The forecast for Box-Jenkins methodology part of the fact that the time series is predicted is generated by a stochastic process whose nature can be characterized by a model. To make such an estimate requires a monthly or quarterly time series that has a large number of observations.
And the forecast for Box-Jenkins methodology involves finding a mathematical model that represents the mathematical behavior of the time series data, allowing setting forecasting only by entering the corresponding time period.
The forecast for Box-Jenkins methodology provides predictions without the existence of any precondition, besides being parsimonious with respect to the coefficients. On the other hand, once you found the model can be made immediately predictions and comparisons between actual data and estimates for observations belonging to the past.
However, besides requiring a large number of observations, estimation and interpretation of their coefficients is complex and provides worse results in long-term forecasts.
PHILOSOPHY OF THE PROCESS OF FORECAST FOR BOX-JENKINS METHODOLOGY
Using the Box-Jenkins method we purse establishing a statistical model that represents the relationship between variations experiencing a temporary serial over certain periods.
To develop these models is part of a series of chronological data which has proven its stability. Otherwise, they have been applied to them to obtain the necessary transformations such stability.
The philosophy of this method is to divide the forecasting process into four stages:
1: Identification of the most suitable model to carry out a specific forecast.
2.1: Is made a forecast with that model and will evaluate them results.
2.2: If the evaluation of the previous step is not satisfactory becomes the first step to identify a new model.
3: If step 2.1 is satisfactory a forecast is made.
4: Is develops an algorithm of control for future use of this technique.
FORECAST FOR BOX-JENKINS METHODOLOGY UNIVARIATE
Oviedo University conducted a study to determine the effectiveness of the forecast for Box-Jenkins methodology analyzing eight time series, for which univariantes models were obtained.
These models were used to make forecasting in two different ways: on the one hand to obtain forecasting in a conventional manner for a number of periods N forward; on the other hand, they forecast a period forward were performed N times for what was necessary to incorporate the model a new real data each time the forecast was made, which was achieved simulate situations where predictions are obtained in real time.
The results obtained by comparing two ways of making forecasts showed the convenience of real-time forecasting wherever possible, due to the great improvement of quality of them.
The results show the forecast for Box-Jenkins methodology forecasting of better quality is obtained in real time. The limitation of this technique is when the observations of the time series are produced at very short time intervals.
On the other hand, this technique would not be applicable in cases where decisions must be made well in advance.
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