Autoregressive moving ARIMA

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. 

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

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. 

The PACF illustrates the order 1 for the AR component, but at this stage of estimation of the model it is unknown if the trend or the seasonal model follow the autoregression with the order of one. No moving average component can be found from the PACF. Deduced possible models are ARIMA (1,1,0)( 1,0,0), ARIMA (0,1,0)( 1,0,0), or ARIMA (1,1,0)(0,0,0). 

The ACF and PACF of the resulting errors from ARIMA (1,1,0)(1,0,0) do not show spikes (Figs. 6-30 and 6-31). This means they do not have significant autoregression or moving average components. 

In ARIMA modeling, the order of the autoregressive component is frequently zero, one or sometimes two. Therefore, only short forecasting intervals are of any use. Disturbances in future values, normally smoothed by the moving average, were set to zero. The following example demonstrates this fact ... 

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,... 

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. 

---