Box–Jenkins method: Difference between revisions

Revision as of 13:45, 17 April 2024

Latest revision as of 08:30, 10 February 2025

(3 intermediate revisions by 2 users not shown)

Line 5:

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

#''[[Model identification]] and [[model selection]]'': making sure that the variables are [[stationary process|stationary]], identifying [[seasonality]] in the dependent series (seasonally differencing it if necessary), and using plots of the [[autocorrelation|autocorrelation (ACF)]] and [[partial autocorrelation|partial autocorrelation (PACF)]] 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 computation algorithms to arrive at coefficients that best fit the selected ARIMA model. The most common methods use [[maximum likelihood estimation]] or [[non-linear least-squares estimation]].

#''[[Statistical model validation|Statistical model checking]]'' by testing whether the estimated model conforms to the specifications of a stationary univariate process. In particular, the residuals should be independent of 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.