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Business Forecasting;Using the United Kingdom statistics locates Banks consumer credit: Gross lending figures from 1993-2003
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The constant term is significant so we can fit an AR(1) to the data with the constant.
The following new variables are being created:
Name Label
FIT_1 Fit for TRENCYC from ARIMA, MOD_1 CON
ERR_1 Error for TRENCYC from ARIMA, MOD_1 CON
LCL_1 95% LCL for TRENCYC from ARIMA, MOD_1 CON
UCL_1 95% UCL for TRENCYC from ARIMA, MOD_1 CON
SEP_1 SE of fit for TRENCYC from ARIMA, MOD_1 CON
From the box of variables in the model above, T-ratio of the AR1 and constant are far away from 0 and bigger than 2 and also the all probabilities of which are significant.
So, the ARIMA Model will be:
Z t = 8144.71650 + 0.98057 Z t-1
Because of using the trendcycle data with ARIMA, the ARIMA forecast data need to be multiplied by factors in order to get the real forecasts and compare to the actual data:
Forecast = (8144.71650 + 0.98057 Z t-1) * factors
After multiplying the forecast data by factors and plotting the forecast data against the actual data, it can be seen that it is very close to the data all over the period of time so this ARIMA model fits to the actual data.
Then check this model by considering the residuals by plotting the error. So, the graph shows removing trend and it is stationary.
So, the graph shows removing trend and it is relatively stationary. Then check with ACF and PACF which do not suggest anything.
All figures of ARIMA forecasting are shown as following table.
Time Data Forecast Error LCL UCL
1994 Jan 1 4129 7737.48 -3798.40 755.31 15534.12
Feb 2 3980 4022.31 -46.50 3240.41 5599.83
Mar 3 4879 4446.90 432.10 3267.19 5626.61
Apr 4 4396 4843.61 -456.74 3762.75 [next page]