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# Fourier Analysis of PSI (POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO)

PSI (POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO) appears to have interesting cyclic behaviour every 46 weeks (6.7612*sine), 43 weeks (6.6586*sine), and 65 weeks (6.3136*cosine).

PSI (POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO) has an average price of 22.06 (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.

## Fourier Analysis

Using data from 6/23/2005 to 11/6/2017 for PSI (POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO POWERSHARES DYNAMIC SEMICONDUCTORS PORTFOLIO), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
022.0645   0
112.86311 -3.39627 (1*2π)/647647 weeks
27.0589 .70162 (2*2π)/647324 weeks
33.3775 3.43318 (3*2π)/647216 weeks
42.89317 2.46852 (4*2π)/647162 weeks
5.41846 3.20189 (5*2π)/647129 weeks
6-2.55731 3.1306 (6*2π)/647108 weeks
7-4.88173 2.55807 (7*2π)/64792 weeks
8-5.77649 .95427 (8*2π)/64781 weeks
9-5.78707 -.10499 (9*2π)/64772 weeks
10-6.3136 -2.75511 (10*2π)/64765 weeks
11-4.75734 -4.73711 (11*2π)/64759 weeks
12-3.6526 -6.09168 (12*2π)/64754 weeks
13-1.33208 -6.31012 (13*2π)/64750 weeks
14.0683 -6.7612 (14*2π)/64746 weeks
152.45383 -6.65864 (15*2π)/64743 weeks
164.08222 -5.26385 (16*2π)/64740 weeks
175.3945 -3.34023 (17*2π)/64738 weeks
186.0851 -1.38532 (18*2π)/64736 weeks
196.09182 .50213 (19*2π)/64734 weeks
205.38015 2.24744 (20*2π)/64732 weeks
214.08476 4.11344 (21*2π)/64731 weeks
222.05336 5.02271 (22*2π)/64729 weeks
23.18644 5.5258 (23*2π)/64728 weeks
24-1.81162 5.16488 (24*2π)/64727 weeks
25-3.51512 4.29171 (25*2π)/64726 weeks
26-4.86385 2.72563 (26*2π)/64725 weeks
27-5.78415 .84875 (27*2π)/64724 weeks
28-6.08846 -.85772 (28*2π)/64723 weeks
29-5.42427 -2.91728 (29*2π)/64722 weeks
30-4.14156 -4.48699 (30*2π)/64722 weeks
31-2.34649 -5.86276 (31*2π)/64721 weeks
32-.78197 -6.3973 (32*2π)/64720 weeks
331.23044 -6.31531 (33*2π)/64720 weeks
342.99783 -5.53891 (34*2π)/64719 weeks
354.59558 -4.10394 (35*2π)/64718 weeks
365.54882 -2.20461 (36*2π)/64718 weeks
375.90274 -.31002 (37*2π)/64717 weeks
385.60728 1.55958 (38*2π)/64717 weeks
394.67529 3.42125 (39*2π)/64717 weeks
402.91615 4.8253 (40*2π)/64716 weeks
411.1229 5.40377 (41*2π)/64716 weeks
42-.88283 5.63125 (42*2π)/64715 weeks
43-2.80028 4.96727 (43*2π)/64715 weeks
44-4.44622 3.79926 (44*2π)/64715 weeks
45-5.59093 2.17814 (45*2π)/64714 weeks
46-6.03592 .12079 (46*2π)/64714 weeks
47-5.77388 -1.81961 (47*2π)/64714 weeks
48-5.1385 -3.76344 (48*2π)/64713 weeks
49-3.59923 -5.03954 (49*2π)/64713 weeks
50-1.6987 -5.88636 (50*2π)/64713 weeks
51.41917 -6.22608 (51*2π)/64713 weeks
522.22358 -5.88107 (52*2π)/64712 weeks
533.91609 -4.70392 (53*2π)/64712 weeks
545.20261 -3.14979 (54*2π)/64712 weeks
555.97191 -1.23878 (55*2π)/64712 weeks
565.71115 .82652 (56*2π)/64712 weeks
575.02577 2.7794 (57*2π)/64711 weeks
583.80611 4.26731 (58*2π)/64711 weeks
592.1463 5.32195 (59*2π)/64711 weeks
60.14158 5.78076 (60*2π)/64711 weeks
61-1.8759 5.47872 (61*2π)/64711 weeks
62-3.73805 4.60097 (62*2π)/64710 weeks
63-5.16339 3.0613 (63*2π)/64710 weeks
64-5.95294 1.3023 (64*2π)/64710 weeks
65-6.09795 -.76496 (65*2π)/64710 weeks
66-5.39467 -2.64168 (66*2π)/64710 weeks
67-4.35746 -4.40828 (67*2π)/64710 weeks
68-2.73025 -5.52114 (68*2π)/64710 weeks
69-.74467 -6.07902 (69*2π)/6479 weeks
701.29996 -5.97833 (70*2π)/6479 weeks
713.09982 -5.22119 (71*2π)/6479 weeks
724.62728 -3.81935 (72*2π)/6479 weeks
735.52498 -2.00657 (73*2π)/6479 weeks
745.95101 -.02413 (74*2π)/6479 weeks
755.58137 1.99386 (75*2π)/6479 weeks
764.53764 3.78575 (76*2π)/6479 weeks
773.02854 5.03269 (77*2π)/6478 weeks
781.1579 5.63513 (78*2π)/6478 weeks
79-.95367 5.67715 (79*2π)/6478 weeks
80-2.82331 5.13227 (80*2π)/6478 weeks
81-4.5029 3.85936 (81*2π)/6478 weeks
82-5.54967 2.17733 (82*2π)/6478 weeks
83-6.08208 .18822 (83*2π)/6478 weeks
84-5.81575 -1.8605 (84*2π)/6478 weeks
85-4.90091 -3.6085 (85*2π)/6478 weeks
86-3.47992 -5.02374 (86*2π)/6478 weeks
87-1.71332 -5.98095 (87*2π)/6477 weeks
88.35525 -6.11434 (88*2π)/6477 weeks
892.2316 -5.61778 (89*2π)/6477 weeks
904.03769 -4.54361 (90*2π)/6477 weeks
915.16228 -2.93487 (91*2π)/6477 weeks
925.8385 -1.02118 (92*2π)/6477 weeks
935.73283 1.04991 (93*2π)/6477 weeks
945.07244 2.88155 (94*2π)/6477 weeks
953.76003 4.43702 (95*2π)/6477 weeks
962.05023 5.51854 (96*2π)/6477 weeks
97-.00799 5.84697 (97*2π)/6477 weeks
98-1.97881 5.56792 (98*2π)/6477 weeks
99-3.77003 4.57685 (99*2π)/6477 weeks
100-5.13232 3.16045 (100*2π)/6476 weeks
101-5.89941 1.26587 (101*2π)/6476 weeks
102-6.03752 -.81526 (102*2π)/6476 weeks
103-5.39948 -2.74477 (103*2π)/6476 weeks
104-4.32305 -4.37061 (104*2π)/6476 weeks
105-2.67674 -5.51972 (105*2π)/6476 weeks
106-.69702 -6.02784 (106*2π)/6476 weeks
1071.35325 -5.85358 (107*2π)/6476 weeks
1083.20255 -5.05026 (108*2π)/6476 weeks
1094.73952 -3.71799 (109*2π)/6476 weeks
1105.70503 -1.86548 (110*2π)/6476 weeks
1115.94557 .05579 (111*2π)/6476 weeks
1125.55558 2.03763 (112*2π)/6476 weeks
1134.52351 3.73362 (113*2π)/6476 weeks
1142.96562 5.06953 (114*2π)/6476 weeks
1151.06778 5.76422 (115*2π)/6476 weeks
116-1.02962 5.81573 (116*2π)/6476 weeks
117-2.96455 5.14948 (117*2π)/6476 weeks
118-4.46941 3.88763 (118*2π)/6475 weeks
119-5.56102 2.16266 (119*2π)/6475 weeks
120-6.04151 .17547 (120*2π)/6475 weeks
121-5.8092 -1.78419 (121*2π)/6475 weeks
122-4.90716 -3.59074 (122*2π)/6475 weeks
123-3.45705 -5.01206 (123*2π)/6475 weeks
124-1.68533 -5.88936 (124*2π)/6475 weeks
125.42734 -6.07645 (125*2π)/6475 weeks
1262.36422 -5.60482 (126*2π)/6475 weeks
1273.99892 -4.47486 (127*2π)/6475 weeks
1285.15614 -2.84605 (128*2π)/6475 weeks
1295.8523 -.88014 (129*2π)/6475 weeks
1305.82529 1.1686 (130*2π)/6475 weeks
1315.04665 2.97135 (131*2π)/6475 weeks
1323.72808 4.5263 (132*2π)/6475 weeks
1331.97596 5.54792 (133*2π)/6475 weeks
134.01292 5.94942 (134*2π)/6475 weeks
135-2.06739 5.59149 (135*2π)/6475 weeks
136-3.78068 4.60451 (136*2π)/6475 weeks
137-5.12254 3.12878 (137*2π)/6475 weeks
138-5.88889 1.21624 (138*2π)/6475 weeks
139-6.00167 -.82216 (139*2π)/6475 weeks
140-5.4523 -2.76842 (140*2π)/6475 weeks
141-4.24952 -4.38817 (141*2π)/6475 weeks
142-2.55004 -5.49062 (142*2π)/6475 weeks
143-.58834 -6.05347 (143*2π)/6475 weeks
1441.43623 -5.84976 (144*2π)/6474 weeks
1453.25967 -5.00029 (145*2π)/6474 weeks
1464.74359 -3.66529 (146*2π)/6474 weeks
1475.62536 -1.83256 (147*2π)/6474 weeks
1485.87916 .18253 (148*2π)/6474 weeks
1495.47988 2.1928 (149*2π)/6474 weeks
1504.47537 3.92733 (150*2π)/6474 weeks
1512.88582 5.14312 (151*2π)/6474 weeks
152.97368 5.81051 (152*2π)/6474 weeks
153-1.04719 5.82446 (153*2π)/6474 weeks
154-2.97027 5.12025 (154*2π)/6474 weeks
155-4.57191 3.87378 (155*2π)/6474 weeks
156-5.65028 2.14354 (156*2π)/6474 weeks
157-6.00753 .19224 (157*2π)/6474 weeks
158-5.72996 -1.80284 (158*2π)/6474 weeks
159-4.82884 -3.63266 (159*2π)/6474 weeks
160-3.43341 -5.04497 (160*2π)/6474 weeks
161-1.56061 -5.85914 (161*2π)/6474 weeks
162.44648 -5.9593 (162*2π)/6474 weeks
1632.42639 -5.51129 (163*2π)/6474 weeks
1644.08552 -4.36691 (164*2π)/6474 weeks
1655.28174 -2.7672 (165*2π)/6474 weeks
1665.84063 -.85556 (166*2π)/6474 weeks
1675.79042 1.15033 (167*2π)/6474 weeks
1684.96335 3.08553 (168*2π)/6474 weeks
1693.65682 4.59291 (169*2π)/6474 weeks
1701.91561 5.63326 (170*2π)/6474 weeks
171-.05904 5.93689 (171*2π)/6474 weeks
172-2.06288 5.59056 (172*2π)/6474 weeks
173-3.82334 4.58557 (173*2π)/6474 weeks
174-5.18848 3.10093 (174*2π)/6474 weeks
175-5.89697 1.20534 (175*2π)/6474 weeks
176-6.00326 -.84371 (176*2π)/6474 weeks
177-5.36065 -2.76466 (177*2π)/6474 weeks
178-4.18728 -4.40893 (178*2π)/6474 weeks
179-2.47567 -5.51625 (179*2π)/6474 weeks
180-.56315 -6.01309 (180*2π)/6474 weeks
1811.49963 -5.83649 (181*2π)/6474 weeks
1823.31015 -4.97874 (182*2π)/6474 weeks
1834.7666 -3.56089 (183*2π)/6474 weeks
1845.67497 -1.73834 (184*2π)/6474 weeks
1855.95979 .25347 (185*2π)/6473 weeks
1865.47137 2.19206 (186*2π)/6473 weeks
1874.4269 3.9219 (187*2π)/6473 weeks
1882.78581 5.2226 (188*2π)/6473 weeks
189.91379 5.86283 (189*2π)/6473 weeks
190-1.11198 5.85455 (190*2π)/6473 weeks
191-3.00283 5.11879 (191*2π)/6473 weeks
192-4.56566 3.83552 (192*2π)/6473 weeks
193-5.65738 2.13236 (193*2π)/6473 weeks
194-6.02811 .17004 (194*2π)/6473 weeks
195-5.78921 -1.8361 (195*2π)/6473 weeks
196-4.84508 -3.63003 (196*2π)/6473 weeks
197-3.39813 -5.04348 (197*2π)/6473 weeks
198-1.51208 -5.86396 (198*2π)/6473 weeks
199.50071 -5.98789 (199*2π)/6473 weeks
2002.45854 -5.4594 (200*2π)/6473 weeks
2014.14878 -4.33195 (201*2π)/6473 weeks
2025.31888 -2.69472 (202*2π)/6473 weeks
2035.88177 -.73892 (203*2π)/6473 weeks
2045.75223 1.29668 (204*2π)/6473 weeks
2054.96986 3.1561 (205*2π)/6473 weeks
2063.64735 4.65821 (206*2π)/6473 weeks
2071.8298 5.63324 (207*2π)/6473 weeks
208-.17506 5.94002 (208*2π)/6473 weeks
209-2.14568 5.59213 (209*2π)/6473 weeks
210-3.86151 4.58948 (210*2π)/6473 weeks
211-5.19948 3.05379 (211*2π)/6473 weeks
212-5.94478 1.16804 (212*2π)/6473 weeks
213-5.98204 -.86508 (213*2π)/6473 weeks
214-5.33152 -2.79205 (214*2π)/6473 weeks
215-4.13821 -4.40706 (215*2π)/6473 weeks
216-2.45499 -5.51174 (216*2π)/6473 weeks
217-.46838 -5.98397 (217*2π)/6473 weeks
2181.55434 -5.78613 (218*2π)/6473 weeks
2193.38608 -4.9121 (219*2π)/6473 weeks
2204.79428 -3.53703 (220*2π)/6473 weeks
2215.6905 -1.70463 (221*2π)/6473 weeks
2225.92346 .28758 (222*2π)/6473 weeks
2235.47098 2.26741 (223*2π)/6473 weeks
2244.37277 3.96031 (224*2π)/6473 weeks
2252.78195 5.21766 (225*2π)/6473 weeks
226.83681 5.84812 (226*2π)/6473 weeks
227-1.15951 5.84682 (227*2π)/6473 weeks
228-3.06387 5.10988 (228*2π)/6473 weeks
229-4.59991 3.86738 (229*2π)/6473 weeks
230-5.68242 2.08767 (230*2π)/6473 weeks
231-6.04264 .11911 (231*2π)/6473 weeks
232-5.74314 -1.86601 (232*2π)/6473 weeks
233-4.79693 -3.61424 (233*2π)/6473 weeks
234-3.29909 -5.02224 (234*2π)/6473 weeks
235-1.43672 -5.81823 (235*2π)/6473 weeks
236.56189 -5.99894 (236*2π)/6473 weeks
2372.53991 -5.39551 (237*2π)/6473 weeks
2384.18004 -4.28203 (238*2π)/6473 weeks
2395.3489 -2.58101 (239*2π)/6473 weeks
2405.88665 -.67262 (240*2π)/6473 weeks
2415.73663 1.37463 (241*2π)/6473 weeks
2424.96277 3.2101 (242*2π)/6473 weeks
2433.60937 4.69602 (243*2π)/6473 weeks
2441.79704 5.64402 (244*2π)/6473 weeks
245-.18894 5.94107 (245*2π)/6473 weeks
246-2.14998 5.54305 (246*2π)/6473 weeks
247-3.91174 4.53828 (247*2π)/6473 weeks
248-5.22271 2.964 (248*2π)/6473 weeks
249-5.9307 1.10011 (249*2π)/6473 weeks
250-5.96343 -.91299 (250*2π)/6473 weeks
251-5.32259 -2.82383 (251*2π)/6473 weeks
252-4.10611 -4.46948 (252*2π)/6473 weeks
253-2.39838 -5.54795 (253*2π)/6473 weeks
254-.43657 -5.98594 (254*2π)/6473 weeks
2551.55949 -5.75548 (255*2π)/6473 weeks
2563.41789 -4.90296 (256*2π)/6473 weeks
2574.85442 -3.45191 (257*2π)/6473 weeks
2585.65592 -1.64117 (258*2π)/6473 weeks
2595.88406 .39248 (259*2π)/6472 weeks
2605.39933 2.3758 (260*2π)/6472 weeks
2614.33019 4.04105 (261*2π)/6472 weeks
2622.70424 5.2731 (262*2π)/6472 weeks
263.79069 5.89685 (263*2π)/6472 weeks
264-1.23335 5.87715 (264*2π)/6472 weeks
265-3.13657 5.10889 (265*2π)/6472 weeks
266-4.6685 3.8157 (266*2π)/6472 weeks
267-5.66272 2.04538 (267*2π)/6472 weeks
268-6.03356 .05702 (268*2π)/6472 weeks
269-5.71627 -1.96218 (269*2π)/6472 weeks
270-4.76549 -3.72325 (270*2π)/6472 weeks
271-3.27791 -5.06212 (271*2π)/6472 weeks
272-1.4263 -5.80439 (272*2π)/6472 weeks
273.61137 -5.92463 (273*2π)/6472 weeks
2742.57619 -5.34077 (274*2π)/6472 weeks
2754.21858 -4.17911 (275*2π)/6472 weeks
2765.36271 -2.53062 (276*2π)/6472 weeks
2775.93147 -.564 (277*2π)/6472 weeks
2785.76469 1.44132 (278*2π)/6472 weeks
2794.94936 3.28073 (279*2π)/6472 weeks
2803.55381 4.75838 (280*2π)/6472 weeks
2811.79809 5.66463 (281*2π)/6472 weeks
282-.25553 5.96643 (282*2π)/6472 weeks
283-2.21707 5.54906 (283*2π)/6472 weeks
284-3.98561 4.51894 (284*2π)/6472 weeks
285-5.24038 2.98085 (285*2π)/6472 weeks
286-5.93054 1.05475 (286*2π)/6472 weeks
287-5.95499 -.96805 (287*2π)/6472 weeks
288-5.3159 -2.88968 (288*2π)/6472 weeks
289-4.04228 -4.46711 (289*2π)/6472 weeks
290-2.32958 -5.52792 (290*2π)/6472 weeks
291-.33383 -6.00051 (291*2π)/6472 weeks
2921.64818 -5.76453 (292*2π)/6472 weeks
2933.45282 -4.85096 (293*2π)/6472 weeks
2944.87964 -3.39331 (294*2π)/6472 weeks
2955.71407 -1.58511 (295*2π)/6472 weeks
2965.88927 .47763 (296*2π)/6472 weeks
2975.3981 2.43551 (297*2π)/6472 weeks
2984.28932 4.07953 (298*2π)/6472 weeks
2992.65705 5.27168 (299*2π)/6472 weeks
300.73183 5.92373 (300*2π)/6472 weeks
301-1.29238 5.86992 (301*2π)/6472 weeks
302-3.1772 5.06998 (302*2π)/6472 weeks
303-4.65446 3.75204 (303*2π)/6472 weeks
304-5.65836 2.03466 (304*2π)/6472 weeks
305-6.00606 .03526 (305*2π)/6472 weeks
306-5.68473 -1.96717 (306*2π)/6472 weeks
307-4.72282 -3.73961 (307*2π)/6472 weeks
308-3.21842 -5.0974 (308*2π)/6472 weeks
309-1.38022 -5.87416 (309*2π)/6472 weeks
310.6607 -5.95102 (310*2π)/6472 weeks
3112.59668 -5.36869 (311*2π)/6472 weeks
3124.26157 -4.16315 (312*2π)/6472 weeks
3135.4022 -2.51088 (313*2π)/6472 weeks
3145.88931 -.55356 (314*2π)/6472 weeks
3155.72745 1.505 (315*2π)/6472 weeks
3164.87614 3.35469 (316*2π)/6472 weeks
3173.52875 4.79366 (317*2π)/6472 weeks
3181.70727 5.71251 (318*2π)/6472 weeks
319-.31833 5.93966 (319*2π)/6472 weeks
320-2.30433 5.52424 (320*2π)/6472 weeks
321-4.0135 4.50592 (321*2π)/6472 weeks
322-5.29868 2.91344 (322*2π)/6472 weeks
323-5.99325 1.04225 (323*2π)/6472 weeks
324-5.99325 -1.04225 (324*2π)/6472 weeks
325-5.29868 -2.91344 (325*2π)/6472 weeks
326-4.0135 -4.50592 (326*2π)/6472 weeks
327-2.30433 -5.52424 (327*2π)/6472 weeks
328-.31833 -5.93966 (328*2π)/6472 weeks
3291.70727 -5.71251 (329*2π)/6472 weeks
3303.52875 -4.79366 (330*2π)/6472 weeks
3314.87614 -3.35469 (331*2π)/6472 weeks
3325.72745 -1.505 (332*2π)/6472 weeks
3335.88931 .55356 (333*2π)/6472 weeks
3345.4022 2.51088 (334*2π)/6472 weeks
3354.26157 4.16315 (335*2π)/6472 weeks
3362.59668 5.36869 (336*2π)/6472 weeks
337.6607 5.95102 (337*2π)/6472 weeks
338-1.38022 5.87416 (338*2π)/6472 weeks
339-3.21842 5.0974 (339*2π)/6472 weeks
340-4.72282 3.73961 (340*2π)/6472 weeks
341-5.68473 1.96717 (341*2π)/6472 weeks
342-6.00606 -.03526 (342*2π)/6472 weeks
343-5.65836 -2.03466 (343*2π)/6472 weeks
344-4.65446 -3.75204 (344*2π)/6472 weeks
345-3.1772 -5.06998 (345*2π)/6472 weeks
346-1.29238 -5.86992 (346*2π)/6472 weeks
347.73183 -5.92373 (347*2π)/6472 weeks
3482.65705 -5.27168 (348*2π)/6472 weeks
3494.28932 -4.07953 (349*2π)/6472 weeks
3505.3981 -2.43551 (350*2π)/6472 weeks
3515.88927 -.47763 (351*2π)/6472 weeks
3525.71407 1.58511 (352*2π)/6472 weeks
3534.87964 3.39331 (353*2π)/6472 weeks
3543.45282 4.85096 (354*2π)/6472 weeks
3551.64818 5.76453 (355*2π)/6472 weeks
356-.33383 6.00051 (356*2π)/6472 weeks
357-2.32958 5.52792 (357*2π)/6472 weeks
358-4.04228 4.46711 (358*2π)/6472 weeks
359-5.3159 2.88968 (359*2π)/6472 weeks
360-5.95499 .96805 (360*2π)/6472 weeks
361-5.93054 -1.05475 (361*2π)/6472 weeks
362-5.24038 -2.98085 (362*2π)/6472 weeks
363-3.98561 -4.51894 (363*2π)/6472 weeks
364-2.21707 -5.54906 (364*2π)/6472 weeks
365-.25553 -5.96643 (365*2π)/6472 weeks
3661.79809 -5.66463 (366*2π)/6472 weeks
3673.55381 -4.75838 (367*2π)/6472 weeks
3684.94936 -3.28073 (368*2π)/6472 weeks
3695.76469 -1.44132 (369*2π)/6472 weeks
3705.93147 .564 (370*2π)/6472 weeks
3715.36271 2.53062 (371*2π)/6472 weeks
3724.21858 4.17911 (372*2π)/6472 weeks
3732.57619 5.34077 (373*2π)/6472 weeks
374.61137 5.92463 (374*2π)/6472 weeks
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