Autoregressive integrated moving-average

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. 

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... 

The observational data were analyzed statistically using the autoregressive integrated moving average (ARIMA) analysis to check for and remove any statistically significant serial dependencies, correlated error, or nonstationary processes,. .. 

Box and Tiao (1975) subsequently developed a procedure for analysis of a time series in the presence of known external interventions. In their approach, there are two types of interventions - pulses and steps. A pulse is an intervention with a finite duration (typically one time period), while a step involves a permanent change or intervention (e.g., the introduction of a new governmental regulation or the permanent loss of a supplier). Intervention analysis is a statistical procedure that enables the researcher to evalnate the impact on a time series, as represented by an ARIMA (Autoregressive Integrated Moving Average) process. 

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