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An application of Box–Jenkins transfer function analysis to consumption–income relationship in South Africa

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Abstract

Using a simple linear regression model for estimation could give misleading results

about the relationship between

Y,

and X,. Possible problems involve (1) feedback from

the output series to the inputs, (2) omitted time-lagged input terms, (3) an autocorrelated

disturbance series and, (4) common autocorrelation patterns shared by Y and X that

can produce spurious correlations. The pri~ary aim of this study was therefore to use

the Box-Jenkins Transfer Function analysis to fit a model that related petroleum

consumption to disposable income> The final Transfer Function Model

z = C(1-w, B) B' z <x> + (1-8 B)a significantly described the data. Forecasts

t (1-o,B) I I I

generated from this model show that petroleum consumption will hit a record of up to 4.8636 in 2014 if disposable income is augmented. There is 95% confidence that the

forecasted value of petroleum consumption will lie between 4.5276 and 5.1997 in 2014.

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