Autoregressive Gamma Processes

1 Autoregressive Gamma Processes We introduce autoregressive gamma processes of order p ARG(p)] with transition distributions which are noncentral gamma up to a change of scale. The paper provides the stationarity a n d ergodicity conditions for ARG processes of any autoregressive order p, including long memory. The analytical expressions of the conditional moments and nonlinear autocorrelations for any ARG(p) are also given. Moreover, the nonlinear state space representation of an ARG process is used to derive the ltering, smoothing and forecasting algorithms. Finally, the paper introduces estimation and inference methods which are illustrated by an application to interquote durations series of an infrequently traded stock listed on the TSE. Processus gamma autoregressif Nous introduisons des processus de Markov, dont les transitions sont d e s distributions gamma d ecentr ees a un facteur d' echelle pr es. Nous etudions les propri et es dynamiques de ces processus. En particulier nous donnons les expressions explicites des deux premiers moments conditionnels, d erivons les autocorr elogrammes d'ordre un et deux et explicitons la d ecomposition canonique non lin eaire du processus. Cette sp eciication est utilis ee pour analyser la dynamique des dur ees entre transactions. Mots cl es : Dur ees, processus gamma, processus de Cox-Ingersoll-Ross, analyse canonique non lin eaire, donn ees haute-fr equence, dur e es entre transactions .

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