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Business Forecasting;Using the United Kingdom statistics locates Banks consumer credit: Gross lending figures from 1993-2003
some seasonal effects showing by the factors. And that means it can forecast more than one period ahead. Considering Autocorrelation model, it depends on the lag3 and lag12 data. It means it can forecast third periods ahead because from its equation has to forecast following the lag3 data.
4. Try a Box-Jenkins ARIMA approach on the same data and compare your forecasts with the rest of the data as before.
The trendcycle data from the question two will be used to analyse on the Box-Jenkins models as the seasonal effect was removed and the trendcycle data is shown at the chart below.
See the ACF and PACF of the trend-cycle data
From ACF, it shows a trend, so we will do the first difference to remove the trend
From Partial ACF, there is one strong spike on lag one and it dies away after one spike so if a model is fitted to the data, it should be an AR(1).
After first different, ACF does not die away so try the Partial ACF.
This PACF does not show any evidence of pattern repeat and does not die away so try the second difference.
The ACF and PACF of the second difference do not give anything helpful.
Therefore, AR(1) model is suggested by the Partial ACF of the trendcycle data. So we will try ARIMA(1,0,0) trendcycle data.
Model Description:
Variable: TRENCYC
Regressors: NONE
Non-seasonal differencing: 0
No seasonal component in model.
Parameters:
AR1 ________
CONSTANT ________
95.00 percent confidence intervals will be generated.
Split group number: 1 Series length: 96
No missing data.
Melard's algorithm will be used for estimation.
Termination criteria:
Parameter epsilon: .001
Maximum Marquardt constant: 1.00E+09
SSQ Percentage: .001
Maximum number of iterations: 10
Initial values:
AR1 .94136
CONSTANT 8089.403
Conclusion of estimation phase.
Estimation terminated at iteration number 3 because:
Sum of squares decreased by less than .001 percent.
FINAL PARAMETERS:
Number of residuals 96
Standard error 592.65186
Log likelihood -749.76257
AIC 1503.5251
SBC 1508.6538
Variables in the Model:
B SEB T-RATIO APPROX. PROB.
AR1 .98057 .01985 49.387288 .00000000
CONSTANT 8144.71650 2173.45330 3.747362