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Fourier Analysis of TMW (SPDR DJ Wilshire Total Market E)


TMW (SPDR DJ Wilshire Total Market E) appears to have interesting cyclic behaviour every 5 weeks (.7942*cosine), 5 weeks (.792*cosine), and 4 weeks (.7286*cosine).

TMW (SPDR DJ Wilshire Total Market E) has an average price of 11.94 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 10/19/2007 to 9/17/2012 for TMW (SPDR DJ Wilshire Total Market E), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
011.9425   0 
11.23205 .22842 (1*2π)/5252 weeks
21.08873 .40336 (2*2π)/5226 weeks
3.89646 .48828 (3*2π)/5217 weeks
4.70893 .47481 (4*2π)/5213 weeks
5.57468 .38443 (5*2π)/5210 weeks
6.5219 .26032 (6*2π)/529 weeks
7.55044 .1523 (7*2π)/527 weeks
8.63359 .10033 (8*2π)/527 weeks
9.72861 .12194 (9*2π)/526 weeks
10.79201 .20805 (10*2π)/525 weeks
11.79422 .32786 (11*2π)/525 weeks
12.72858 .4409 (12*2π)/524 weeks
13.61192 .51154 (13*2π)/524 weeks
14.47701 .52094 (14*2π)/524 weeks
15.35993 .47233 (15*2π)/523 weeks
16.28708 .38821 (16*2π)/523 weeks
17.26646 .30086 (17*2π)/523 weeks
18.28601 .23995 (18*2π)/523 weeks
19.31922 .22163 (19*2π)/523 weeks
20.33587 .24312 (20*2π)/523 weeks
21.31357 .28431 (21*2π)/522 weeks
22.24626 .31569 (22*2π)/522 weeks
23.14649 .30954 (23*2π)/522 weeks
24.04095 .25028 (24*2π)/522 weeks
25-.03906 .14044 (25*2π)/522 weeks
26-.06885   (26*2π)/522 weeks
27-.03906 -.14044 (27*2π)/522 weeks
28.04095 -.25028 (28*2π)/522 weeks
29.14649 -.30954 (29*2π)/522 weeks
30.24626 -.31569 (30*2π)/522 weeks
31.31357 -.28431 (31*2π)/522 weeks
32.33587 -.24312 (32*2π)/522 weeks
33.31922 -.22163 (33*2π)/522 weeks
34.28601 -.23995 (34*2π)/522 weeks
35.26646 -.30086 (35*2π)/521 weeks
36.28708 -.38821 (36*2π)/521 weeks
37.35993 -.47233 (37*2π)/521 weeks
38.47701 -.52094 (38*2π)/521 weeks
39.61192 -.51154 (39*2π)/521 weeks
40.72858 -.4409 (40*2π)/521 weeks
41.79422 -.32786 (41*2π)/521 weeks
42.79201 -.20805 (42*2π)/521 weeks
43.72861 -.12194 (43*2π)/521 weeks
44.63359 -.10033 (44*2π)/521 weeks
45.55044 -.1523 (45*2π)/521 weeks
46.5219 -.26032 (46*2π)/521 weeks
47.57468 -.38443 (47*2π)/521 weeks
48.70893 -.47481 (48*2π)/521 weeks
49.89646 -.48828 (49*2π)/521 weeks
501.08873 -.40336 (50*2π)/521 weeks

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