The Dynamic Skellam Model with Applications

Tinbergen Institute Discussion Paper 14-032/IV/DSF73

32 Pages Posted: 11 Mar 2014

See all articles by Siem Jan Koopman

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Rutger Lit

VU University Amsterdam

Andre Lucas

Vrije Universiteit Amsterdam; Tinbergen Institute

Date Written: March 6, 2014

Abstract

We introduce a dynamic statistical model for Skellam distributed random variables. The Skellam distribution can be obtained by taking differences between two Poisson distributed random variables. We treat cases where observations are measured over time and where possible serial correlation is modeled via stochastically time-varying intensities of the underlying Poisson counts. The likelihood function for our model is analytically intractable and we evaluate it via a multivariate extension of numerically accelerated importance sampling techniques. We illustrate the new model by two empirical studies and verify whether our framework can adequately handle large data sets. First, we analyze long univariate high-frequency time series of U.S. stock price changes, which evolve as discrete multiples of a fixed tick size of one dollar cent.

In a second illustration, we analyze the score differences between rival soccer teams using a large, unbalanced panel of seven seasons of weekly matches in the German Bundesliga.In both empirical studies, the new model provides interesting and non-trivial dynamics with a clear interpretation.

Keywords: dynamic count data models, non-Gaussian multivariate time series models, importance sampling, numerical integration, volatility models, sports data

JEL Classification: C22, C32, C58

Suggested Citation

Koopman, Siem Jan and Lit, Rutger and Lucas, Andre, The Dynamic Skellam Model with Applications (March 6, 2014). Tinbergen Institute Discussion Paper 14-032/IV/DSF73, Available at SSRN: https://ssrn.com/abstract=2406867 or http://dx.doi.org/10.2139/ssrn.2406867

Siem Jan Koopman (Contact Author)

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

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

Rutger Lit

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Andre Lucas

Vrije Universiteit Amsterdam ( email )

SBE/EDS, De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
271
Abstract Views
1,360
Rank
205,242
PlumX Metrics