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Forecasting and estimating the future: AutoRegressive Integrated Moving Average. Explanation of ARIMA of Box and Jenkins. ('76)

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Nobody can really look into the future. But modern statistical methods, econometric models, and Business Intelligence software can to some extent help businesses to forecast and to estimate what is going to happen in the future.


ARIMA stands for AutoRegressive Integrated Moving Average.


The ARIMA Time Series Analysis uses lags and shifts in the historical data to uncover patterns (e.g. moving averages, seasonality) and predict the future. The ARIMA model was first developed in the late 60s but it was systemized by Box and Jenkins in 1976. ARIMA can be more complex to use than other statistical forecasting techniques, although when implemented properly ARIMA can be quite powerful and flexible.
 

ARIMA is a method for determining two things:

  1. How much of the past should be used to predict the next observation (length of weights)
  2. The values of the weights.

For example y(t)= 1/3 * y(t-3) + 1/3 * y(t-2) + 1/3 * y(t-1) is an ARIMA model; another ARIMA MODEL is y(t)= 1/6 * y(t-3) + 4/6 * y(t-2) + 1/6 * y(t-1)

Thus the correct ARIMA model requires identification of the right number of lags and the coefficients that should be used.
ARIMA model identification uses autoregressions to identify the underling model.
Care must be taken to robustly identify and estimate parameters as outliers (pulses, level shifts , local time trends ) can wreak havoc.
 

Book: Alan Pankratz - Forecasting with Univariate Box Jenkins Models : Concepts and Cases -

Book: Jeffrey Wooldridge - Introductory Econometrics: A Modern Approach -


ARIMA Forum
  What is Moving Average?
What is the moving average and how can we calculate this?...
     
 
  ARIMA model or Time Fourier series
The ARIMA model is a useful model, but not precise enough.
An interesting application for phenomenons estimated as cyclic, is the Time Fourier series.
Particularly for short-time projecting, I think it very useful (But , I repeat, only for ...
     
 
  Updating the ARIMA model
I think even if we develop the best ARIMA model there will surely be some amount of error. If we develop a nonlinear or regression model (with influencing parameters) for the error and add it to the ARIMA, it will considerably reduce error....
     
 

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