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Business Forecasting;Using the United Kingdom statistics locates Banks consumer credit: Gross lending figures from 1993-2003
103 14723 14384.38 325.60 12299.2205 15363.0462
Aug 104 13215 13700.5 -462.38 11516.1862 14580.012
Sep 105 12989 13587.12 -598.12 12055.2049 15119.0307
Oct 106 13494 13448.75 45.25 11916.8368 14980.6626
Nov 107 12942 13275.48 -333.48 11743.5704 14807.3962
Dec 108 13922 14003.47 -78.34 11932.9626 14996.7884
2003 Jan 109 13598 12646.74 1001.33 11780.4406 14844.2664
Feb 110 12272 11824.77 491.47 11462.3352 14526.161
Sum of squared errors = 5523929.19
Mean-squared error (MSE) = 394566.37
Root-mean-squared error (RMSE) = 628.15
This RMSE is about 4.76 % of the mean for the rest of data during the forecast period
However, overall the plot graph below (During 1994-2003) shows that the predict data relatively fits the real data.
5. Discuss the differences between the Box-Jenkins results and the other methods you have used. In particular comment on the different mathematical forms of the models selected.
Decomposition Model:
Forecast = Trend * Factors
= (3945.164 + 84.357 * Time) * Factors
Autocorrelation Model:
Forecast = 0.439 * (Data lagged3) + 0.651 * (Data lagged12)
ARIMA Model:
Forecast (Zt) = (8144.71650 + 0.98057 Z t-1) * Factors
First of all, decomposition model is a linear model which depends on the trendcycle, runs following time, and seasonal effects showing by the factors. So it can forecast more than one period ahead.
Second, autocorrelation model is based on [next page]