# SARIMA Process Forecasting Model

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This Demonstration applies the Wolfram Language's built-in function SARIMAProcess to construct a forecasting SARIMA (seasonal autoregressive integrated moving average) model based on Monte Carlo simulation.

Contributed by: Michail Bozoudis (August 2014)

Suggested by: Michail Boutsikas

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Suppose that you have identified a SARIMA process , after the analysis of historical data [1], [2]. You can adjust the sliders to the coefficients' specific values, integration orders (differencing), seasonal order, and white noise () variance; then, select the number of pseudorandom SARIMA paths and the number of future periods (*T*) to predict. The more SARIMA paths, the better the approximation, but this will require more computational effort.

You can choose among four display sets:

1st display set: The upper graph shows the simulation process as a bundle of SARIMA paths, from *t*=1 to *T*. The histogram shows the probability density function (PDF) for . Use the "seed" control to generate new pseudorandom SARIMA paths.

2nd display set: The 3-D plot and its 2-D epilogue illustrate the density of the SARIMA paths bundle.

3rd display set: Shows the expectation algorithm according to the selected SARIMA model.

4th display set: Calculates the expectation formula according to the selected coefficients' specific values, integration orders, and seasonal order.

References

[1] G. E. P. Box and G. M. Jenkins, "Time Series Analysis, Forecasting and Control", *Holden-Day*, 1970, San Francisco.

[2] P. Newbold, "The Principles of the Box-Jenkins Approach"*, Operational Research Quarterly*, 26(2), 1975 pp. 397–412.

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