Extreme Overdispersion and Persistence in Time-Series of Counts

46 Pages Posted: 4 Sep 2020

See all articles by Leopoldo Catania

Leopoldo Catania

Aarhus University - School of Business and Social Sciences; Aarhus University - CREATES

Eduardo Rossi

Department of Economics and Management

Paolo Santucci de Magistris

Luiss Guido Carli University

Date Written: July 23, 2020

Abstract

Time series of counts are often characterized by high overdispersion and persistence. These extreme features challenge the existing models. We approach this problem by combining the framework of INAR with a latent Markov structure. We call it HMM-INAR since it belongs to the class of hidden Markov models. We study the probabilistic properties of HMM-INAR model and illustrate conditions for the existence of an ergodic and stationary solution. We show that the HMM-INAR model is identifiable and can be estimated by maximum likelihood via an efficient expectation-maximization (EM) algorithm with steps available in closed form. The HMM-INAR well predicts the distributional and dynamic features of the time series of counts under investigation, i.e. the number of monthly bankruptcies in South Korea, and the number of trades and volume of several NYSE stocks observed at high frequency. Finally, the model proves empirically superior to other INAR specifications.

Keywords: Integer number autoregressive, counts, hidden-Markov, overdispersion, high-frequency, trading volume

JEL Classification: C22, C51, C58

Suggested Citation

Catania, Leopoldo and Rossi, Eduardo and Santucci de Magistris, Paolo, Extreme Overdispersion and Persistence in Time-Series of Counts (July 23, 2020). Available at SSRN: https://ssrn.com/abstract=3661266 or http://dx.doi.org/10.2139/ssrn.3661266

Leopoldo Catania (Contact Author)

Aarhus University - School of Business and Social Sciences ( email )

Fuglesangs Allé 4
Aarhus V, DK-8210
Denmark
+4587165536 (Phone)

HOME PAGE: http://pure.au.dk/portal/en/leopoldo.catania@econ.au.dk

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Eduardo Rossi

Department of Economics and Management ( email )

Via San Felice 5
27100 Pavia
Italy
++ (Phone)

Paolo Santucci de Magistris

Luiss Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

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