Box–Jenkins Methodology

This chapter is devoted to so-called Box–Jenkins methodology applying special stochastic models (ARMA, ARIMA, SARIMA, and others) to time series analysis (e.g., to time series predictions). It enables us to model satisfactorily time series with general courses that cannot be handled by the classical decomposition approach (see also Sect. 2.2.2 ). The methodology is entitled according to the well-known monograph by Box and Jenkins (1970). The authors summarized the temporary knowledge on this issue and transferred theoretical results to algorithmic form. The methodology has some typical features: in particular, it prefers the (auto)correlation analysis as the main instrument of time series analysis, it models the trend and seasonality in a stochastic way, and other particularities can be stressed. It implies that time series with strongly (auto)correlated observations can be studied using this approach. Indeed, the linear models such as ARMA offer the most popular approach to the routine correlatedness among observations in time (however, the financial time series require specific nonlinear modifications of linear models; see, e.g., models GARCH in Sect. 8.3 , even if the basic principles are the same). In this chapter, we describe the given issue in a systematic way. We start introducing some pros and cons of Box–Jenkins methodology: