GENERALIZED AUTOREGRESSIVE SCORE MODELS WITH APPLICATIONS

We propose a class of observation‐driven time series models referred to as generalized autoregressive score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time‐varying parameters in a wide class of nonlinear models. The GAS model encompasses other well‐known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time‐varying mean. In addition, our approach can lead to new formulations of observation‐driven models. We illustrate our framework by introducing new model specifications for time‐varying copula functions and for multivariate point processes with time‐varying parameters. We study the models in detail and provide simulation and empirical evidence. Copyright © 2012 John Wiley & Sons, Ltd.     

Detecting overdispersion in INARCH(1) processes

A statistical test for the degree of overdispersion of count data time series based on the empirical version of the (Poisson) index of dispersion is considered. The test design relies on asymptotic properties of this index of dispersion, which in turn have been analyzed for time series stemming from a compound Poisson (Poisson‐stopped sum) INAR(1) model. This approach is extended to the popular Poisson INARCH(1) model, which exhibits unconditional overdispersion but has an (equidispersed) conditional Poisson distribution. The asymptotic distribution of the index of dispersion if applied to time series stemming from such a model is derived. These results allow us to investigate the ability of the dispersion test to discriminate between Poisson INAR(1) and INARCH(1) models. Furthermore, the question is considered if the index of dispersion could be used to test the null of a Poisson INARCH(1) model against the alternative of an INARCH(1) model with additional conditional overdispersion.     

Investigating the impact of excess zeros on hurdle‐generalized Poisson regression model with right censored count data

Typically, a Poisson model is assumed for count data. In many cases, there are many zeros in the dependent variable, thus the mean is not equal to the variance value of the dependent variable. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, we suggest using a hurdle‐generalized Poisson regression model. Furthermore, the response variable in such cases is censored for some values because of some big values. A censored hurdle‐generalized Poisson regression model is introduced on count data with many zeros in this paper. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness‐of‐fit for the regression model is examined. An example and a simulation will be used to illustrate the effects of right censoring on the parameter estimation and their standard errors.     

Multiple imputation of incomplete zero‐inflated count data

Empirical count data are often zero‐inflated and overdispersed. Currently, there is no software package that allows adequate imputation of these data. We present multiple‐imputation routines for these kinds of count data based on a Bayesian regression approach or alternatively based on a bootstrap approach that work as add‐ons for the popular multiple imputation by chained equations (mice ) software in R (van Buuren and Groothuis‐Oudshoorn , Journal of Statistical Software, vol. 45, 2011, p. 1). We demonstrate in a Monte Carlo simulation that our procedures are superior to currently available count data procedures. It is emphasized that thorough modeling is essential to obtain plausible imputations and that model mis‐specifications can bias parameter estimates and standard errors quite noticeably. Finally, the strengths and limitations of our procedures are discussed, and fruitful avenues for future theory and software development are outlined.     

Goodness-of-fit tests for Poisson count time series based on the Stein–Chen identity

To test the null hypothesis of a Poisson marginal distribution, test statistics based on the Stein–Chen identity are proposed. For a wide class of Poisson count time series, the asymptotic distribution of different types of Stein–Chen statistics is derived, also if multiple statistics are jointly applied. The performance of the tests is analyzed with simulations, as well as the question which Stein–Chen functions should be used for which alternative. Illustrative data examples are presented, and possible extensions of the novel Stein–Chen approach are discussed as well.     

Semiparametric time series models driven by latent factor

We introduce a class of semiparametric time series models (SemiParTS) driven by a latent factor process. The proposed SemiParTS class is flexible because, given the latent process, only the conditional mean and variance of the time series are specified. These are the primary features of SemiParTS: (i) no parametric form is assumed for the conditional distribution of the time series given the latent process; (ii) it is suitable for a wide range of data: non-negative, count, bounded, binary, and real-valued time series; (iii) it does not constrain the dispersion parameter to be known. The quasi-likelihood inference is employed in order to estimate the parameters in the mean function. Here, we derive explicit expressions for the marginal moments and for the autocorrelation function of the time series process so that a method of moments can be employed to estimate the dispersion parameter and also the parameters related to the latent process. Simulated results that aim to check the proposed estimation procedure are presented. Forecasting procedures are proposed and evaluated in simulated and real data. Analyses of the number of admissions in a hospital due to asthma and a total insolation time series illustrate the potential for practical situations that involve the proposed models.     

Local influence analysis for Poisson autoregression with an application to stock transaction data

In statistical diagnostics and sensitivity analysis, the local influence method plays an important role and has certain advantages over other methods in several situations. In this paper, we use this method to study time series of count data when employing a Poisson autoregressive model. We consider case‐weights, scale, data, and additive perturbation schemes to obtain their corresponding vectors and matrices of derivatives for the measures of slope and normal curvatures. Based on the curvature diagnostics, we take a stepwise local influence approach to deal with data with possible masking effects. Finally, our established results are illustrated to be effective by analyzing a stock transactions data set.     

Bivariate exponentiated‐exponential geometric regression model

A bivariate exponentiated‐exponential geometric regression model that allows negative, zero, or positive correlation is defined and studied. The model can accommodate under‐ or over‐dispersed count data. The regression model is based on the univariate exponentiated‐exponential geometric distribution, and the marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness of fit are discussed. A simulation study is conducted to compare the model with the bivariate generalized Poisson regression model. One numerical data set is used to illustrate the application of the regression model.     

On the inclusion of bivariate marked point processes in graphical models

Graphical models use graphs to represent conditional independence relationships among random variables of a multivariate probability distribution. This paper introduces a new kind of chain graph models in which nodes also represent marked point processes. This is relevant to the analysis of event history data, i.e. data consisting of random sequences of events or time durations of states. Survival analysis and duration models are particular cases. This article considers the case of two marked point processes. The idea consists of representing a whole process by a single node and a conditional independence statement by a lack of connection. We refer to the resulting models as graphical duration models.     

Narrow Replication of Fisman and Miguel's (2007a) ‘Corruption,Norms, and Legal Enforcement: Evidence from Diplomatic Parking Tickets’

This note provides a narrow replication of Fisman and Miguel's (Journal of Political Economy, 2007a; 115 (6): 1020–1048) original findings about estimating negative binomial count models to study corruption practices among United Nations diplomats. We present estimates based on zero‐inflated count models, given the possible presence of excessive zero counts in the dependent variable of the main specifications. Our results confirm Fisman and Miguel's original findings. However, they also suggest the importance of considering distinct generating processes for zero outcomes. We cannot reject hypotheses favoring the use of zero‐inflated negative binomial models over its simpler versions in this context. Copyright © 2016 John Wiley & Sons, Ltd.     

Change-point analysis through integer-valued autoregressive process with application to some COVID-19 data

In this article, we consider the problem of change-point analysis for the count time series data through an integer-valued autoregressive process of order 1 (INAR(1)) with time-varying covariates. These types of features we observe in many real-life scenarios especially in the COVID-19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time-varying smoothing covariate. By using such model, we can model both the components in the active cases at time-point t namely, (i) number of nonrecovery cases from the previous time-point and (ii) number of new cases at time-point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID-19 data sets and compare our proposed model with another PINAR(1) process which has time-varying covariate but no change-point, to demonstrate the overall performance of our proposed model.     

Expectation-based scan statistics for monitoring spatial time series data

We consider the simultaneous monitoring of a large number of spatially localized time series in order to detect emerging spatial patterns. For example, in disease surveillance, we detect emerging outbreaks by monitoring electronically available public health data, e.g. aggregate daily counts of Emergency Department visits. We propose a two-step approach based on the expectation-based scan statistic: we first compute the expected count for each recent day for each spatial location, then find spatial regions (groups of nearby locations) where the recent counts are significantly higher than expected. By aggregating information across multiple time series rather than monitoring each series separately, we can improve the timeliness, accuracy, and spatial resolution of detection. We evaluate several variants of the expectation-based scan statistic on the disease surveillance task (using synthetic outbreaks injected into real-world hospital Emergency Department data), and draw conclusions about which models and methods are most appropriate for which surveillance tasks.     

Forecasting with vector autoregressive (VAR) models subject to business cycle restrictions

In the last decade VAR models have become a widely-used tool for forecasting macroeconomic time series. To improve the out-of-sample forecasting accuracy of these models, Bayesian random-walk prior restrictions are often imposed on VAR model parameters. This paper focuses on whether placing an alternative type of restriction on the parameters of unrestricted VAR models improves the out-of-sample forecasting performance of these models. The type of restriction analyzed here is based on the business cycle characteristics of U.S. macroeconomic data, and in particular, requires that the dynamic behavior of the restricted VAR model mimic the business cycle characteristics of historical data. The question posed in this paper is: would a VAR model, estimated subject to the restriction that the cyclical characteristics of simulated data from the model “match up” with the business cycle characteristics of U.S. data, generate more accurate out-of-sample forecasts than unrestricted or Bayesian VAR models?     

Dynamic stochastic copula models: estimation,inference and applications

We propose a new dynamic copula model in which the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling. We discuss goodness‐of‐fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that the proposed model outperforms standard competing models. Copyright © 2010 John Wiley & Sons, Ltd.     

Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm

Typical data that arise from surveys, experiments, and observational studies include continuous and discrete variables. In this article, we study the interdependence among a mixed (continuous, count, ordered categorical, and binary) set of variables via graphical models. We propose an ?₁‐penalized extended rank likelihood with an ascent Monte Carlo expectation maximization approach for the copula Gaussian graphical models and establish near conditional independence relations and zero elements of a precision matrix. In particular, we focus on high‐dimensional inference where the number of observations are in the same order or less than the number of variables under consideration. To illustrate how to infer networks for mixed variables through conditional independence, we consider two datasets: one in the area of sports and the other concerning breast cancer.     

A latent class poisson regression model for heterogeneous count data

In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing distribution is discrete, resulting in a finite mixture model formulation. An EM algorithm for estimation is described, and the algorithm is applied to data on customer purchases of books offered through direct mail. Our model is compared empirically to a number of other approaches that deal with heterogeneity in Poisson regression models.     

Inference on endogenously censored regression models using conditional moment inequalities

Under a quantile restriction, randomly censored regression models can be written in terms of conditional moment inequalities. We study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring, endogenous censoring and endogenous regressors. These inequalities restrict the parameters to a set. We show regular point identification can be achieved under a set of interpretable sufficient conditions. We then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content. Our method obviates the need for nonparametric estimation, which would require the selection of smoothing parameters and trimming procedures. Without the point identification conditions, our objective function can be used to do inference on the partially identified parameter. Maintaining the point identification conditions, we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest, and has an asymptotically normal distribution. A small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance.     

Asymptotic distributions of some scale estimators in nonlinear models

Often in the robust analysis of regression and time series models there is a need for having a robust scale estimator of a scale parameter of the errors. One often used scale estimator is the median of the absolute residuals s ₁. It is of interest to know its limiting distribution and the consistency rate. Its limiting distribution generally depends on the estimator of the regression and/or autoregressive parameter vector unless the errors are symmetrically distributed around zero. To overcome this difficulty it is then natural to use the median of the absolute differences of pairwise residuals, s ₂, as a scale estimator. This paper derives the asymptotic distributions of these two estimators for a large class of nonlinear regression and autoregressive models when the errors are independent and identically distributed. It is found that the asymptotic distribution of a suitably standardizes s ₂ is free of the initial estimator of the regression/autoregressive parameters. A similar conclusion also holds for s ₁ in linear regression models through the origin and with centered designs, and in linear autoregressive models with zero mean errors.  This paper also investigates the limiting distributions of these estimators in nonlinear regression models with long memory moving average errors. An interesting finding is that if the errors are symmetric around zero, then not only is the limiting distribution of a suitably standardized s ₁ free of the regression estimator, but it is degenerate at zero. On the other hand a similarly standardized s ₂ converges in distribution to a normal distribution, regardless of the errors being symmetric or not. One clear conclusion is that under the symmetry of the long memory moving average errors, the rate of consistency for s ₁ is faster than that of s ₂.     

Forecasting aggregates using panels of nonlinear time series

Macroeconomic time series such as total unemployment or total industrial production concern data which are aggregated across regions, sectors, or age categories. In this paper we examine whether forecasts for these aggregates can be improved by considering panel models for the disaggregate series. As many macroeconomic variables have nonlinear properties, we specifically focus on panels of nonlinear time series. We discuss the representation of such models, parameter estimation and a method for generating forecasts. We illustrate the usefulness of our approach for simulated data and for the US coincident index, making use of state-specific component series.