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Business Forecasting;Using the United Kingdom statistics locates Banks consumer credit: Gross lending figures from 1993-2003
on two explanatory variables which are data lagged3 and data lagged12. So it can forecast third periods ahead because from its equation has to forecast following the lag3 data.
Finally, Box-Jenkins model or ARIMA model shows the form of an ARIMA(1,0,0) or AR(1) model which depends on the constant term and Zt-1 as well as factors.
The graph below illustrates the comparisons of actual data and three forecasting data which are generated from decomposition model, autocorrelation model and ARIMA model.
It is very difficult to say which model is better because most forecast data are relatively close to real data and some periods one is fitter to the actual data more than others but some periods do contrast. Therefore, we can not tell much different among them.
Next, we will focus on the most appropriate of these three models by considering the error.
Compare the errors of the data for model fit.
From the graph above, it can be seen that the autocorrelation model is more appropriate than other two because of more accuracy. Moreover, it involves only the lag data and does not have any influences from the factors like other two models. If you look at the actual data graph below, it shows a trend pattern but does not show a seasonal pattern. It is emphasised to use autocorrelation model. On the other hand, if the graph shows obviously seasonal pattern, decomposition model should be better. And because of using the trendcycle data to use for ARIMA forecasting, it involves seasonal effects (factors); so make ARIMA model not a proper method as well.
However, there has some lost data at the beginning and at the end by using autocorrelation model to forecast because its data is need to be lagged and it can not forecast a bit more future like Box-Jenkins or ARIMA model.
6. Comment on the impact of your choice of where to split the data in order to use some data to fit the model and other data to check it.
The data at the end (2002-2003) has been used to check the forecast. From the graph below, we can see that at the beginning and middle of the rest data, the forecast data from autocorrelation model and ARIMA model is close to data but other periods, significant errors will occur. However, there are considerable errors occurred.
Then, trying new data model, we choose data model from 1995-2003 and data in 1993-1994 is used for checking. The graph below shows errors from old data (split at the end) against errors from new data (split at the beginning)
The magnitudes of errors from two ways to split data all over the period are similar but they do not overlap at the same time so it does some impact on where to split the data. However, it should be consider the pattern of actual data and choose the appropriate method to forecast rather than think about where to split the data.