Integer-valued APARCH processes

Time Series Analysis and Forecasting. Selected Contributions from the ITISE Conference. (I. Rojas and H. Pomares, eds.), Springer International Publishing, Switzerland. ISBN 978-3-319-28723-2, (2016), 189-202
http://www.springer.com/gp/book/9783319287232

The Asymmetric Power ARCH representation for the volatility was introduced by Ding et al. (J Empir Financ 1:83–106, 1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices, or share prices. As reported by Brännäs and Quoreshi (Appl Financ Econ 20:1429–1440, 2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.