Tests for time series of counts based on the probability-generating function

Abstract

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.

Keywords:

• INAR model
• Poisson autoregression
• goodness-of-fit test
• empirical probability-generating function

AMS Subject Classification:

• 62M10
• 62F03
• 62F40

Acknowledgements

We thank to both anonymous referees for careful reading and a number of valuable comments which led to improvement the presentation of the results.

Funding

The research of Simos Meintanis was partially supported by grant number 11699 of the Special Account for Research Grants (ELKE) of the National and Kapodistrian University of Athens. The research of Marie Hušková was partially supported by grant GAČR P201/12/1277. The research of Šárka Hudecová was partially supported by the Czech Science Foundation project ‘DYME Dynamic Models in Economics’ No. P402/12/G097.