Integrated moving-average model

Autoregressive Integrated Moving Average Model (ARIMA) ... 

A general approach was developed by G.E.P. Box and G.M. Jenkins (S) which combines these various methods into an analysis which permits choice of the most appropriate model, checks the forecast precision, and allows for interpretation. The Box-Jenkins analysis is an autoregressive integrated moving average model (ARIMA). This approach, as implemented in the MINITAB computer program is one used for the analyses reported here. 

Liu W.S. 2005. The study of Shanghai stock price index based on Grey Theory and Autiregressive integrated moving average models. Master dissertation. HoHai University, Nan Jing. 

ARIMA connects both autoregressive and moving average models and includes integrating effects, e.g. trends or seasonal effects. 

Comparing this with equation (3) shows that this can be considered as the output of a first order transfer function in response to a random input sequence. More generally, most stochastic disturbances can be modelled by a general autoregressive-integrated moving-average (ARIMA) time series model of order (p,d,q), that is,... 

The most general, time series model called a seasonal, autoregressive, integrated, moving-average (SARIMA) model of order (p, d, q) x (P, D, 2) has the form... 

ARIMA is a sophisticated univariate modeling technique. ARIMA is the abbreviation of Autoregressive integrated moving average (also known as the Box-Jenkins model). It was developed in 1970 for forecasting purposes and relies solely on the past behavior of the variable being forecasted. The model creates the value of F, with input from previous values of the same dataset. This input includes a factor of previous values as well as the elasticity of the... 

AR) model, while case (d) is called an integrated moving-average (IMA) model. 

It is easy to interpret Eq. 6-49, difficult as it may look. The series for the moving average term equals a combination of the current disturbance and of the disturbance of one previous seasonal period. The original series, therefore, follows a model integrated from the ARMA model of the stationary series, see Eq. 6-47. 

The specification of ARIMA models is very expensive for the operator who analyzes time series. The first phase is the estimation of the order of three inherent processes, autoregression, integration, and moving average. 

Figure 17.13 Four models for d(k) a) stationary white noise disturbance b) stationary autoregressive disturbance (c) nonstationary disturbance (random walk) (d[) integrated (nonstationary) moving-average disturbance (adapted from Box and Luceno, 1997).

---