions, we propose a non‐parametric regression framework to estimate state occupation probabilities at a given time and state exit/entry distributions, utilizing weighted monotonic regression and smoothing techniques. We demonstrate the superior performance of our proposed weighted estimators over the unweighted counterparts via a simulation study and illustrate the methodology using a dataset on periodontal disease.