ARIMA forecasting

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. 

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 ... 

Table 8 is an extension of Table 3 but adding a column with the results when considering the ARIMA models to forecast demand in the first level of the supply chain (BW5). Furthermore, we show the reduction achieved in each case. 

The results presented in this section show that the use of advanced forecasting methods leads to the reduction of Bullwhip Effect. Thus, the inclusion of ARIMA models at the lowest level of the supply chain provides very interesting results, and it can significantly reduce, in many cases, the Bullwhip Effect. In these circumstances, we... 

To develop the tool, we have considered only simple forecasting methods, such as moving averages and exponential smoothing, so that each level of the chain uses the best one that suits the demand it should deal with. With them, it is possible to achieve great results in reducing Bullwhip Effect. Even so, we have also shown that the inclusion of more advanced forecasting methods (ARIMA models) allows an even better system performance. 

The empirical analysis of ARIMA multiplicative seasonal model to forecast the total number of coal mine accidents... 

ABSTRACT This paper is to research an application of the multiplicative seasonal model to forecast the total number of China s coal mine accidents. By the empirical analysis on the data of coal mine accidents from January 2006 to December 2010, an accepted multiplicative seasonal forecasting model ARIMA(4,1,1)(1,1,1) is built up after differing the series to be stationary and estimating the order and parameters of the model. Furthermore, the test of this multiplicative seasonal model shows that it has a desirable fitting effect on the data of coal mine accidents. At last, this model is applied to forecast the number of national coal mine accidents from January 2010 to December 2010, and the forecasted values have a high accuracy when compared to the actual data. 

After calculation, each model meets the conditions of stationary and invertible in the ARMA modeling process. At the same time, the models are reasonably defined and desirably fitting the data. Among these models, the AIC value of the 3rd model is the smallest. Therefore, it is appropriate to choose the 3rd model ARIMA(4,1,1)(1, 1, as the final model to forecast. 

Compared to ordinary time series models, the Multiplicative Seasonal Model needs more historical data, and the Multiplicative Seasonal Model can be applied to a wider field because data in daily life always have an obvious trend and seasonal features. Therefore, the Multiplicative Seasonal Model can well solve such problems that involve some issues about forecasting, and as well as reach a high precision. The model in this paper, ARIMA (4,1,1)(1,1,1) well matches the monthly changing number of national coal mine accidents. Moreover, the more historical data, the more accurate the forecasted result is. AH above, the Multiplicative Seasonal Model is a practical tool for us to forecast or to apply in many other fields. 

We apply the ARIMA(4, 1, 1)(1, 1, 1) model to forecast the number of national coal mine accidents from January 2010 to December 2010. The forecasted value is shown in table 4. 

GM (1,1) model based on ARIMA residual error correction is established and the combined model takes advantages of the two kinds of mathematical model, gray forecast model and ARIMA model. Compared with simply using the grey forecasting model, it could improve the prediction accuracy of gas concentration and reduce the relative prediction error. 

Thus, we observe that even if both supply chain members observe the data the forecast errors of the demands at both levels may be different. Consider, for example, the ARIMA(0,1,1) model of Graves (1999), and recall that in his setting the supplier fully observes the information ... 

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... 

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