
 60 PERIOD COMPARISON

====================================================================

 (WILDER FORMULA)

WILDER:   [ TOTWGT=0.707 @ BAR 73, TOTWGT=0.85 @ 113 ]
 BAR  WGT   TOTWGT
   1 .0167  .0167    0%
   6 .0153  .0959   10%
  15 .0132  .2228   25%    BAR 1-15 WGT SLOPE = 1.27
  30 .0102  .3960   50%    BAR 1-30 WGT SLOPE = 1.64
  45 .0080  .5306   75%    BAR 1-45 WGT SLOPE = 2.09
  60 .0062  .6352  100%    BAR 1-60 WGT SLOPE = 2.69

 120 .0032  .8669  x2
 180 .0008  .9515  x3
 240 .0003  .9823  x4  ***
 274 .0002  .9900  x4.57
 300 .0001  .9935  x5
-------------------------

 (WILDER, VERY CLOSE APPROX)

EMA_K*MULT @ MULT=0.5:   [ TOTWGT=0.707 @ BAR 74, TOTWGT=0.85 @ 115 ]
 BAR  WGT   TOTWGT
   1 .0164  .0164    0%
   6 .0151  .0944   10%
  15 .0130  .2196   25%    BAR 1-15 WGT SLOPE = 1.26
  30 .0102  .3910   50%    BAR 1-30 WGT SLOPE = 1.61
  45 .0079  .5247   75%    BAR 1-45 WGT SLOPE = 2.08
  60 .0062  .6291  100%    BAR 1-60 WGT SLOPE = 2.65

 120 .0023  .8624  x2
 180 .0008  .9498  x3
 240 .0003  .9811  x4  ***
 279 .0002  .9900  x4.65
-------------------------

 (SAME AS EMA FORMULA)

EMA_K*MULT @ MULT=1:    [ TOTWGT=0.707 @ BAR 37, TOTWGT=0.85 @ 57 ]
 BAR  WGT   TOTWGT
   1 .0328  .0328    0%
   6 .0278  .1813   10%
  15 .0206  .3935   25%    BAR 1-15 WGT SLOPE = 1.59
  20 .0174  .4866   33%.. 
  30 .0125  .6322   50%    BAR 1-30 WGT SLOPE = 2.62
  40 .0089  .7364   66%..
  45 .0076  .7769   75%    BAR 1-45 WGT SLOPE = 4.32
  60 .0046  .8647  100%    BAR 1-60 WGT SLOPE = 7.13

 120 .0006  .9817  x2  ***
 138 .0003  .9900  x2.3
 180 .0001  .9975  x3
-------------------------

 (DTI, CLOSE APPROX)

EMA_K*MULT @ MULT=1.55:   [ TOTWGT=0.707 @ BAR 24, TOTWGT=0.85 @ 36 ]
 BAR  WGT   TOTWGT
   1 .0508  .0508    0%
   6 .0392  .2687   10%
  15 .0245  .5427   25%    BAR 1-15 WGT SLOPE = 2.07
  30 .0112  .7908   50%    BAR 1-30 WGT SLOPE = 4.54
  45 .0051  .9043   75%    BAR 1-45 WGT SLOPE = 9.96   
  60 .0023  .9563  100%    BAR 1-60 WGT SLOPE = 22.1

  88 .0005  .9900  x1.47  ***
 120 .0001  .9981  x2
-------------------------------

 (DTI, CLOSE APPROX)

EMA_K*MULT @ MULT=1.5:   [ TOTWGT=0.707 @ BAR 24, TOTWGT=0.85 @ 38 ]
 BAR  WGT   TOTWGT       [ BARWGT=0.707 @ BAR   , BARWGT=0.85 @    ]
   1 .0492  .0492    0%
   6 .0382  .2611   10%
  15 .0243  .5307   25%    BAR 1-15 WGT SLOPE = 2.02
  30 .0114  .7797   50%    BAR 1-30 WGT SLOPE = 4.32
  45 .0053  .8966   75%    BAR 1-45 WGT SLOPE = 9.28   
  60 .0025  .9515  100%    BAR 1-60 WGT SLOPE = 19.7
-------------------------------

====================================================================

 (LINEAR WMA FORMULA)

WMA:                  [ TOTWGT=0.707 @ BAR 28, TOTWGT=0.85 @ 37 ]
 BAR  WGT   TOTWGT
   1 .0328   .0328    0%  
   6 .0301   .1885   10%
  15 .0251   .4344   25%    BAR 1-15 WGT SLOPE = 1.31
  20 .0224   .5519   33%.. 
  30 .0169   .7459   50%    BAR 1-30 WGT SLOPE = 1.94
  40 .0115   .8852   66%..
  45 .0087   .9344   75%    BAR 1-45 WGT SLOPE = 3.77
  60 .0001  1.000   100%    BAR 1-60 WGT SLOPE = 328
-------------------------

====================================================================

 (SMA, EXPONET WEIGHTED, SAME RESULTS AS SMA FORMULA)

EWMA:  KMUL = 0.00       [ TOTWGT=0.707 @ BAR 42, TOTWGT=0.85 @ 51 ]
 BAR  WGT   TOTWGT
   1 .0167   .0167    0%
   6 .0167   .1000   10%
  15 .0167   .2500   25%    BAR 1-15 WGT SLOPE = 1.00
  20 .0167   .3333   33%.. 
  30 .0167   .5000   50%    BAR 1-30 WGT SLOPE = 1.00
  40 .0167   .6666   66%..  
  45 .0167   .7500   75%    BAR 1-45 WGT SLOPE = 1.00
  60 .0167  1.000   100%    BAR 1-60 WGT SLOPE = 1.00
-------------------------

 (HALF OF WILDER, EXPONET WEIGHTED)

EWMA:  KMUL = 0.225       [ TOTWGT=0.707 @ BAR 40, TOTWGT=0.85 @ 49 ]
 BAR  WGT   TOTWGT
   1 .0206   .0206    0%
   6 .0198   .1211   10%
  15 .0185   .2931   25%    BAR 1-15 WGT SLOPE = 1.11
  20 .0179   .3837   33%.. 
  30 .0166   .555    50%    BAR 1-30 WGT SLOPE = 1.24
  40 .0154   .715    66%..
  45 .0148   .790    75%    BAR 1-45 WGT SLOPE = 1.39
  60 .0133  1.000   100%    BAR 1-60 WGT SLOPE = 1.55
-------------------------

 (HALF OF WILDER, EXPONET WEIGHTED)

EWMA:  KMUL = 0.25       [ TOTWGT=0.707 @ BAR 39, TOTWGT=0.85 @ 49 ]
 BAR  WGT   TOTWGT
   1 .0210   .0210    0%
   6 .0202   .1236   10%
  15 .0187   .2980   25%    BAR 1-15 WGT SLOPE = 1.12
  20 .0180   .3895   33%.. 
  30 .0166   .5614   50%    BAR 1-30 WGT SLOPE = 1.27
  40 .0153   .720    66%..
  45 .0146   .794    75%    BAR 1-45 WGT SLOPE = 1.44
  60 .0129  1.000   100%    BAR 1-60 WGT SLOPE = 1.63
-------------------------

 (WILDER APPROX IN BAR VS WGT SLOPE ONLY,  AND  APPROX AN "IBD_RS" STEP WMA, EXPONET WEIGHTED)

EWMA:  KMUL = 0.45
 BAR  WGT   TOTWGT
   1 .0250   .0250    0%
   6 .0232   .1446   10%
  15 .0203   .3387   25%    BAR 1-15 WGT SLOPE = 1.23
  20 .0189   .4358   33%.. 
  30 .0162   .6097   50%    BAR 1-30 WGT SLOPE = 1.54
  40 .0140   .7595   66%..
  45 .0130   .8265   75%    BAR 1-45 WGT SLOPE = 1.92
  60 .0104  1.000   100%    BAR 1-60 WGT SLOPE = 2.40
-------------------------

 (WILDER EXACT IN BAR VS WGT SLOPE, EXPONET WEIGHTED)

EWMA:  KMUL = 0.50     [ TOTWGT=0.707 @ BAR 36, TOTWGT=0.85 @ 46 ]
 BAR  WGT   TOTWGT
   1 .0261   .0261    0%
   6 .0240   .1501   10%
  15 .0207   .3491   25%    BAR 1-15 WGT SLOPE = 1.26
  20 .0190   .4475   33%.. 
  30 .0161   .6215   50%    BAR 1-30 WGT SLOPE = 1.62
  40 .0137   .7690   66%..
  45 .0126   .8341   75%    BAR 1-45 WGT SLOPE = 2.07
  60 .0098  1.000   100%    BAR 1-60 WGT SLOPE = 2.66
-------------------------
  
 (EMA, CLOSE APPROX @ 25%-50%  &  #1 BAR WGT, EXPONET WEIGHTED)

EWMA:  KMUL = 0.78
 BAR  WGT   TOTWGT
   1 .0324   .0324    0%  
   6 .0285   .1825   10%
  15 .0226   .4083   25%    BAR 1-15 WGT SLOPE = 1.43
  20 .0198   .5127   33%.. 
  30 .0153   .6851   50%    BAR 1-30 WGT SLOPE = 2.12
  40 .0118   .8181   66%..
  45 .0104   .8728   75%    BAR 1-45 WGT SLOPE = 3.12
  60 .0070  1.0000  100%    BAR 1-60 WGT SLOPE = 4.63
-------------------------

(EMA, VERY CLOSE APPROX IN BAR VS WGT SLOPE, EXPONET WEIGHTED)

EWMA:  KMUL = 1.00       [ TOTWGT=0.500 @ BAR 17,  TOTWGT=0.702 @ BAR 28,  TOTWGT=0.852 @ 40 ]
 BAR  WGT   TOTWGT       [ BARWGT=0.496 @ BAR 22,  BARWGT=0.694 @ BAR 12,  BARWGT=0.847 @  6 ]
  1  .0379   .0379    0%  
  6  .0321   .2097   10%
  15 .0238   .4313   25%    BAR 1-15 WGT SLOPE = 1.59
  20 .0201   .5628   33%.. 
  30 .0144   .7311   50%    BAR 1-30 WGT SLOPE = 2.63
  40 .0103   .8517   66%..
  45 .0087   .8985   75%    BAR 1-45 WGT SLOPE = 4.36
  60 .0053  1.000   100%    BAR 1-60 WGT SLOPE = 7.15
-------------------------

 (S&P DTI, EXPONET WEIGHTED, EXACTLY)  [ WITH 60=PERIOD,  NOT THE DTI 7=PERIOD WEIGHTING ]

EWMA:  KMUL = 1.5        [ TOTWGT=0.707 @ BAR 22, TOTWGT=0.85 @ 33 ]
 BAR  WGT   TOTWGT
   1 .0517   .0517    0%
   6 .0402   .2744   10%
  15 .0255   .5577   25%    BAR 1-15 WGT SLOPE =  2.03
  20 .0198   .6677   33%.. 
  30 .0120   .8195   50%    BAR 1-30 WGT SLOPE =  4.31
  40 .0072   .9112   66%..
  45 .0056   .9423   75%    BAR 1-45 WGT SLOPE =  9.23
  60 .0026  1.000   100%    BAR 1-60 WGT SLOPE = 19.88
-------------------------

==================================================================

 (IBD_RS WMA,  4 STEP WEIGHTED: 40%, 20%, 20%, 20%)

SWMA:                  [ TOTWGT=0.707 @ BAR 38, TOTWGT=0.85 @ 49 ] 
 BAR  WGT   TOTWGT
   1 .0267   .0267    0%
   6 .0267   .1600   10%
  15 .0267   .4000   25%    BAR 1-15 WGT SLOPE = 1.00
  20 .0133   .4667   33%.. 
  30 .0133   .6000   50%    BAR 1-30 WGT SLOPE = 2.01
  40 .0133   .7333   66%..
  45 .0133   .8000   75%    BAR 1-45 WGT SLOPE = 2.01
  60 .0133  1.000   100%    BAR 1-60 WGT SLOPE = 2.01
------------------------- 

 ( 3 STEP WMA,  3 STEP WEIGHTED: 50%, 33.33%, 16.67%)

SWMA:
 BAR  WGT   TOTWGT
  1  .02500   .0250    0%
  15 .02500   .3750   25%    BAR 1-15 WGT SLOPE = 1.00
  20 .02500   .5000   33%.. 
  30 .01666   .6666   50%    BAR 1-30 WGT SLOPE = 1.50
  40 .01666   .8332   66%..
  45 .00834   .8749   75%    BAR 1-60 WGT SLOPE = 3.00
  60 .00834  1.000   100%    BAR 1-60 WGT SLOPE = 3.00
-------------------------   

====================================================================

WILDER FORMULA & EWMA COMPARISON, FOR DIFFERENT PERIODS, WITH CONSTANT MULTIPLIER OF 0.5

=======================
 60 PERIOD COMPARISON
=======================

 (WILDER, EXACTLY, WILDER FORMULA)

WILDER:
 BAR  WGT   TOTWGT
   1 .0167  .0167    0%
   6 .0153  .0959   10%
  15 .0132  .2228   25%    BAR 1-15 WGT SLOPE = 1.27
  30 .0102  .3960   50%    BAR 1-30 WGT SLOPE = 1.64
  45 .0080  .5306   75%    BAR 1-45 WGT SLOPE = 2.09
  60 .0062  .6352  100%    BAR 1-60 WGT SLOPE = 2.69

 120 .0032  .8669  x2
 180 .0008  .9515  x3
 240 .0003  .9823  x4  ***
 274 .0002  .9900  x4.57
 300 .0001  .9935  x5
-------------------------

 (WILDER EXACT IN BAR VS WGT SLOPE, EXPONET WEIGHTED)

EWMA:  KMUL = 0.50
 BAR  WGT   TOTWGT
   1 .0261   .0261    0%
   6 .0240   .1501   10%
  15 .0207   .3491   25%    BAR 1-15 WGT SLOPE = 1.26
  20 .0190   .4475   33%.. 
  30 .0161   .6215   50%    BAR 1-30 WGT SLOPE = 1.62
  40 .0137   .7690   66%..
  45 .0126   .8341   75%    BAR 1-45 WGT SLOPE = 2.07
  60 .0098  1.000   100%    BAR 1-60 WGT SLOPE = 2.66
-------------------------
  
=======================
 200 PERIOD COMPARISON
=======================

 (WILDER, EXACTLY, WILDER FORMULA)

WILDER:
 BAR  WGT   TOTWGT
   1 .0050  .0050    0%
  20 .0045  .0999   10%
  50 .0039  .2217   25%    BAR 1-15 WGT SLOPE = 1.28
  66 .0036  .2817   33..  
 100 .0030  .3942   50%    BAR 1-30 WGT SLOPE = 1.67
 132 .0026  .4840   66..
 150 .0024  .5285   75%    BAR 1-45 WGT SLOPE = 2.08
 200 .0018  .6330  100%    BAR 1-60 WGT SLOPE = 2.78

-------------------------

 (WILDER EXACT IN BAR VS WGT SLOPE, EXPONET WEIGHTED MOVING AVERAGE)

EWMA:  KMUL = 0.50
 BAR  WGT   TOTWGT
   1 .0079   .0079    0%
  20 .0072   .1504   10%
  50 .0062   .3497   25%    BAR 1-15 WGT SLOPE = 1.27
  66 .0057   .4444   33%.. 
 100 .0048   .6222   50%    BAR 1-30 WGT SLOPE = 1.65
 132 .0041   .7641   66%..
 150 .0037   .8345   75%    BAR 1-45 WGT SLOPE = 2.14
 200 .0029  1.000   100%    BAR 1-60 WGT SLOPE = 2.72
-------------------------

 (SAME AS EMA FORMULA)

EMA_K*MULT @ MULT=1:
 BAR  WGT   TOTWGT
   1 .0100  .0100    0%
  20 .0082  .1813   10%
  50 .0061  .3935   25%    BAR 1-50 WGT SLOPE = 
  66 .0052  .4832   33%.. 
 100 .0037  .6321   50%    BAR 1-100 WGT SLOPE = 
 132 .0027  .7329   66%..
 150 .0022  .7769   75%    BAR 1-150 WGT SLOPE = 
 200 .0014  .8647  100%    BAR 1-200 WGT SLOPE = 

 230 .0010  .8997  x1.15 
 300 .0005  .9502  x1.5
 391 .0002  .9800  x2  ***
 461 .0001  .9900  x2.3
-------------------------

(EMA, VERY CLOSE APPROX IN BAR VS WGT SLOPE, EXPONET WEIGHTED)

EWMA:  KMUL = 1.00
 BAR  WGT   TOTWGT
  1  .0115   .0115    0%  
  20 .0095   .2096   10%
  50 .0070   .4551   25%    BAR 1-50 WGT SLOPE = 
  66 .0060   .5588   33%.. 
 100 .0043   .7311   50%    BAR 1-100 WGT SLOPE = 
 132 .0031   .8476   66%..
 150 .0026   .8985   75%    BAR 1-150 WGT SLOPE = 
 200 .0016  1.000   100%    BAR 1-200 WGT SLOPE = 
-------------------------


=======================
 20 PERIOD COMPARISON
=======================

 (WILDER, EXACTLY, WILDER FORMULA)

WILDER:
 BAR  WGT   TOTWGT
  1 .0500  .0500    0%
  2 .0475  .0975   10%
  5 .0407  .2262   25%    BAR 1-15 WGT SLOPE = 1.229
  7 .0368  .3017   33..  
 10 .0315  .4013   50%    BAR 1-30 WGT SLOPE = 1.587
 13 .0270  .4867   66..
 15 .0244  .5367   75%    BAR 1-45 WGT SLOPE = 2.049
 20 .0189  .6415  100%    BAR 1-60 WGT SLOPE = 2.646

-------------------------

 (WILDER APPROX IN BAR VS WGT SLOPE, EXPONET WEIGHTED)

EWMA:  KMUL = 0.50
 BAR  WGT   TOTWGT
  1 .0764   .0764    0%
  2 .0728   .1492   10%
  5 .0629   .3474   25%    BAR 1-15 WGT SLOPE = 1.215
  7 .0570   .4643   33%.. 
 10 .0493   .6196   50%    BAR 1-30 WGT SLOPE = 1.550
 13 .0426   .7538   66%..
 15 .0386   .8329   75%    BAR 1-45 WGT SLOPE = 1.979
 20 .0302  1.000   100%    BAR 1-60 WGT SLOPE = 2.530
----------------------------------
----------------------------------

  RiskMetricsTM, (PERIOD=509) a financial risk management company, tends to use a lambda of 0.94, or 94%

EWMA:  KMUL = 15.29   PERIOD = 509
 BAR  WGT   TOTWGT
  1 .0600   .0600    0%      [ 6.00 <- SHOULD BE ]
  2 .0564   .1163     %      [ 5.64     "        ]
  3 .0530   .1693     %      [ 5.30     "        ]
  4 .0498   .2191     %      [ 4.98     "        ]
 11 .0323   .4935     %    <- HALF TOTWGT
 12 .0304   .5238     %    <- HALF WGT OF BAR 1
 20 .0185   .7097     %
 22 .0164   .7434     %
 26 .0128   .7996     %
 31 .0094   .8529     %     
 37 .0065   .8985     %
 49 .0031   .9517     %    
 63 .0013   .9797    8% 
509 .0000  1.000   100%    
-------------------------

------------------------------------------------------------------
------------------------------------------------------------------

$SPX:
 EXPONET WMA,    EMA M=1.50, 50 200 CROSS  ON  MAY 14 2009
 EXPONET WMA,    EMA M=1.33, 50 200 CROSS  ON  MAY 18 2009
 LINEAR  WMA     ----------, 50 200 CROSS  ON  MAY 18 2009    DAY 70 FROM MARCH 2009 LOW
 EXPONET WMA,    EMA M=1.00, 50 200 CROSS  ON  MAY 29 2009    50=880.55  200=878.70 ;  EMA= 868.9 & 943.9
 EXPONET WMA, WILDER M=0.50, 50 200 CROSS  ON JUNE 10 2009
 EXPONET WMA,    SMA M=0.00, 50 200 CROSS  ON JUNE 23 2009
 SMA,            ----------, 50 200 CROSS  ON JUNE 23 2009    JULY 25 = $NYSI
 EMA,  1.5 MONTH ----------, 50 200 CROSS  ON  AUG 11 2009    ONLY 86% WITHIN PERIOD,  95% WITHIN 1.5 * PERIOD

 --------------- WEEKLY ------------- WEEKLY ----------------------
$SPX:
 EXPONET WMA,    EMA M=1.0, 10 40 CROSS  ON  MAY 18 2009     WEEKLY
 EMA,            ---------, 10 40 CROSS  ON  AUG  3 2009     WEEKLY  

 --------------- WEEKLY ------------- WEEKLY ----------------------
SPX:
 DOW THEORY  . . . . . . . . . . . . . . . . . .  ON 23 JULY 2009
 MACD(7,15,15)  MACD LINE ABOVE OR BELOW ZERO+1.0%,  01  MAY 2009 BUY,  WEEKLY  INTERMED
 MACD(12,26,9)  MACD LINE ABOVE OR BELOW ZERO,       22 JUNE 2009 BUY,  WEEKLY  LONG  OR  13 JUL 2009
 MACD(13,34,9)  MACD LINE ABOVE OR BELOW ZERO,       01  AUG 2009 BUY,  WEEKLY  LONG

-----------------------------------------------------------------
