Box–Jenkins method: Difference between revisions

Revision as of 17:57, 14 September 2015

Revision as of 18:41, 21 December 2015

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Seasonality (or periodicity) can usually be assessed from an autocorrelation plot, a [[seasonal subseries plot]], or a [[spectral plot]].

====Differencing to achieve stationarity====

Box and Jenkins recommend the differencing approach to achieve stationarity. However, [[curve fitting|fitting a curve]] and subtracting the fitted values from the original data can also be used in the context of Box–Jenkins models.

====Seasonal differencing====

At the model identification stage, the goal is to detect seasonality, if it exists, and to identify the order for the seasonal autoregressive and seasonal moving average terms. For many series, the period is known and a single seasonality term is sufficient. For example, for monthly data one would typically include either a seasonalsl AR 12 term or a seasonal MA 12 term. For Box–Jenkins models, one does not explicitly remove seasonality before fitting the model. Instead, one includes the order of the seasonal terms in the model specification to the [[ARIMA]] estimation software. However, it may be helpful to apply a seasonal difference to the data and regenerate the autocorrelation and partial autocorrelation plots. This may help in the model identification of the non-seasonal component of the model. In some cases, the seasonal differencing may remove most or all of the seasonality effect.

===Identify ''p'' and ''q''===