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

Abstract

Using a simple linear regression model for estimation could give misleading results about the relationship between Yt, and Xt, . Possible problems involve (1) feedback from the output series to the inputs, (2) omitted time-lagged input terms, (3) an auto correlated disturbance series and, (4) common autocorrelation patterns shared by Y and X that can produce spurious correlations. The primary 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 z1t=)C(1-w1 B)/((1-δ1 B) B^5 Z(t^((x) +(1-θ1 B)at significantly described the data. Forecasts 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.