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  • #1777
Closed
Open
Created Feb 18, 2021 by Willi Mutschler@wmutschlDeveloper

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
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