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Convex Analysisの二,三の進展について

SUMMARY This paper is concerned with a general class of observation-driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modelling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which the large-sample properties of the maximum likelihood estimators can be derived. Simulations are provided to give additional insight into the finite-sample behaviour of the estimators. Finally an application to a regression model for daily counts of asthma presentations at a Sydney hospital is described.

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Observation-driven models for Poisson counts

This article discusses the modelling of integer-valued time series with overdispersion and potential extreme observations. For the problem, a negative binomial INGARCH model, a generalization of the Poisson INGARCH model, is proposed and stationarity conditions are given as well as the autocorrelation function. For estimation, we present three approaches with the focus on the maximum likelihood approach. Some results from numerical studies are presented and indicate that the proposed methodology performs better than the Poisson and double Poisson model-based methods.

https://papers.ssrn.com/sol3/Delivery.cfm/j_1467-9892_2010_00684_x_wml.pdf?abstractid=1727937&mirid=1

A negative binomial integer-valued GARCH model

cycles in international relations. Scholars use event-count models to analyze a wide variety of political science data. For example, the large sets of data on cooperative and conflictual international events often use event-count models (Huang, Kim, and Wu 1992; Sayrs 1992; Volgy and Imwalle 1995). These data have also been analyzed using time-series methods, particularly when transformed into indices of conflict and cooperation that consider the severity of each event and are no longer purely event counts (Goldstein 1991; Goldstein and Freeman 1990; Schneider, Widmer, and Ruloff 1993; Ward and Rajmaira 1992). Other event counts commonly analyzed in international relations include the number of wars (Benoit 1996; Mansfield 1992), militarized interstate disputes (Gowa 1998; Pollins 1996; Senese 1997), or other incidents of conflict and cooperation between states (BrophyBaerman and Conybeare 1994; Eyerman and Hart 1996; Kinsella 1995; Kinsella and Tillema 1995; O'Brien 1996; Fordham 1998a, 1998b; Remmer 1998). Scholars in American politics have also employed event-count models for time-series data to analyze presidential activity (Brace and Hinckley 1993), Federal Reserve decisions (Krause 1994), federal contract awards (Mayer 1995), executive orders (Krause and Cohen 1997), and Supreme Court decisions (Caldeira and Zorn 1998). The same issues confront the smaller number of comparativists using such data (Moore, Lindstrom, and O'Regan 1996).

Dynamic modeling for persistent event-count time series

This paper introduces and evaluates new models for time series count data. The Autoregressive Conditional Poisson model (ACP) makes it possible to deal with issues of discreteness, overdispersion (variance greater than the mean) and serial correlation. A fully parametric approach is taken and a marginal distribution for the counts is specified, where conditional on past observations the mean is autoregressive. This enables to attain improved inference on coefficients of exogenous regressors relative to static Poisson regression, which is the main concern of the existing literature, while modelling the serial correlation in a flexible way. A variety of models, based on the double Poisson distribution of Efron (1986) is introduced, which in a first step introduce an additional dispersion parameter and in a second step make this dispersion parameter time-varying. All models are estimated using maximum likelihood which makes the usual tests available. In this framework autocorrelation can be tested with a straightforward likelihood ratio test, whose simplicity is in sharp contrast with test procedures in the latent variable time series count model of Zeger (1988). The models are applied to the time series of monthly polio cases in the U.S between 1970 and 1983 as well as to the daily number of price change durations of .75$ on the IBM stock. A .75$ price-change duration is defined as the time it takes the stock price to move by at least .75$. The variable of interest is the daily number of such durations, which is a measure of intradaily volatility, since the more volatile the stock price is within a day, the larger the counts will be. The ACP models provide good density forecasts of this measure of volatility.

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Modelling time series count data: an Autoregressive Conditional Poisson model

SUMMARY This paper develops a practical approach to diagnosing the existence of a latent stochastic process in the mean of a Poisson regression model. The asymptotic distribution of standard generalised linear model estimators is derived for the case where an autocorrelated latent process is present. Simple formulae for the effect of autocovariance on standard errors of the regression coefficients are also provided. Methods for adjusting for the severe bias in previously proposed estimators of autocovariance are derived and their behaviour is investigated. Applications of the methods to time series of monthly polio counts in the U.S.A. and daily asthma presentations at a hospital in Sydney are used to illustrate the results and methods.

Ying Wang

Papers

On autocorrelation in a Poisson regression model