Box Jenkins Methodology
The BoxJenkins methodology used in analysis and forecasting
is widely regarded to be the most efficient forecasting technique, and
is used extensively  specially for univariate time series. The three
step strategy of identification, estimation and diagnostic checking,
requires the person in charge of producing forecasts to have experience
and knowledge.
In contrast to other techniques, BoxJenkins is a procedure
which uses a variable's past behavior to select the best forecasting model
from a general class of models. It assumes that any time series pattern
can be represented by one of three categories of models. These categories
include:
• Autoregressive
models: forecasts of a variable based on
linear function of its past values
• Moving Average
models: forecasts based on linear combination
of past errors
• AutoregressiveMoving
Average models: combination of the previous
two categories
Note that one of the key questions is how many past values (the focal
variable and/or its errors) should be included in the model.
There are essentially three stages to a BoxJenkins procedure:
1. Identifying the tentative model. Which of the three categories listed
above is identified as the appropriate category is determined by first
making the data stationary (usually by differencing the data) and then
analyzing the autocorrelations and partial autocorrelations of the stationary
data. Note that there are theoretical autocorrelation and partial autocorrelation
profiles for each of the possible models. Therefore, determining the appropriate
type of model for a specific situation is mainly a matter of matching
the observed correlations to the theoretical correlations.
2. Determining the parameters of the model. This is similar to estimating
the parameters in regression analysis.
3. Application of the model.
Advantages: BoxJenkins approaches to forecasting provide
some of the most accurate shortterm forecasts. Limitations: However, it requires a very large amount of data.
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