Many social (trends, polls), sporting, economic (indicators), business (trading, sales, marketing), natural, and engineering events can be represented quantitatively by (hourly, daily, weekly, monthly, quarterly, yearly) time-series. Researches and reports reveal that (a) many of these time-series interact one another directly or though underlying common factors and (b) many time-series are influenced by their own histories as well. Vector autoregressive (VAR) model is the simplest model trying to find out predictive model of linear, mutual and temporal causality underlying these time-series.

The long-memory vector autoregressive (LMVAR) algorithm estimates influences of longer histories of time-series or common factors with objective data-driven constraints. Without constraints, “estimated influences of long histories” can be contaminated by all kinds of random coincidences. Subjective constraints need specific assumptions which may not apply to real data sets at hand. The data-driven constraints make LMVAR accommodate wider range of values of model parameters, especially model learning parameters. The wider ranges can further enhance the power of machine learning.