Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

Particle filters for continuous likelihood evaluation and maximisation

In this paper, a method is introduced for approximating the likelihood for the unknown parameters of a state space model. The approximation converges to the true likelihood as the simulation size goes to infinity. In addition, the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions. The approach advocated is fast and robust, and it avoids many of the pitfalls associated with current techniques based upon importance sampling. We assess the performance of the method by considering a linear state space model, comparing the results with the Kalman filter, which delivers the true likelihood. We also apply the method to a non-Gaussian state space model, the stochastic volatility model, finding that the approach is efficient and effective. Applications to continuous time finance models and latent panel data models are considered. Two different multivariate approaches are proposed. The neoclassical growth model is considered as an application.     

Bayesian Enhancement of Speech and Audio Signals which can be Modelled as ARMA Processes

In application areas which involve digitised speech and audio signals, such as coding, digital remastering of old recordings and recognition of speech, it is often desirable to reduce the effects of noise with the aim of enhancing intelligibility and perceived sound quality. We consider the case where noise sources contain non-Gaussian, impulsive elements superimposed upon a continuous Gaussian background. Such a situation arises in areas such as communications channels, telephony and gramophone recordings where impulsive effects might be caused by electromagnetic interference (lightning strikes), electrical switching noise or defects in recording media, while electrical circuit noise or the combined effect of many distant atmospheric events lead to a continuous Gaussian component.
In this paper we discuss the background to this type of noise degradation and describe briefly some existing statistical techniques for noise reduction. We propose new methods for enhancement based upon Markov chain Monte Carlo (MCMC) simulation. Signals are modelled as autoregressive moving-average (ARMA); while noise sources are treated as discrete and continuous mixtures of Gaussian distributions. Results are presented for both real and artificially corrupted data sequences, illustrating the potential of the new methods.     

Nowcasting and forecasting global financial sector stress and credit market dislocation

We introduce a new international model for the systematic distress risk of financial institutions from the US, the European Union, and the Asia-Pacific region. Our proposed dynamic factor model can be represented as a nonlinear, non-Gaussian state space model with parameters that we estimate using Monte Carlo maximum likelihood methods. We construct measures of global financial sector risk and of credit market dislocation, where credit market dislocation is defined as a significant and persistent decoupling of the credit risk cycle from macro-financial fundamentals in one or more regions. We show that, in the past, such decoupling has preceded episodes of systemic financial distress. Our new measure provides a risk-based indicator of credit conditions, and as such, complements earlier quantity-based indicators from the literature. In an extensive comparison with such quantity-based systemic risk indicators, we find that the behaviour of the new indicator is competitive with that of the best quantity-based indicators.     

单位累犯制度若干问题研究

由于现行刑法的明确规定,单位成为和自然人并列的一类犯罪主体,这为打击实践中纷繁复杂的单位犯罪问题提供了有效的法律保障。然而,刑法在肯定单位犯罪主体地位的同时,对与之密切相关的一系列刑罚制度问题并没有做出明确的规定,单位累犯制度就是其中之一。文章旨在通过对单位累犯相关问题的探析,为完善单位犯罪刑罚制度提出拙见。     

Measuring Discontinuities in Time Series Obtained with Repeated Sample Surveys

A key requirement of repeated surveys conducted by national statistical institutes is the comparability of estimates over time, resulting in uninterrupted time series describing the evolution of finite population parameters. This is often an argument to keep survey processes unchanged as long as possible. It is nevertheless inevitable that a survey process will need to be redesigned from time to time, for example, to improve or update methods or implement more cost-effective data collection procedures. It is important to quantify the systematic effects or discontinuities of a new survey process on the estimates of a repeated survey to avoid a disturbance in the comparability of estimates over time. This paper reviews different statistical methods that can be used to measure discontinuities and manage the risk due to a survey process redesign.     

Turning from crime: A dynamic perspective

This paper examines criminal choice using a variant of the human capital model. The innovation of our approach is that it attempts to disaggregate individual capital, not unlike production-based studies which disaggregate physical capital into equipment and structures. We disaggregate an individual’s capital stock into the standard human capital component as well as a utility generating component that we call social capital. In our set-up, social capital is used to account for the influence of social norms on the decision to participate in crime. This is done by modeling the stigma of arrest as a reduction in the individual’s social capital stock. We also allow individuals to account for the impact of their criminal actions on their probability of arrest. In order to estimate the structural parameters underlying the model, we make use of computationally intensive methods involving simulated generalized method of moments and value function approximation. The empirical results, based on panel data from the Delinquency in a Birth Cohort II Study, support the social capital model of crime and reveal significant state dependence in the decision to participate in crime.     

Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes

In epidemiology and clinical research, there is often a proportion of unexposed individuals resulting in zero values of exposure, meaning that some individuals are not exposed and those exposed have some continuous distribution. Examples are smoking or alcohol consumption. We will call these variables with a spike at zero (SAZ). In this paper, we performed a systematic investigation on how to model covariates with a SAZ and derived theoretical odds ratio functions for selected bivariate distributions. We consider the bivariate normal and bivariate log normal distribution with a SAZ. Both confounding and effect modification can be elegantly described by formalizing the covariance matrix given the binary outcome variable Y. To model the effect of these variables, we use a procedure based on fractional polynomials first introduced by Royston and Altman (1994, Applied Statistics 43: 429–467) and modified for the SAZ situation (Royston and Sauerbrei, 2008, Multivariable model‐building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables, Wiley; Becher et al., 2012, Biometrical Journal 54: 686–700). We aim to contribute to theory, practical procedures and application in epidemiology and clinical research to derive multivariable models for variables with a SAZ. As an example, we use data from a case–control study on lung cancer.     

Continuous-time modelling of irregularly spaced panel data using a cubic spline model

Continuous-time modelling remains a somewhat 'idealized' representation tool. Even though conceptualizing a dynamic process as a continuous process has clear appeal from a theoretical standpoint, practical tools that allow researchers to effectively map an idealized continuous model onto a set of discrete-time observed data are still lacking observed data. Irregularly spaced longitudinal data frequently arise in empirical settings because of the prevalence of longitudinal studies with partially randomized measurement intervals and other related designs. We present a practical approach that capitalizes on a nonparametric spline interpolation approach to impute the gaps in irregularly spaced panel data. Simulated and empirical examples are provided to demonstrate the applicability of the proposed approach to studies of group-based dynamics using panel data.     

The multi-state latent factor intensity model for credit rating transitions

A new empirical reduced-form model for credit rating transitions is introduced. It is a parametric intensity-based duration model with multiple states and driven by exogenous covariates and latent dynamic factors. The model has a generalized semi-Markov structure designed to accommodate many of the stylized facts of credit rating migrations. Parameter estimation is based on Monte Carlo maximum likelihood methods for which the details are discussed in this paper. A simulation experiment is carried out to show the effectiveness of the estimation procedure. An empirical application is presented for transitions in a 7 grade rating system. The model includes a common dynamic component that can be interpreted as the credit cycle. Asymmetric effects of this cycle across rating grades and additional semi-Markov dynamics are found to be statistically significant. Finally, we investigate whether the common factor model suffices to capture systematic risk in rating transition data by introducing multiple factors in the model.     

Recovering default risk from CDS spreads with a nonlinear filter

We propose a nonlinear filter to estimate the time-varying default risk from the term structure of credit default swap (CDS) spreads. Based on the numerical solution of the Fokker–Planck equation (FPE) using a meshfree interpolation method, the filter performs a joint estimation of the risk-neutral default intensity and CIR model parameters. As the FPE can account for nonlinear functions and non-Gaussian errors, the proposed framework provides outstanding flexibility and accuracy. We test the nonlinear filter on simulated spreads and apply it to daily CDS data of the Dow Jones Industrial Average component companies from 2005 to 2010 with supportive results.     

Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters

We introduce a class of multivariate seasonal time series models with periodically varying parameters, abbreviated by the acronym SPVAR. The model is suitable for multivariate data, and combines a periodic autoregressive structure and a multiplicative seasonal time series model. The stationarity conditions (in the periodic sense) and the theoretical autocovariance functions of SPVAR stochastic processes are derived. Estimation and checking stages are considered. The asymptotic normal distribution of the least squares estimators of the model parameters is established, and the asymptotic distributions of the residual autocovariance and autocorrelation matrices in the class of SPVAR time series models are obtained. In order to check model adequacy, portmanteau test statistics are considered and their asymptotic distributions are studied. A simulation study is briefly discussed to investigate the finite-sample properties of the proposed test statistics. The methodology is illustrated with a bivariate quarterly data set on travelers entering in to Canada.     

Macroeconomic forecasting using approximate factor models with outliers

In this paper we consider estimating an approximate factor model in which candidate predictors are subject to sharp spikes such as outliers or jumps. Given that these sharp spikes are assumed to be rare, we formulate the estimation problem as a penalized least squares problem by imposing a norm penalty function on those sharp spikes. Such a formulation allows us to disentangle the sharp spikes from the common factors and estimate them simultaneously. Numerical values of the estimates can be obtained by solving a principal component analysis (PCA) problem and a one-dimensional shrinkage estimation problem iteratively. In addition, it is easy to incorporate methods for selecting the number of common factors in the iterations. We compare our method with PCA by conducting simulation experiments in order to examine their finite-sample performances. We also apply our method to the prediction of important macroeconomic indicators in the U.S., and find that it can deliver performances that are comparable to those of the PCA method.     

Prediction regions for interval-valued time series

We approximate probabilistic forecasts for interval-valued time series by offering alternative approaches. After fitting a possibly non-Gaussian bivariate vector autoregression (VAR) model to the center/log-range system, we transform prediction regions (analytical and bootstrap) for this system into regions for center/range and upper/lower bounds systems. Monte Carlo simulations show that bootstrap methods are preferred according to several new metrics. For daily S&P 500 low/high returns, we build joint conditional prediction regions of the return level and volatility. We illustrate the usefulness of obtaining bootstrap forecasts regions for low/high returns by developing a trading strategy and showing its profitability when compared to using point forecasts.     

FIRM HETEROGENEITY,PERSISTENT AND TRANSIENT TECHNICAL INEFFICIENCY: A GENERALIZED TRUE RANDOM‐EFFECTS model

This paper considers a panel data stochastic frontier model that disentangles unobserved firm effects (firm heterogeneity) from persistent (time‐invariant/long‐term) and transient (time‐varying/short‐term) technical inefficiency. The model gives us a four‐way error component model, viz., persistent and time‐varying inefficiency, random firm effects and noise. We use Bayesian methods of inference to provide robust and efficient methods of estimating inefficiency components in this four‐way error component model. Monte Carlo results are provided to validate its performance. We also present results from an empirical application that uses a large panel of US commercial banks. Copyright © 2012 John Wiley & Sons, Ltd.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

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.     

Searching for synchrony

Authorities working on economic-crime investigation in Finland are trying to change their form of collaboration from the sequential passing of documents towards parallel, interorganizational collaboration: the on-line investigation of an ongoing crime. The synchronization of events and the outputs of various participants proved to be difficult in this emerging process. This new model of crime investigation also requires a new kind of time management. This article explores how the change is being constructed in everyday practice by examining three economic-crime-investigation cases. It is claimed that individual efforts to manage time allocation suffice only in terms of co-ordination of events. It is suggested that a successful shift to parallel, interorganizational collaboration requires more than the common marking of calendars. The object of the work and the forms of interaction should be taken as subjects of reflective negotiation. New kinds of collective time-management tools are needed in this effort.     

GEFCom2012: Electric load forecasting and backcasting with semi-parametric models

We sum up the methodology of the team tololo for the Global Energy Forecasting Competition 2012: Load Forecasting. Our strategy consisted of a temporal multi-scale model that combines three components. The first component was a long term trend estimated by means of non-parametric smoothing. The second was a medium term component describing the sensitivity of the electricity demand to the temperature at each time step. We use a generalized additive model to fit this component, using calendar information as well. Finally, a short term component models local behaviours. As the factors that drive this component are unknown, we use a random forest model to estimate it.     

Data-based mechanistic modelling and forecasting globally averaged surface temperature

The main objective of this paper it to model the dynamic relationship between global averaged measures of Total Radiative Forcing (RTF) and surface temperature, measured by the Global Temperature Anomaly (GTA), and then use this model to forecast the GTA. The analysis utilizes the Data-Based Mechanistic (DBM) approach to the modelling and forecasting where, in this application, the unobserved component model includes a novel hybrid Box-Jenkins stochastic model in which the relationship between RTF and GTA is based on a continuous time transfer function (differential equation) model. This model then provides the basis for short term, inter-annual to decadal, forecasting of the GTA, using a transfer function form of the Kalman Filter, which produces a good prediction of the ‘pause’ or ‘levelling’ in the temperature rise over the period 2000 to 2011. This derives in part from the effects of a quasi-periodic component that is modelled and forecast by a Dynamic Harmonic Regression (DHR) relationship and is shown to be correlated with the Atlantic Multidecadal Oscillation (AMO) index.