Temporal Disaggregation: Methods,Information Loss,and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.     

Combined survival analysis of cardiac patients by a Cox PH model and a Markov chain

The control and treatment of dyslipidemia is a major public health challenge, particularly for patients with coronary heart diseases. In this paper we propose a framework for survival analysis of patients who had a major cardiac event, focusing on assessment of the effect of changing LDL-cholesterol level and statins consumption on survival. This framework includes a Cox PH model and a Markov chain, and combines their results into reinforced conclusions regarding the factors that affect survival time. We prospectively studied 2,277 cardiac patients, and the results show high congruence between the Markov model and the PH model; both evidence that diabetes, history of stroke, peripheral vascular disease and smoking significantly increase hazard rate and reduce survival time. On the other hand, statin consumption is correlated with a lower hazard rate and longer survival time in both models. The role of such a framework in understanding the therapeutic behavior of patients and implementing effective secondary and primary prevention of heart diseases is discussed here.     

Some remarks on measurement models in the structural equation model: an application for socially responsible food consumption

Considering the structural equation model (SEM), usually the main researches are based on the structural model rather than on the measurement one. So, this context implies some problems: construct misspecification, identification and validation. Starting from the most recent articles in terms of these issues, we achieve – and formalize through two tables – a general framework that could help researchers select and assess both formative and reflective measurement models with special attention on statistical implications. To show this general framework, we present a survey on customer behaviours for socially responsible food consumption. The survey was carried out by delivering a questionnaire administered to a representative sample of 332 families. In order to detect the main aspects impacting consumers’ preferences, a factor analysis has been performed. Then the general framework has been used to select and assess the measurement models in SEM. The estimation of the SEM has been worked out by partial least squares. The significance of the indicators has been tested using bootstrap. As far as we know, it is the first time that a model for the analysis of the consumers’ behaviour for social responsibility is formalized through a SEM.     

Predictive Accuracy Gain From Disaggregate Sampling in ARIMA Models

We compare the forecast accuracy of autoregressive integrated moving average (ARIMA) models based on data observed with high and low frequency, respectively. We discuss how, for instance, a quarterly model can be used to predict one quarter ahead even if only annual data are available, and we compare the variance of the prediction error in this case with the variance if quarterly observations were indeed available. Results on the expected information gain are presented for a number of ARIMA models including models that describe the seasonally adjusted gross national product (GNP) series in the Netherlands. Disaggregation from annual to quarterly GNP data has reduced the variance of short-run forecast errors considerably, but further disaggregation from quarterly to monthly data is found to hardly improve the accuracy of monthly forecasts.     

Multivariate temporal disaggregation with cross-sectional constraints

Multivariate temporal disaggregation deals with the historical reconstruction and nowcasting of economic variables subject to temporal and contemporaneous aggregation constraints. The problem involves a system of time series that are related not only by a dynamic model but also by accounting constraints. The paper introduces two fundamental (and realistic) models that implement the multivariate best linear unbiased estimation approach that has potential application to the temporal disaggregation of the national accounts series. The multivariate regression model with random walk disturbances is most suitable to deal with the chained linked volumes (as the nature of the national accounts time series suggests); however, in this case the accounting constraints are not binding and the discrepancy has to be modeled by either a trend-stationary or an integrated process. The tiny, compared with other driving disturbances, size of the discrepancy prevents maximum-likelihood estimation to be carried out, and the parameters have to be estimated separately. The multivariate disaggregation with integrated random walk disturbances is suitable for the national accounts aggregates expressed at current prices, in which case the accounting constraints are binding.     

On discrete distributions generated from drawing balls with bivariate labels

In this article, we consider urn models under three types of sampling schemes in terms of the probability-generating functions. The tools are developed for the evaluation of the distributions arising from the urn models along with some examples. Furthermore, the distributions are investigated by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of urn models. As examples, we propose new class of probability models, which are called multiple-player problems and examine their properties. Finally, we treat the parameter estimation problem in the waiting time distributions with a numerical example.     

Costing Mixed Coxian Phase-type Systems with Poisson Arrivals

Previously, we developed a modeling framework which classifies individuals with respect to their length of stay (LOS) in the transient states of a continuous-time Markov model with a single absorbing state; phase-type models are used for each class of the Markov model. We here add costs and obtain results for moments of total costs in (0, t], for an individual, a cohort arriving at time zero and when arrivals are Poisson. Based on stroke patient data from the Belfast City Hospital we use the overall modelling framework to obtain results for total cost in a given time interval.     

ON CONFIDENCE REGIONS OF EMBEDDED MODELS IN REGULAR PARAMETRIC FAMILIES (A GEOMETRIC APPROACH)

Regular parametric families are commonly encountered in statistical problems (e.g. Cox & Hinkley, 1974). In this paper, we propose a differential geometric framework for the embedded models in these families. Our framework may be regarded as an extension of that presented by Bates & Watts (1980) for nonlinear regression models. As an application, we use this geometric framework to derive three kinds of improved approximate confidence regions for the parameter and parameter subsets in terms of curvatures. The results obtained by Hamilton et al. (1982) and Hamilton (1986) are extended to embedded models in regular parametric families.     

Random coefficient regressions: parametric goodness-of-fit tests

Random coefficient regression models have been applied in different fields during recent years and they are a unifying frame for many statistical models. Recently, Beran and Hall (Ann. Statist. 20 (1992) 1970) raised the question of the nonparametric study of the coefficients distribution. Nonparametric goodness-of-fit tests were considered in Delicado and Romo (Ann. Inst. Statist. Math. 51 (1999) 125). In this nonparametric framework, the study of parametric families for the coefficient distributions was started by Beran (Ann. Inst. Statist. Math. (1993) 639). Here we propose statistics for parametric goodness-of-fit tests and we obtain their asymptotic distributions. Moreover, we construct bootstrap approximations to these distributions, proving their validity. Finally, a simulation study illustrates our results.     

Heterogeneity in Consumer Price Stickiness

We examine heterogeneity in price stickiness using a large, original, set of individual price data collected at the retail level for the computation of the French consumer price index. For that purpose, we estimate at a very high level of disaggregation, a piecewise-constant hazard model, as well as competing-risks duration models that distinguish between price increases, price decreases, and product replacements. The main findings are the following: (a) at the product–outlet-type level, the baseline hazard function of a price spell is nondecreasing; (b) cross-product and cross-outlet-type heterogeneity is pervasive, both in the shape and the level of the hazard function as well as in the impact of covariates; (c) there is strong evidence of state dependence, especially for price increases; (d) there is an asymmetry because determinants of price increases differ from those of price decreases.     

面板数据的可加分位回归模型研究与应用

本文在贝叶斯分析的框架下讨论了面板数据的可加模型分位回归建模方法。首先通过低秩薄板惩罚样条展开和个体效应虚拟变量的引进将非参数模型转换为参数模型,然后在假定随机误差项服从非对称Laplace分布的基础上建立了贝叶斯分层分位回归模型。通过对非对称Laplace分布的分解,论文给出了所有待估参数的条件后验分布,并构造了待估参数的 Gibbs抽样估计算法。计算机模拟仿真结果显示,新提出的方法相比于传统的可加模型均值回归方法在估计稳健性上明显占优。最后以消费支出面板数据为例研究了我国农村居民收入结构对消费支出的影响,发现对于农村居民来说,无论是高、中、低消费群体,工资性收入与经营净收入的增加对其消费支出的正向刺激作用更为明显。进一步,相比于高消费农村居民人群,低消费农村居民人群随着收入的增加消费支出上升速度较为缓慢。     

Degree-based goodness-of-fit tests for heterogeneous random graph models: Independent and exchangeable cases

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness of fit for a given random graph model. In this paper, we introduce goodness-of-fit tests for two classes of models. First, we consider the case of independent graph models such as the heterogeneous Erdös-Rényi model in which the edges have different connection probabilities. Second, we consider a generic model for exchangeable random graphs called the W-graph. The stochastic block model and the expected degree distribution model fall within this framework. We prove the asymptotic normality of the degree mean square under these independent and exchangeable models and derive formal tests. We study the power of the proposed tests and we prove the asymptotic normality under specific sparsity regimes. The tests are illustrated on real networks from social sciences and ecology, and their performances are assessed via a simulation study.     

Posterior Predictive p-values in Bayesian Hierarchical Models

Abstract.  The present work focuses on extensions of the posterior predictive p -value (ppp-value) for models with hierarchical structure, designed for testing assumptions made on underlying processes. The ppp-values are popular as tools for model criticism, yet their lack of a common interpretation limit their practical use. We discuss different extensions of ppp-values to hierarchical models, allowing for discrepancy measures that can be used for checking properties of the model at all stages. Through analytical derivations and simulation studies on simple models, we show that similar to the standard ppp-values, these extensions are typically far from uniformly distributed under the model assumptions and can give poor power in a hypothesis testing framework. We propose a calibration of the p -values, making the resulting calibrated p -values uniformly distributed under the model conditions. Illustrations are made through a real example of multinomial regression to age distributions of fish.     

Bayesian bridge-randomized penalized quantile regression estimation for linear regression model with AP(q) perturbation

Bridge penalized regression has many desirable statistical properties such as unbiasedness, sparseness as well as ‘oracle’. In Bayesian framework, bridge regularized penalty can be implemented based on generalized Gaussian distribution (GGD) prior. In this paper, we incorporate Bayesian bridge-randomized penalty and its adaptive version into the quantile regression (QR) models with autoregressive perturbations to conduct Bayesian penalization estimation. Employing the working likelihood of the asymmetric Laplace distribution (ALD) perturbations, the Bayesian joint hierarchical models are established. Based on the mixture representations of the ALD and generalized Gaussian distribution (GGD) priors of coefficients, the hybrid algorithms based on Gibbs sampler and Metropolis-Hasting sampler are provided to conduct fully Bayesian posterior estimation. Finally, the proposed Bayesian procedures are illustrated by some simulation examples and applied to a real data application of the electricity consumption.     

Two-sided Bayesian and frequentist tolerance intervals: general asymptotic results with applications

It is well known that that the construction of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. In a general framework of parametric models, we derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals. In the process, probability matching priors for such intervals are characterized and their role in finding frequentist tolerance intervals via a Bayesian route is indicated. Furthermore, in situations where matching priors are hard to obtain, we develop purely frequentist tolerance intervals as well. The findings are applied to real data. Simulation studies are seen to lend support to the asymptotic results in finite samples.     

Insights into the appropriate level of disaggregation for efficient time series model forecasting

This paper provides a potentially valuable insight on how to assess if the forecasts from an autoregressive moving average model based on aggregated data could be substantially improved through disaggregation. It is argued that, theoretically, the absence of moving average (MA) terms indicates that no forecasting efficiency improvements can be achieved through disaggregation. In practice, it is found that there is a strong correlation between the statistical significance of the MA component in the aggregate model and the magnitude of the forecast mean square error (MSE) decreases that can be achieved through disaggregation. That is, if a model includes significant MA terms, the forecast MSE improvements that may be gained from disaggregation could be substantial. Otherwise, they are more likely to be relatively small or non-existent.     

Temporal Disaggregation of Economic Time Series using Artificial Neural Networks

Several methods based on smoothing or statistical criteria have been used for deriving disaggregated values compatible with observed annual totals. The present method is based on the artificial neural networks. This article evaluates the use of artificial neural networks (ANNs) for the disaggregation of annual US GDP data to quarterly time increments. A feed-forward neural network with back-propagation algorithm for learning was used. An ANN model is introduced and evaluated in this paper. The proposed method is considered as a temporal disaggregation method without related series. A comparison with previous temporal disaggregation methods without related series has been done. The disaggregated quarterly GDP data compared well with observed quarterly data. In addition, they preserved all the basic statistics such as summing to the annual data value, cross correlation structure among quarterly flows, etc.     

Fused least absolute shrinkage and selection operator for credit scoring

Credit scoring can be defined as the set of statistical models and techniques that help financial institutions in their credit decision makings. In this paper, we consider a coarse classification method based on fused least absolute shrinkage and selection operator (LASSO) penalization. By adopting fused LASSO, one can deal continuous as well as discrete variables in a unified framework. For computational efficiency, we develop a penalization path algorithm. Through numerical examples, we compare the performances of fused LASSO and LASSO with dummy variable coding.     

Estimation of patterned covariance in the multivariate linear models: an outer product least-squares approach

In this article, we present a framework of estimating patterned covariance of interest in the multivariate linear models. The main idea in it is to estimate a patterned covariance by minimizing a trace distance function between outer product of residuals and its expected value. The proposed framework can provide us explicit estimators, called outer product least-squares estimators, for parameters in the patterned covariance of the multivariate linear model without or with restrictions on regression coefficients. The outer product least-squares estimators enjoy the desired properties in finite and large samples, including unbiasedness, invariance, consistency and asymptotic normality. We still apply the framework to three special situations where their patterned covariances are the uniform correlation, a generalized uniform correlation and a general q-dependence structure, respectively. Simulation studies for three special cases illustrate that the proposed method is a competent alternative of the maximum likelihood method in finite size samples.