Efficient Estimation of Auto-Regression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models

The paper

• Drost., F.C., Van den Akker, R., and Werker, B.J.M. (2009). Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR(p) models, Journal of the Royal Statistical Society: series B 71(2), pp. 467–485.

contained an appendix with proofs that was unfortunately not published alongside the paper. This appendix can be retrieved here.

See

• Faymonville, M. Javiera. Riffo, J. Rieger, and C. Jentsch (2024). spINAR: An R Package for Semiparametric and Parametric Estimation and Bootstrapping of Integer-Valued Autoregressive (INAR) Models, Journal of Open Source Software 9(97), pages 5386,

for an implementation in R. See link for the associated GitHub repository.

Other contributions to the literature on integer-valued time series:

• Van den Akker, R. (2007). Integer-Valued Time Series. CentER dissertation series, Tilburg: Tilburg University Press.
• Drost., F.C., Van den Akker, R., and Werker, B.J.M. (2008). Local asymptotic normality and efficient estimation for INAR(p) models, Journal of Time Series Analysis, 29(5), pp.783-801.
  • Working paper version
• Drost., F.C., Van den Akker, R., and Werker, B.J.M. (2008). Note on integer-valued bilinear time series models, Statistics & probability letters 78(8), pp.992-996.
  • Working paper version
• Drost., F.C., Van den Akker, R., and Werker, B.J.M. (2009). The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models, Bernoulli 15(2), pp.297-324.
  • Slides