Time series representation and appropriate estimation

Abstract

We present a discussion on time series models, particularly, on ARMA and ARIMA model. Considering non-uniqueness of the model represen- tation, we propose to select an appropriate model optimizing simultaneously two criteria: “fit” and “model complexity”.

These criteria are discordant. Therefore, we have to consider their suitable combination; e.g.

AIC or BIC criterion. Our contribution is in larger set of competitive models than mono- graphs suggest.

Keywords

• ARMA process
• ARIMA process
• AIC criterion
• algebra of polynomials.