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Fourier Analysis of STP (SPDR MSCI Europe Materials UCIT)


STP (SPDR MSCI Europe Materials UCIT) appears to have interesting cyclic behaviour every 76 weeks (285.2129*sine), 82 weeks (262.5034*sine), and 89 weeks (181.2111*sine).

STP (SPDR MSCI Europe Materials UCIT) has an average price of 671.87 (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 8/8/1996 to 1/16/2017 for STP (SPDR MSCI Europe Materials UCIT), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0671.8671   0 
11,240.448 -442.0989 (1*2π)/10681,068 weeks
2966.3165 -783.6971 (2*2π)/1068534 weeks
3590.9261 -966.82 (3*2π)/1068356 weeks
4199.3955 -965.2031 (4*2π)/1068267 weeks
5-114.9578 -801.7949 (5*2π)/1068214 weeks
6-292.5847 -548.2744 (6*2π)/1068178 weeks
7-323.9656 -284.1402 (7*2π)/1068153 weeks
8-233.0018 -79.38644 (8*2π)/1068134 weeks
9-80.08513 18.73475 (9*2π)/1068119 weeks
1066.13649 11.81409 (10*2π)/1068107 weeks
11158.4615 -70.67058 (11*2π)/106897 weeks
12168.2572 -181.2111 (12*2π)/106889 weeks
13104.6365 -262.5034 (13*2π)/106882 weeks
148.21956 -285.2129 (14*2π)/106876 weeks
15-84.15357 -248.3241 (15*2π)/106871 weeks
16-138.4244 -163.4879 (16*2π)/106867 weeks
17-131.5734 -68.17713 (17*2π)/106863 weeks
18-77.90514 -2.19243 (18*2π)/106859 weeks
19-4.83766 20.26126 (19*2π)/106856 weeks
2061.77379 -3.829 (20*2π)/106853 weeks
2193.49197 -60.49846 (21*2π)/106851 weeks
2281.16273 -118.1106 (22*2π)/106849 weeks
2337.50515 -152.9719 (23*2π)/106846 weeks
24-18.6329 -152.2492 (24*2π)/106845 weeks
25-60.66867 -115.7228 (25*2π)/106843 weeks
26-70.5994 -63.82484 (26*2π)/106841 weeks
27-49.47119 -17.51524 (27*2π)/106840 weeks
28-4.34864 6.71921 (28*2π)/106838 weeks
2944.81435 -4.34831 (29*2π)/106837 weeks
3072.97845 -42.26891 (30*2π)/106836 weeks
3172.55157 -87.16758 (31*2π)/106834 weeks
3245.06771 -124.0643 (32*2π)/106833 weeks
33-1.27216 -136.2089 (33*2π)/106832 weeks
34-44.33128 -116.9761 (34*2π)/106831 weeks
35-66.9567 -77.99264 (35*2π)/106831 weeks
36-63.14746 -34.04987 (36*2π)/106830 weeks
37-34.12247 -2.43362 (37*2π)/106829 weeks
385.5643 3.65585 (38*2π)/106828 weeks
3938.57555 -14.56399 (39*2π)/106827 weeks
4053.04983 -49.2593 (40*2π)/106827 weeks
4140.75693 -85.43703 (41*2π)/106826 weeks
428.40193 -104.2773 (42*2π)/106825 weeks
43-27.96567 -100.1168 (43*2π)/106825 weeks
44-56.39041 -74.87936 (44*2π)/106824 weeks
45-63.62505 -35.78944 (45*2π)/106824 weeks
46-45.15365 -1.41197 (46*2π)/106823 weeks
47-11.6484 14.81665 (47*2π)/106823 weeks
4825.23199 8.98434 (48*2π)/106822 weeks
4951.3595 -19.06318 (49*2π)/106822 weeks
5053.89533 -56.42889 (50*2π)/106821 weeks
5135.17521 -87.08578 (51*2π)/106821 weeks
521.92885 -102.7126 (52*2π)/106821 weeks
53-35.36177 -95.11314 (53*2π)/106820 weeks
54-59.08154 -67.6058 (54*2π)/106820 weeks
55-63.27055 -35.0439 (55*2π)/106819 weeks
56-50.43766 -6.21109 (56*2π)/106819 weeks
57-23.28385 8.76077 (57*2π)/106819 weeks
583.6575 2.86778 (58*2π)/106818 weeks
5918.27034 -14.7989 (59*2π)/106818 weeks
6019.78115 -36.08479 (60*2π)/106818 weeks
615.77093 -53.31662 (61*2π)/106818 weeks
62-15.9954 -54.17748 (62*2π)/106817 weeks
63-30.75274 -41.37653 (63*2π)/106817 weeks
64-36.11763 -22.94683 (64*2π)/106817 weeks
65-28.32647 -1.93279 (65*2π)/106816 weeks
66-6.19784 8.22179 (66*2π)/106816 weeks
6714.97718 1.05207 (67*2π)/106816 weeks
6827.53774 -14.70753 (68*2π)/106816 weeks
6930.18644 -36.71236 (69*2π)/106815 weeks
7016.03226 -56.96041 (70*2π)/106815 weeks
71-7.25352 -61.67229 (71*2π)/106815 weeks
72-26.87148 -52.98652 (72*2π)/106815 weeks
73-39.66256 -34.48214 (73*2π)/106815 weeks
74-37.34342 -9.93109 (74*2π)/106814 weeks
75-19.70582 5.64553 (75*2π)/106814 weeks
761.00007 7.89786 (76*2π)/106814 weeks
7721.02626 -1.10973 (77*2π)/106814 weeks
7831.75885 -23.89413 (78*2π)/106814 weeks
7923.06367 -47.37417 (79*2π)/106814 weeks
804.62409 -58.86848 (80*2π)/106813 weeks
81-16.81132 -60.96461 (81*2π)/106813 weeks
82-39.18433 -48.74271 (82*2π)/106813 weeks
83-47.57014 -23.46642 (83*2π)/106813 weeks
84-39.27526 -1.77545 (84*2π)/106813 weeks
85-23.55971 11.67259 (85*2π)/106813 weeks
86-1.81536 15.09805 (86*2π)/106812 weeks
8716.79776 3.1736 (87*2π)/106812 weeks
8822.21459 -15.10894 (88*2π)/106812 weeks
8917.49345 -31.36676 (89*2π)/106812 weeks
903.20405 -42.24471 (90*2π)/106812 weeks
91-14.77677 -39.30648 (91*2π)/106812 weeks
92-23.81334 -26.62049 (92*2π)/106812 weeks
93-24.86627 -13.30089 (93*2π)/106811 weeks
94-17.87835 .7134 (94*2π)/106811 weeks
95-.39665 6.1007 (95*2π)/106811 weeks
9614.17596 -3.19178 (96*2π)/106811 weeks
9718.64158 -16.45076 (97*2π)/106811 weeks
9816.98329 -30.16335 (98*2π)/106811 weeks
995.37279 -42.3451 (99*2π)/106811 weeks
100-12.51364 -42.52309 (100*2π)/106811 weeks
101-24.7933 -31.85882 (101*2π)/106811 weeks
102-29.11659 -17.1012 (102*2π)/106810 weeks
103-23.70357 -1.56522 (103*2π)/106810 weeks
104-9.36074 6.60134 (104*2π)/106810 weeks
1055.62671 4.61382 (105*2π)/106810 weeks
10617.42098 -5.08454 (106*2π)/106810 weeks
10720.86016 -21.78518 (107*2π)/106810 weeks
10811.34457 -35.9558 (108*2π)/106810 weeks
109-2.7619 -39.81112 (109*2π)/106810 weeks
110-15.76255 -36.76743 (110*2π)/106810 weeks
111-26.53397 -25.76519 (111*2π)/106810 weeks
112-26.68913 -8.81311 (112*2π)/106810 weeks
113-15.62937 2.5606 (113*2π)/10689 weeks
114-1.7948 4.76257 (114*2π)/10689 weeks
11511.11052 -.90067 (115*2π)/10689 weeks
11618.15428 -14.13649 (116*2π)/10689 weeks
11715.19972 -28.82214 (117*2π)/10689 weeks
1184.14675 -39.01978 (118*2π)/10689 weeks
119-11.71129 -40.4757 (119*2π)/10689 weeks
120-24.53682 -31.1325 (120*2π)/10689 weeks
121-28.39512 -17.63678 (121*2π)/10689 weeks
122-25.44466 -4.9453 (122*2π)/10689 weeks
123-14.92937 5.00434 (123*2π)/10689 weeks
124.36374 4.66367 (124*2π)/10689 weeks
1259.59541 -5.44134 (125*2π)/10689 weeks
12610.63533 -16.96043 (126*2π)/10688 weeks
1275.20206 -27.59948 (127*2π)/10688 weeks
128-7.42199 -32.67505 (128*2π)/10688 weeks
129-20.39934 -27.45141 (129*2π)/10688 weeks
130-27.42115 -15.69651 (130*2π)/10688 weeks
131-26.5823 -.92207 (131*2π)/10688 weeks
132-15.65135 10.88367 (132*2π)/10688 weeks
133-.49481 12.90343 (133*2π)/10688 weeks
13412.46673 7.55371 (134*2π)/10688 weeks
13522.25058 -4.59654 (135*2π)/10688 weeks
13621.68146 -22.01889 (136*2π)/10688 weeks
13710.22685 -33.0756 (137*2π)/10688 weeks
138-2.20607 -35.44054 (138*2π)/10688 weeks
139-14.56712 -32.57959 (139*2π)/10688 weeks
140-23.60236 -21.10665 (140*2π)/10688 weeks
141-21.33093 -7.42846 (141*2π)/10688 weeks
142-12.98149 -.47654 (142*2π)/10688 weeks
143-3.30524 1.61511 (143*2π)/10687 weeks
1446.9542 -3.56636 (144*2π)/10687 weeks
1459.50565 -14.8908 (145*2π)/10687 weeks
1464.46786 -22.99297 (146*2π)/10687 weeks
147-3.10705 -27.61842 (147*2π)/10687 weeks
148-14.5256 -26.70719 (148*2π)/10687 weeks
149-21.89895 -16.15576 (149*2π)/10687 weeks
150-19.44348 -5.4082 (150*2π)/10687 weeks
151-13.71443 1.49121 (151*2π)/10687 weeks
152-3.36197 6.23183 (152*2π)/10687 weeks
1539.60369 1.00334 (153*2π)/10687 weeks
15413.86383 -11.23685 (154*2π)/10687 weeks
15511.48876 -21.25054 (155*2π)/10687 weeks
1564.84687 -30.64061 (156*2π)/10687 weeks
157-8.88245 -33.99244 (157*2π)/10687 weeks
158-19.9699 -26.68901 (158*2π)/10687 weeks
159-23.91782 -17.3383 (159*2π)/10687 weeks
160-24.3338 -6.9189 (160*2π)/10687 weeks
161-16.4714 2.86576 (161*2π)/10687 weeks
162-4.81494 2.69507 (162*2π)/10687 weeks
1631.09646 -3.10305 (163*2π)/10687 weeks
1644.15609 -9.8193 (164*2π)/10687 weeks
1651.65418 -19.58216 (165*2π)/10686 weeks
166-9.03681 -23.74932 (166*2π)/10686 weeks
167-17.97446 -19.13395 (167*2π)/10686 weeks
168-23.16522 -12.00519 (168*2π)/10686 weeks
169-24.79765 -.81322 (169*2π)/10686 weeks
170-17.05541 9.84489 (170*2π)/10686 weeks
171-5.71995 12.13778 (171*2π)/10686 weeks
1723.72327 9.91683 (172*2π)/10686 weeks
17312.5328 2.58837 (173*2π)/10686 weeks
17413.59958 -9.90377 (174*2π)/10686 weeks
1756.64813 -17.34752 (175*2π)/10686 weeks
176-.11678 -19.43125 (176*2π)/10686 weeks
177-7.99492 -18.78077 (177*2π)/10686 weeks
178-13.90636 -11.05646 (178*2π)/10686 weeks
179-10.98586 -2.21858 (179*2π)/10686 weeks
180-4.4746 1.01254 (180*2π)/10686 weeks
1812.34425 1.03767 (181*2π)/10686 weeks
1829.29347 -4.04104 (182*2π)/10686 weeks
18310.44603 -13.28203 (183*2π)/10686 weeks
1845.87934 -20.34644 (184*2π)/10686 weeks
185-1.63083 -24.29914 (185*2π)/10686 weeks
186-11.37723 -22.51985 (186*2π)/10686 weeks
187-16.82347 -14.22945 (187*2π)/10686 weeks
188-15.95609 -6.12576 (188*2π)/10686 weeks
189-12.11385 .57756 (189*2π)/10686 weeks
190-3.32656 4.77862 (190*2π)/10686 weeks
1916.58956 .67558 (191*2π)/10686 weeks
19210.05281 -8.12165 (192*2π)/10686 weeks
1938.64113 -15.89305 (193*2π)/10686 weeks
1943.42967 -22.63065 (194*2π)/10686 weeks
195-5.90889 -24.82761 (195*2π)/10685 weeks
196-14.23786 -20.37847 (196*2π)/10685 weeks
197-18.05877 -12.21679 (197*2π)/10685 weeks
198-16.04367 -3.35798 (198*2π)/10685 weeks
199-9.05332 1.62552 (199*2π)/10685 weeks
200-1.72369 1.59504 (200*2π)/10685 weeks
2014.90906 -1.77592 (201*2π)/10685 weeks
2028.65006 -10.01788 (202*2π)/10685 weeks
2034.60308 -18.56953 (203*2π)/10685 weeks
204-2.78424 -20.88586 (204*2π)/10685 weeks
205-8.57835 -19.71743 (205*2π)/10685 weeks
206-14.0068 -15.71051 (206*2π)/10685 weeks
207-15.17498 -7.82239 (207*2π)/10685 weeks
208-10.0756 -2.08385 (208*2π)/10685 weeks
209-3.29699 -1.34722 (209*2π)/10685 weeks
2102.81253 -5.01072 (210*2π)/10685 weeks
2114.91045 -12.67702 (211*2π)/10685 weeks
2121.35236 -19.58358 (212*2π)/10685 weeks
213-5.00306 -23.91061 (213*2π)/10685 weeks
214-14.94859 -24.67359 (214*2π)/10685 weeks
215-24.26577 -16.90979 (215*2π)/10685 weeks
216-25.1446 -5.73533 (216*2π)/10685 weeks
217-21.65853 2.0685 (217*2π)/10685 weeks
218-15.55799 9.48221 (218*2π)/10685 weeks
219-3.56081 11.94171 (219*2π)/10685 weeks
2205.83705 4.92746 (220*2π)/10685 weeks
2217.91823 -3.46192 (221*2π)/10685 weeks
2227.03581 -10.88605 (222*2π)/10685 weeks
2231.18185 -17.44135 (223*2π)/10685 weeks
224-7.42425 -17.36534 (224*2π)/10685 weeks
225-12.49943 -12.73748 (225*2π)/10685 weeks
226-14.74537 -6.42404 (226*2π)/10685 weeks
227-11.49637 1.21331 (227*2π)/10685 weeks
228-3.32448 3.05105 (228*2π)/10685 weeks
2291.81983 -.2572 (229*2π)/10685 weeks
2305.69947 -3.96648 (230*2π)/10685 weeks
2317.66697 -12.32101 (231*2π)/10685 weeks
232.75901 -19.91394 (232*2π)/10685 weeks
233-7.52561 -18.88823 (233*2π)/10685 weeks
234-11.75796 -16.00214 (234*2π)/10685 weeks
235-16.55524 -11.35435 (235*2π)/10685 weeks
236-16.19234 -2.18838 (236*2π)/10685 weeks
237-8.86978 2.47205 (237*2π)/10685 weeks
238-2.66053 1.56195 (238*2π)/10684 weeks
2392.86087 -1.37158 (239*2π)/10684 weeks
2405.80526 -9.02172 (240*2π)/10684 weeks
2411.72054 -16.09994 (241*2π)/10684 weeks
242-4.10992 -18.60165 (242*2π)/10684 weeks
243-11.0117 -19.23913 (243*2π)/10684 weeks
244-18.63102 -13.76087 (244*2π)/10684 weeks
245-18.93444 -4.43508 (245*2π)/10684 weeks
246-14.8061 .49861 (246*2π)/10684 weeks
247-10.70583 4.25383 (247*2π)/10684 weeks
248-2.54126 5.49736 (248*2π)/10684 weeks
2493.61959 -.93196 (249*2π)/10684 weeks
2502.65508 -7.42831 (250*2π)/10684 weeks
251.48606 -11.06033 (251*2π)/10684 weeks
252-3.93023 -14.52827 (252*2π)/10684 weeks
253-10.5065 -12.83117 (253*2π)/10684 weeks
254-12.45745 -7.41065 (254*2π)/10684 weeks
255-11.36491 -3.55544 (255*2π)/10684 weeks
256-8.43702 .06999 (256*2π)/10684 weeks
257-2.3376 .13708 (257*2π)/10684 weeks
258.93828 -4.88149 (258*2π)/10684 weeks
259.18166 -9.4434 (259*2π)/10684 weeks
260-2.15274 -13.83564 (260*2π)/10684 weeks
261-8.87124 -16.7251 (261*2π)/10684 weeks
262-16.31587 -13.04071 (262*2π)/10684 weeks
263-19.12377 -6.34091 (263*2π)/10684 weeks
264-19.15959 .52945 (264*2π)/10684 weeks
265-14.98939 7.93251 (265*2π)/10684 weeks
266-6.40041 10.90598 (266*2π)/10684 weeks
2671.10125 8.4735 (267*2π)/10684 weeks
2686.33487 3.47441 (268*2π)/10684 weeks
2698.1976 -4.21738 (269*2π)/10684 weeks
2704.43402 -10.87662 (270*2π)/10684 weeks
271-1.28431 -13.07586 (271*2π)/10684 weeks
272-6.5932 -12.42761 (272*2π)/10684 weeks
273-10.93449 -8.43146 (273*2π)/10684 weeks
274-10.9707 -2.40859 (274*2π)/10684 weeks
275-7.28427 1.36357 (275*2π)/10684 weeks
276-2.62556 2.29994 (276*2π)/10684 weeks
2771.96508 .2359 (277*2π)/10684 weeks
2783.96293 -4.3356 (278*2π)/10684 weeks
2792.95175 -8.55642 (279*2π)/10684 weeks
280-.00653 -11.66872 (280*2π)/10684 weeks
281-4.76843 -11.99221 (281*2π)/10684 weeks
282-7.58816 -8.57894 (282*2π)/10684 weeks
283-6.92442 -5.48168 (283*2π)/10684 weeks
284-5.39105 -3.60615 (284*2π)/10684 weeks
285-2.0416 -2.55678 (285*2π)/10684 weeks
2861.77471 -5.4871 (286*2π)/10684 weeks
2871.66267 -10.60958 (287*2π)/10684 weeks
288-1.39818 -14.26739 (288*2π)/10684 weeks
289-6.40386 -16.25375 (289*2π)/10684 weeks
290-12.61267 -14.40298 (290*2π)/10684 weeks
291-16.20315 -9.0279 (291*2π)/10684 weeks
292-16.82345 -2.78761 (292*2π)/10684 weeks
293-13.6329 4.17502 (293*2π)/10684 weeks
294-5.44235 7.29152 (294*2π)/10684 weeks
2951.51702 4.06189 (295*2π)/10684 weeks
2965.21248 -.47116 (296*2π)/10684 weeks
2977.84577 -7.27287 (297*2π)/10684 weeks
2984.17576 -16.1008 (298*2π)/10684 weeks
299-4.66712 -18.7934 (299*2π)/10684 weeks
300-11.04025 -16.3363 (300*2π)/10684 weeks
301-16.17144 -12.5276 (301*2π)/10684 weeks
302-18.98932 -4.78964 (302*2π)/10684 weeks
303-15.29962 2.71828 (303*2π)/10684 weeks
304-9.1987 5.63086 (304*2π)/10684 weeks
305-2.83491 5.62423 (305*2π)/10684 weeks
3062.6908 1.12748 (306*2π)/10683 weeks
3072.86676 -5.17552 (307*2π)/10683 weeks
308.60379 -8.69229 (308*2π)/10683 weeks
309-2.66465 -12.04542 (309*2π)/10683 weeks
310-9.49156 -11.85475 (310*2π)/10683 weeks
311-12.52736 -5.56103 (311*2π)/10683 weeks
312-9.95008 -1.79025 (312*2π)/10683 weeks
313-8.74122 -.22598 (313*2π)/10683 weeks
314-5.28686 2.74783 (314*2π)/10683 weeks
315.60217 .34128 (315*2π)/10683 weeks
316.72317 -5.34816 (316*2π)/10683 weeks
317-1.97711 -7.4498 (317*2π)/10683 weeks
318-4.33609 -8.77608 (318*2π)/10683 weeks
319-8.72872 -8.04675 (319*2π)/10683 weeks
320-10.82179 -3.29352 (320*2π)/10683 weeks
321-9.24753 .96994 (321*2π)/10683 weeks
322-5.86091 4.64442 (322*2π)/10683 weeks
3231.19622 5.66431 (323*2π)/10683 weeks
3246.84675 .45836 (324*2π)/10683 weeks
3257.57427 -5.19553 (325*2π)/10683 weeks
3267.7644 -10.48511 (326*2π)/10683 weeks
3273.67758 -17.75709 (327*2π)/10683 weeks
328-5.65286 -19.17538 (328*2π)/10683 weeks
329-11.08433 -14.44279 (329*2π)/10683 weeks
330-13.2587 -10.51155 (330*2π)/10683 weeks
331-14.86711 -4.78528 (331*2π)/10683 weeks
332-10.88685 1.57274 (332*2π)/10683 weeks
333-4.14243 2.23058 (333*2π)/10683 weeks
334.13937 -.56584 (334*2π)/10683 weeks
3352.72098 -4.88443 (335*2π)/10683 weeks
3361.8441 -10.5213 (336*2π)/10683 weeks
337-2.26666 -13.79953 (337*2π)/10683 weeks
338-6.82273 -14.6808 (338*2π)/10683 weeks
339-12.12094 -12.96563 (339*2π)/10683 weeks
340-14.73126 -7.33729 (340*2π)/10683 weeks
341-12.52225 -2.95082 (341*2π)/10683 weeks
342-10.26877 -1.4897 (342*2π)/10683 weeks
343-7.67408 .03027 (343*2π)/10683 weeks
344-3.68374 -1.38721 (344*2π)/10683 weeks
345-3.3704 -5.64383 (345*2π)/10683 weeks
346-6.35372 -7.26589 (346*2π)/10683 weeks
347-8.63397 -6.56841 (347*2π)/10683 weeks
348-10.71257 -4.96777 (348*2π)/10683 weeks
349-11.69081 -1.2894 (349*2π)/10683 weeks
350-9.55733 2.75486 (350*2π)/10683 weeks
351-5.0215 4.85026 (351*2π)/10683 weeks
352.33348 3.7912 (352*2π)/10683 weeks
3534.0017 -.32529 (353*2π)/10683 weeks
3544.90658 -5.30229 (354*2π)/10683 weeks
3553.65414 -10.2721 (355*2π)/10683 weeks
356-.54107 -14.26983 (356*2π)/10683 weeks
357-6.27771 -14.58619 (357*2π)/10683 weeks
358-10.16756 -11.89173 (358*2π)/10683 weeks
359-11.89087 -8.44652 (359*2π)/10683 weeks
360-11.60329 -4.87874 (360*2π)/10683 weeks
361-9.36879 -2.63819 (361*2π)/10683 weeks
362-6.76526 -2.50529 (362*2π)/10683 weeks
363-4.96817 -4.17224 (363*2π)/10683 weeks
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