Particle filtering for partially observed Gaussian state space models

Summary. Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed Gaussian state space models. This algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms. It differs from previous algorithms which were only applicable to conditionally linear Gaussian state space models. Computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models.     

A New Approach to Volatility Modeling: The Factorial Hidden Markov Volatility Model

A new process—the factorial hidden Markov volatility (FHMV) model—is proposed to model financial returns or realized variances. Its dynamics are driven by a latent volatility process specified as a product of three components: a Markov chain controlling volatility persistence, an independent discrete process capable of generating jumps in the volatility, and a predictable (data-driven) process capturing the leverage effect. An economic interpretation is attached to each one of these components. Moreover, the Markov chain and jump components allow volatility to switch abruptly between thousands of states, and the transition matrix of the model is structured to generate a high degree of volatility persistence. An empirical study on six financial time series shows that the FHMV process compares favorably to state-of-the-art volatility models in terms of in-sample fit and out-of-sample forecasting performance over time horizons ranging from 1 to 100 days. Supplementary materials for this article are available online.     

Distance Testing for Selecting the Best Population

Consider testing the null hypothesis that a given population has location parameter greater than or equal to the largest location parameter of k competing populations. This paper generalizes tests proposed by Gupta and Bartholomew by considering tests based on p -distances from the parameter estimate to the null parameter space. It is shown that all tests are equivalent when k →∞ for a class of distributions that includes the normal and the uniform. The paper proposes the use of adaptive quantiles. Under suitable assumptions the resulting tests are asymptotically equivalent to the uniformly most powerful test for the case that the location parameters of all but one of the populations are known. The increase in power obtained by using adaptive tests is confirmed by a simulation study.     

Using Adjacent-category Logits Procedure for Estimating Receiver Operating Characteristic Surface

This article presents a semiparametric method for estimating receiver operating characteristic surface under density ratio model. The construction of the proposed method is based on the adjacent-category logit model and the empirical likelihood approach. A bootstrap approach for the VUS estimator inference is presented. In a simulation study, the proposed estimator is compared with the existing parametric and nonparametric estimators in terms of bias, standard error, and mean square error. Finally, a real data example and some discussions on the proposed method are provided.     

Sparse Change-point HAR Models for Realized Variance

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015.     

Autoregressive Moving Average Infinite Hidden Markov-Switching Models

Markov-switching models are usually specified under the assumption that all the parameters change when a regime switch occurs. Relaxing this hypothesis and being able to detect which parameters evolve over time is relevant for interpreting the changes in the dynamics of the series, for specifying models parsimoniously, and may be helpful in forecasting. We propose the class of sticky infinite hidden Markov-switching autoregressive moving average models, in which we disentangle the break dynamics of the mean and the variance parameters. In this class, the number of regimes is possibly infinite and is determined when estimating the model, thus avoiding the need to set this number by a model choice criterion. We develop a new Markov chain Monte Carlo estimation method that solves the path dependence issue due to the moving average component. Empirical results on macroeconomic series illustrate that the proposed class of models dominates the model with fixed parameters in terms of point and density forecasts.     

The Sonoran Desert’s Domestic Bracero Programme: Institutional Actors and the Creation of Labour Migration Streams

This paper traces the journeys of male migrants to Empalme, Sonora, Mexico to uncover the development of the often overlooked domestic bracero programme that operated in conjunction with its well‐known international equivalent. Drawing on interviews and observations with ex‐braceros who met at a park near the Mexico‐US border, I examine their experiences and participation in Mexico’s domestic bracero program, an unintended and unexplored consequence of its international counterpart. The study shows how regulation and control were constantly reinvented at every step of the selection process by state actors and their affiliates in Mexico. The paper reveals how the oversupply of labour and modernization of agriculture in Sonora resulted in the development of a migration industry where local municipal leaders, coyotes, the state, and Mexican agribusiness capitalized from men’s displacement. The migration industry during the bracero selection process controlled who gained access to the United States labour market by capturing migrant labour en route to the United States in the process fueling a thriving cotton industry in the otherwise stagnant Sonoran Desert economy. The study concludes by taking the lessons from the historic domestic bracero programme to show one instance in which internal and international labour markets were closely interwoven. In the end, I call for more research that examines the relationship between markets on both sides of the border that uncovers how networks are not only structured by personal ties but also by state and market relations.     

Academic Paths,Ageing and the Living Conditions of Students in the Late 20th Century*

Le monde étudiant est profondément marqué par la diversité des tra‐jectoires individuelles, qui sont souvent très éloignées d'un déroule‐ment linéaire des études. Les conséquences sur l'âge des étudiants sont majeures, et la condition étudiante ne peut plus être définie comme une expérience strictement juvénile. Or, entre 20 et 30 ans, l'âge engendre des impératifs différentiels sur le plan des conditions et des modes de vie qui ne sont pas toujours compatibles avec la condition étudiante classique. Cette étude des parcours et de la situation financière des étudiants des universités québécoises de langue françhise et anglaise montre comment s'opère la déconnexion entre jeunesse et condition étudiante, et comment cette déconnexion influe sur la différenciation des conditions de vie et de financement des études. Student life is profoundly marked by the diversity of individual trajectories, which are in stark contrast with the linear path traditionally taken by students. The impact on the age of the student population is significant: indeed, student life can no longer be qualified as strictly for the young. Between the ages of 20 and 30 years, different imperatives come into play in terms of living conditions and lifestyle. These imperatives are not always compatible with the conditions of classic student life. This study of the academic paths and the financial situation of Quebec university students shows how the disconnection between student condition and youth occurs and how this disconnection impacts the differentiation of student's living conditions and modes of financing university studies.     

Discrete q-distributions on Bernoulli trials with a geometrically varying success probability

Consider a sequence of independent Bernoulli trials and assume that the odds of success (or failure) or the probability of success (or failure) at the ith trial varies (increases or decreases) geometrically with rate (proportion) q, for increasing i=1,2,…. Introducing the notion of a geometric sequence of trials as a sequence of Bernoulli trials, with constant probability, that is terminated with the occurrence of the first success, a useful stochastic model is constructed. Specifically, consider a sequence of independent geometric sequences of trials and assume that the probability of success at the jth geometric sequence varies (increases or decreases) geometrically with rate (proportion) q, for increasing j=1,2,…. On both models, let X_n be the number of successes up the nth trial and T_k (or W_k) be the number of trials (or failures) until the occurrence of the kth success. The distributions of these random variables turned out to be q-analogues of the binomial and Pascal (or negative binomial) distributions. The distributions of X_n, for n→∞$n\to \infty$, and the distributions of W_k, for k→∞$k\to \infty$, can be approximated by a q  -Poisson distribution. Also, as k→0$k\to 0$, a zero truncated negative q  -binomial distribution _Uk=_Wk|_Wk>0$U_k=W_k|W_k>0$ can be approximated by a q-logarithmic distribution. These discrete q-distributions and their applications are reviewed, with critical comments and additions. Finally, consider a sequence of independent Bernoulli trials and assume that the probability of success (or failure) is a product of two sequences of probabilities with one of these sequences depending only the number of trials and the other depending only on the number of successes (or failures). The q-distributions of the number X_n of successes up to the nth trial and the number T_k of trials until the occurrence of the kth success are similarly reviewed.