Robert C. Jung

Time series of count data: modeling, estimation and diagnostics

Various models for time series of counts which can account for discreteness, overdispersion and serial correlation are compared. Besides observation- and parameter-driven models based upon corresponding conditional Poisson distributions, a dynamic ordered probit model as a flexible specification to capture the salient features of time series of counts is also considered. For all models, appropriate efficient estimation procedures are presented. For the parameter-driven specification this requires Monte-Carlo procedures like simulated maximum likelihood or Markov chain Monte Carlo. The methods, including corresponding diagnostic tests, are illustrated using data on daily admissions for asthma to a single hospital. Estimation results turn out to be remarkably similar across the different models.

Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions

Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal distribution is compa-red with SV specifications using conditional heavy-tailed distributions, especially Students i-distribution and the generalized error distribution. To estimate the SV specifications a si-mulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and low but slowly decaying autocorrelation function of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional heavy-tailed distribution. Finally, it turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process.

Two aspects of labor mobility: A bivariate Poisson regression approach

SummaryThe study introduces a distinction between two types of labor mobility. Direct job to job changes (which are assumed to be voluntary) and job changes after experiencing an unemployment spell (assumed to be involuntary). Exploiting the close relationship between those two phenomena we adopt a bivariate regression framework for our empirical analysis of data on male individuals in the German labor market. To account for the non-negative and discrete nature of the two counts of job changes in a ten year interval a new econometric model is proposed: the bivariate Poisson regression proves to be superior to the univariate specification. Further, the empirical content of distinguishing between two types of mobility is subject to a test, and, in fact, supported by the data: The hypothesis that both measures are observationally equivalent can be rejected.

Estimation in conditional first order autoregression with discrete support

We consider estimation in the class of first order conditional linear autoregressive models with discrete support that are routinely used to model time series of counts. Various groups of estimators proposed in the literature are discussed: moment-based estimators; regression-based estimators; and likelihood-based estimators. Some of these have been used previously and others not. In particular, we address the performance of new types of generalized method of moments estimators and propose an exact maximum likelihood procedure valid for a Poisson marginal model using backcasting. The small sample properties of all estimators are comprehensively analyzed using simulation. Three situations are considered using data generated with: a fixed autoregressive parameter and equidispersed Poisson innovations; negative binomial innovations; and, additionally, a random autoregressive coefficient. The first set of experiments indicates that bias correction methods, not hitherto used in this context to our knowledge, are some-times needed and that likelihood-based estimators, as might be expected, perform well. The second two scenarios are representative of overdispersion. Methods designed specifically for the Poisson context now perform uniformly badly, but simple, bias-corrected, Yule-Walker and least squares estimators perform well in all cases.

Binomial thinning models for integer time series

This article considers some simple observation-driven time series models for counts. We provide a brief description of the class of integer-valued autoregressive (INAR) and integer-valued moving average (INMA) processes. These classes of models may be attractive when the data exhibit a significant serial dependence structure. We, therefore, briefly review various testing procedures useful for assessing the serial correlation in the data. Once it is established that the data are not serially independent, suitable INAR or INMA processes may be employed to model the data. In the important first order INAR model, we discuss various methods of estimating the structural parameters of the process. We also give a short account of the extension of some of these estimation procedures to second order INAR models. Moving average counterparts of both models are also entertained. Throughout, the models and methods are illustrated in the context of a famous data set from the branching process literature that turns out to be surprisingly difficult to model satisfactorily.

Financial market spillovers around the globe

This article investigates the transmission of return and volatility spillovers around the globe. It draws on index futures of three representative indices, namely the Dow Jones Euro Stoxx 50, the S&P 500 and the Nikkei 225. Devolatized returns and realized volatilities are modelled separately using a Structural Vector Autoregressive (SVAR) model, thereby accounting for the particular sequential time structure of the trading venues. Within this framework, we test hypotheses in the spirit of Granger causality tests, investigate the short-run dynamics in the three markets using Impulse Response (IR) functions, and identify leadership effects through variance decomposition. Our key results are as follows. We find weak and short-lived return spillovers, in particular from the USA to Japan. Volatility spillovers are more pronounced and persistent. The information from the home market is most important for both returns and volatilities; the contribution from foreign markets is less pronounced in the case of returns than in the case of volatility. Possible gains in terms of forecasting precision when applying our modelling strategy are illustrated by a forecast evaluation.

Testing for Serial Dependence in Time Series Models of Counts

In analysing time series of counts, the need to test for the presence of a dependence structure routinely arises. Suitable tests for this purpose are considered in this paper. Their size and power properties are evaluated under various alternatives taken from the class of INARMA processes. We find that all the tests considered except one are robust against extra binomial variation in the data and that tests based on the sample autocorrelations and the sample partial autocorrelations can help to distinguish between integer-valued first-order and second-order autoregressive as well as first-order moving average processes. Copyright 2003 Blackwell Publishing Ltd.

Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint distribution with respect to the unobserved dynamic factors. We rely upon the Monte Carlo integration procedure known as efficient importance sampling, which produces fast and numerically accurate estimates of the likelihood function. The model is applied to time series data consisting of numbers of trades in 5-min intervals for five New York Stock Exchange (NYSE) stocks from two industrial sectors. The estimated model provides a good parsimonious representation of the contemporaneous correlation across the individual stocks and their serial correlation. It also provides strong evidence of a common factor, which we interpret as reflecting market-wide news.

Estimation of a First Order Autoregressive Process with Poisson Marginals for Count Data

Count data play an important role in modern microeconometric models. However, a proper dynamic specification in case of panel data has not yet been discussed: So far only variance components have been specified which show constant autocorrelation over time. In the present paper an autoregressive process for count data is considered as suggested independently by Al-Osh and Alzaid (Journal of Time Series Analysis 1987) and McKenzie (Advances in Applied Probability 1988). Simulation results demonstrate that it is necessary to take proper account of the ’initial conditions’ of the stochastic process when small sample sizes (about 5 or 10) are considered which is the typical number of waves in panel data collected for econometric reseach.

Convolution-Closed Models for Count Time Series with Applications

There has recently been an upsurge of interest in time series models for count data. Many papers focus on the model with first-order (Markov) dependence and Poisson innovations. Our paper considers practical models that can capture higher-order dependence based on the work of Joe (1996). In this framework we are able to model both equidispersed and overdispersed marginal distributions of data. The latter is approached using generalized Poisson innovations. Central to the models is the use of the property of closure under convolution of certain families of random variables. The models can be thought of as stationary Markov chains of finite order. Parameter estimation is undertaken by maximum likelihood, inference procedures are considered and means of assessing model adequacy employed. Applications to two new data sets are provided.