Pruned theoretical moments: provide a more detailed decomposition of effects
I think we should provide a more detailed decomposition of theoretical unconditional moments at higher-order with pruning as there might be huge differences between e.g. the second and third order system's moments. So something similar to the output of the nlma toolbox:
THEORETICAL MEAN
VARIABLE MEAN(1st Order Accurate) MEAN(2nd and 3rd Order Accurate)
c 4.8675 29.9263
y 4.8675 29.9263
MEAN(2nd and 3rd Order Accurate) DECOMPOSITION IN LEVEL
VARIABLE Mean(2nd and 3rd Order Accurate) Det. Steady State Risk Adj. from Var. of Future Shock Risk Adj. from Var. of Past Shock
c 29.9263 4.8675 27.8139 -2.7551
y 29.9263 4.8675 27.8139 -2.7551
THEORETICAL STANDARD DEVIATION AND VARIANCE
VARIABLE STD.(1st Order Accurate) STD.(2nd Order Accurate) STD.(3rd Order Accurate) VAR.(1st Order Accurate) VAR.(2nd Order Accurate) VAR.(3rd Order Accurate)
c 14.8060 16.0911 53.0529 219.2180 258.9244 2814.6081
y 3.5188 6.8786 63.4057 12.3816 47.3149 4020.2871
THEORETICAL CORRELATIONS(1st Order Accurate)
Variables c y
c 1.0000 0.5852
y 0.5852 1.0000
THEORETICAL CORRELATIONS(2nd Order Accurate)
Variables c y
c 1.0000 0.5201
y 0.5201 1.0000
THEORETICAL CORRELATIONS(3rd Order Accurate)
Variables c y
c 1.0000 0.8925
y 0.8925 1.0000
THEORETICAL COEFFICIENTS OF AUTOCORRELATION(1st Order Accurate)
Order 1 2 3 4 5
c 0.9602 0.9222 0.8861 0.8518 0.8191
y 0.9960 0.9919 0.9877 0.9834 0.9791
THEORETICAL COEFFICIENTS OF AUTOCORRELATION(2nd Order Accurate)
Order 1 2 3 4 5
c 0.9651 0.9319 0.9001 0.8698 0.8408
y 0.9917 0.9833 0.9747 0.9660 0.9573
THEORETICAL COEFFICIENTS OF AUTOCORRELATION(3rd Order Accurate)
Order 1 2 3 4 5
c 0.9944 0.9891 0.9839 0.9789 0.9741
y 0.9979 0.9958 0.9934 0.9909 0.9882
VARIANCE (3rd Order Accurate) DECOMPOSITION IN PERCENTAGE
VARIABLE Total Risk Adj. Total Amp. Total Risk-Amp. Interplay
c 127.42 32.41 -59.83
y 127.42 12.82 -40.24
COMPLETE VARIANCE (3rd Order Accurate) DECOMPOSITION IN PERCENTAGE
VARIABLE Total Risk Adj. 1st Order Amp. 2nd Order Incre. Amp. 3rd Order Incre. Amp. 1st-3rd Order Incre. Amp. 3rd Order Incre. Risk-Amp. Interplay 1st-3rd Order Incre. Risk-Amp. Interplay
c 127.42 7.79 1.41 22.44 0.76 -30.31 -29.51
y 127.42 0.31 0.87 10.10 1.55 -28.00 -12.24