On temporal aggregation of some nonlinear time-series models

Recently, economic globalisation and advances in computer technologies have accelerated the development of ‘big data’ analysis. Time-series data are routinely collected from the Internet and machine transactions at mixed frequencies. The problem of temporal aggregation arises when time-series data are observed at a lower frequency than the data generation frequency of the underlying basic model. The resulting aggregated series, which contains less information, may lead to an erroneous view of the true model and flawed decisions. Therefore, it is important to study the effects of temporal aggregation to avoid making possibly improper decisions based on distorted information from the aggregated data. Temporal aggregation of linear time-series processes has been widely studied. The effects of temporal aggregation on the first two moments of some nonlinear time-series models are assessed. More specifically, four types of nonlinear time-series models are studied: the Markov switching autoregressive (MSAR) model, the bilinear (BL) model, the mixture autoregressive (MAR) model, and the self-exciting threshold autoregressive (SETAR) model.