Business Forecasting

Business forecasting

Autoregressive integrated moving average (ARIMA) models are a class of linear models that are capable or representing stationary as well as nonstationary time series. Recall that stationary processes vary about a fixed level and that nonstationary processes have no natural constant mean level.

The Box-Jenkins methodology of forecasting is different from most methods because it does not assume any particular pattern in the historical data of the series to be forecast. It uses an iterative approach of identifying a possible model from a general class of models. The chosen model is then checked against the historical data to see whether it accurately describes the series. The model fits well if the residuals are generally small and randomly distributed and contain no useful information. If the specified model is not satisfactory, the procces is repeatead using a new model designed to improve on the original one. This iterative procedure continues until a satisfactory model is found.

* Postulate General Class of Models-->Identify Model to Be Tentatively Entertained-->

* The Box-Jenkins methodology refers to a set of procedures for identifying, fitting, and checking ARIMA models with time series data. Forecast follow directly from the form of the fitted model.

Advantages and Disadvantages of ARIMA Models
The Box-Jenkins approach to time series analysis is a very powerfull tool for providing accurate short-range forecasts. ARIMA models are quite flexible and can represent a wide range of characteristic of time series that occur in practice. Formal procedures for testing the adequacy of the model are available. Moreover, forecasts and prediction intervals follow directly from the fitted model.
However, ARIMA modelling has some drawbacks.
  1. A relatively large amount of data is required. It should be recognized that, if the data are seasonal with, say, a seasonal period of S = 12, the monthly observations for one year essentially constitute one data point (one look at the seasonal pattern), not 12. Generally speaking, for nonseasonal data, about 40 observations or more are required to develop an ARIMA model. For seasonal data, about 6 to 10 years of data-depending on the length of the seasonal period-are required to construct an ARIMA model.
  2. There are no easy ways to update the parameters of an ARIMA model as new data become available, as there are in some smoothing methods. The models has to be periodically completely refitted, and sometimes a new model must be developed.
  3. The construction of a satisfactory ARIMA model often a large investment of time and other resources. The costs of data manipulation and model development can be substantially higher for ARIMA models than for the more traditional forecasting techniques such as smoothing.

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