Sparse Markov Chains for Sequence Data

Finite memory sources and variable‐length Markov chains have recently gained popularity in data compression and mining, in particular, for applications in bioinformatics and language modelling. Here, we consider denser data compression and prediction with a family of sparse Bayesian predictive models for Markov chains in finite state spaces. Our approach lumps transition probabilities into classes composed of invariant probabilities, such that the resulting models need not have a hierarchical structure as in context tree‐based approaches. This can lead to a substantially higher rate of data compression, and such non‐hierarchical sparse models can be motivated for instance by data dependence structures existing in the bioinformatics context. We describe a Bayesian inference algorithm for learning sparse Markov models through clustering of transition probabilities. Experiments with DNA sequence and protein data show that our approach is competitive in both prediction and classification when compared with several alternative methods on the basis of variable memory length.     

A Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries

In Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developed in Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar],c) where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic default intensities and random recoveries in the bottom-up modeling framework of Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]) while preserving numerical tractability. These two features are of primary importance for applications like CVA computations on credit derivatives (Assefa et al., 2011 Assefa , S. , Bielecki , T. R. , Crépey , S. , Jeanblanc , M. ( 2011 ). CVA computation for counterparty risk assessment in credit portfolios . In: Bielecki , T.R. , Brigo , D. , Patras , F. , Eds., Credit Risk Frontiers . Hoboken : Wiley/Bloomberg-Press . [Google Scholar]; Bielecki et al., 2012 Bielecki , T. R. , Crépey , S. , Jeanblanc , M. , Zargari , B. ( 2012 ). Valuation and Hedging of CDS counterparty exposure in a markov copula model . Int. J. Theoret. Appl. Fin. 15 ( 1 ): 1250004 .[Crossref] , [Google Scholar]), as CVA is sensitive to the stochastic nature of credit spreads and random recoveries allow to achieve satisfactory calibration even for “badly behaved” data sets. This article is thus a complement to Bielecki et al. (2014a Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014a ). Dynamic hedging of portfolio credit risk in a markov copula model . J. Optimiz. Theor. Applic . doi: DOI 10.1007/s10957-013-0318-4 (forthcoming) .[Crossref] , [Google Scholar]), Bielecki et al. (2014b Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014b ). A bottom-up dynamic model of portfolio credit risk - Part I: Markov copula perspective . In: Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.1844574) . [Google Scholar]) and Bielecki et al. (2014c Bielecki , T. R. , Cousin , A. , Crépey , S. , Herbertsson , A. ( 2014c ). A bottom-up dynamic model of portfolio credit risk - Part II: Common-shock interpretation, calibration and hedging issues . Recent Adv. Fin. Eng. 2012 , World Scientific (preprint version available at http://dx.doi.org/10.2139/ssrn.2245130) . [Google Scholar]).     

LSTAR-GARCH模型的单位根检验

LSTAR模型的单位根检验往往易忽视其条件方差的时变性,实际上,对许多经济变量尤其是金融变量建立LSTAR模型后,经常发现其条件方差存在GARCH效应。针对LSTAR-GARCH模型的平稳性检验,本文构建了检验统计量tNG,之后在极大似然估计的基础上,推导出tNG的渐近分布,通过蒙特卡洛模拟方法得到该统计量的渐近临界值,并在此基础上研究了tNG检验的检验功效。在与刘雪燕和张晓峒(2009)提出的tNL检验、Ling等(2003)提出的tLG检验以及DF单位根检验进行比较后,发现tNG检验具备明显优势。     

中国地区收入与二氧化碳排放的联合动态性研究

本文分析了社会福利的两个主要因素—收入和二氧化碳排放。在收入和二氧化碳排放关系分析的基础上,利用马尔科夫链分析了收入-二氧化碳排放的联合状态转移机制。研究结果表明,收入是影响二氧化碳排放的重要因素,高收入对应着高排放。低收入水平地区倾向于通过增加排放来带动经济发展。目前,高收入-高排放处于稳定状态,但从长期看,该状态的地区比重很小。我国没有进入低收入-高排放的收入环境陷阱。     

递归均值调整单位根检验能提高检验功效吗?

根据备择假设成立时均值是否为零,讨论了三类单位根检验统计量的检验功效。理论研究表明:在大样本下,检验功效只与检验类型有关,与均值取值无关。蒙特卡洛模拟表明:在有限样本下,均值会影响检验功效,当均值为零时,第一类DF检验功效最高;当均值大于零时,在绝大多数场合下,第二类DF检验功效最优。因此,递归均值调整单位根检验功效仅在有限条件下最大。     

Multistate Survival Models as Transient Electrical Networks

In multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan–Meier mass function. Thus, the Kaplan–Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause‐specific Kaplan–Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model.     

Simulation/Regression Pricing Schemes for CVA Computations on CDO Tranches

We devise simulation/regression numerical schemes for pricing the CVA on CDO tranches, where CVA stands for Credit Valuation Adjustment, or price correction accounting for the defaultability of a counterparty in an OTC derivatives transaction. This is done in the setup of a continuous-time Markov chain model of default times, in which dependence between credit names is represented by the possibility of simultaneous defaults. The main idea of this article is to perform the nonlinear regressions which are used for computing conditional expectations, in the time variable for a given state of the model, rather than in the space variables at a given time in diffusive setups. This idea is formalized as a lemma which is valid in any continuous-time Markov chain model. It is then implemented on the targeted application of CVA computations on CDO tranches.     

Strong Law of Large Numbers for Countable Asymptotic Circular Markov Chains

In this article, we introduce the notion of a countable asymptotic circular Markov chain, and prove a strong law of large numbers: as a corollary, we generalize a well-known version of the strong law of large numbers for nonhomogeneous Markov chains, and prove the Shannon-McMillan-Breiman theorem in this context, extending the result for the finite case.     

非线性Granger因果检验方法的检验功效及有限样本性质的模拟分析

为了克服传统Granger因果检验方法因忽略经济变量的非线性特征而导致结论出现显著偏差的局限性,非线性Granger因果检验方法在近年来正逐步成为经济学研究领域的重要分析工具。然而,迄今为止,学术界仍较少对非线性Granger因果检验方法在不同非线性模型中的有限样本性质展开系统性的比较与分析,因此,本文通过数据生成过程（DGP）,结合Monte Carlo模拟对Diks和Panchenko（2006）等主流的非线性Granger因果检验方法的检验功效、过度拒绝等问题展开比较研究,并对共同滞后阶数、带宽参数的不同设置可能引发结论敏感性变化进行深入分析,在此基础上我们从动态非线性滚动分析的角度对其有限样本性质展开进一步的讨论,并提出对未来非线性应用研究具有实际指导价值的若干建议。     

On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models

Variational Bayes (VB) estimation is a fast alternative to Markov Chain Monte Carlo for performing approximate Baesian inference. This procedure can be an efficient and effective means of analyzing large datasets. However, VB estimation is often criticised, typically on empirical grounds, for being unable to produce valid statistical inferences. In this article we refute this criticism for one of the simplest models where Bayesian inference is not analytically tractable, that is, the Bayesian linear model (for a particular choice of priors). We prove that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors. In addition to these results we introduce two VB information criteria: the variational Akaike information criterion and the variational Bayesian information criterion. We show that variational Akaike information criterion is asymptotically equivalent to the frequentist Akaike information criterion and that the variational Bayesian information criterion is first order equivalent to the Bayesian information criterion in linear regression. These results motivate the potential use of the variational information criteria for more complex models. We support our theoretical results with numerical examples.