A0177
Title: Mixed causal-noncausal count process
Authors: Jian Pei - Jilin University (Canada)
Yang Lu - Concordia University (Canada) [presenting]
Abstract: Recently, a study introduced a class of (Markov) noncausal count processes. These processes are obtained by time-reverting a standard count process (such as INAR(1)) but have quite different dynamic properties. In particular, they can feature bubble-type phenomena, which are epochs of steady increase followed by sharp decreases. This is in contrast to usual INAR and INGARCH type models, which only feature "reverse bubbles'', which are epochs of sharp increase followed by steady decreases. In practice, however, in many datasets, sudden jumps or crashes are rare, and instead, it is more frequent to observe epochs of steady increase or decrease. In practice, count time series data can feature both bubbles and reverse bubbles. This raises the question of what model to use if the modeler cannot discriminate a priori between the causal and noncausal models. The mixed causal-noncausal integer-valued autoregressive (MINAR(1,1)) process is introduced by superposing a causal and a noncausal INAR(1) process, sharing the same sequence of error terms. This process inherits some key properties from the noncausal INAR(1), such as the bi-modality of the predictive distribution and the irreversibility of the dynamics, while at the same time allowing different accumulation and burst speeds for the bubble. A GMM estimation method is proposed, its finite sample performance is investigated, testing procedures are developed, and the methodology is applied to stock transaction data.
