### Ellipsis

June 23, 2009
– Comments (48)

"Inspired" by the paper by Wong on moving averages and stuff (see this post by tastylunch) I have a suggestion for an S&P 500 index "fit" for the recent few weeks:

f(t) = p(0) * exp (1/15 * t^(1/17)),

where t is numbering the trading days starting with t=0 for 03/09/09.

If you have excel or open office calc or any other spreadsheet application you can draw it. Maybe you can add the resulting figure in the comment section.

This function fits the graph of the closing prices of the S&P 500 index p(t) starting with 03/09/09 to some degree. If you have alternative fits please post them here.

Actually you can see that the fit does a decent job much easier when you "take the logarithm of both sides" and compare log(p(t)) - log(p(0)) to 1/15 * t^(1/17) or just draw the difference log(p(t)) - log(p(0)) - 1/15 * t^(1/17).

(log is exp^(-1), not some other logarithm.)

To make life easier for those who like to play around with the numbers and find a better fit (I spend about 10 seconds on choosing the parameters 15 and 0.37 so there should be a better fit even using "the same function" and I am pretty sure there are lots of other ideas for a "fit") here are the numbers I used: The time variable t is numbering the trading days (t=0 for 03/09/09, t=1 for 03/10/09, ...) and the S&P 500 index closing prices (from now on always starting with t=0 and ending with t=76 (06/22/09)) from here:

676.53

719.60

721.36

750.74

756.55

753.89

778.12

794.35

784.04

768.54

822.92

806.12

813.88

832.86

815.94

787.53

797.87

811.08

834.38

842.50

835.48

815.55

825.16

856.56

858.73

841.50

852.06

865.30

869.60

832.39

850.08

843.55

851.92

866.23

857.51

855.16

873.64

872.81

877.52

907.24

903.80

919.53

907.39

929.23

909.24

908.35

883.92

893.07

882.88

909.71

908.13

903.47

888.33

887.00

910.33

893.06

906.83

919.14

942.87

944.74

931.76

942.46

940.09

939.14

942.43

939.15

944.89

946.21

923.72

911.97

910.71

918.37

921.23

893.04.