Box-Jenkins

Box-Jenkins

In econometrics, the Box-Jenkins methodology, named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average ARMA or ARIMA models to find the best fit of a time series to past values of this time series, in order to make forecasts.

Modeling approach

The original model uses an iterative three-stage modeling approach:

#"Model identification and model selection": making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation and partial autocorrelation functions of the dependent time series to decide which (if any) autoregressive or moving average component should be used in the model.
#"Parameter estimation" using econometric computation algorithms to arrive at coefficients which best fit the selected ARIMA model. The most common methods use maximum likelihood estimation or non-linear least-squares estimation.
#"Model checking" by testing whether the estimated model conforms to the specifications of a stationary univariate process. In particular, the residuals should be independent from each other and constant in mean and variance over time. (Plotting the mean and variance of residuals over time and performing a Ljung-Box test or plotting autocorrelation and partial autocorrelation of the residuals are helpful to identify misspecification.) If the estimation is inadequate, we have to return to step one and attempt to build a better model.The data they used was from a gas furnace. This data is well-known as the Box and Jenkins gas furnace data for benchmarking predictive models.

References

* Box, George and Jenkins, Gwilym (1970) "Time series analysis: Forecasting and control", San Francisco: Holden-Day.
* Pankratz, Alan (1983) "Forecasting with univariate Box–Jenkins models: concepts and cases", New York: John Wiley & Sons.

External links

* [http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc445.htm Box-Jenkins models] in the Engineering Statistics Handbook of NIST


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