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Fourier Analysis of HSI


HSI appears to have interesting cyclic behaviour every 183 weeks (1490.995*sine), 134 weeks (981.8428*sine), and 201 weeks (934.5315*cosine).

HSI has an average price of 9,114.88 (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 1/31/1975 to 3/13/2017 for HSI, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09,114.883   0 
1-542.5325 -8,076.524 (1*2π)/20112,011 weeks
2-511.655 -3,971.477 (2*2π)/20111,006 weeks
3-2,253.313 -1,353.799 (3*2π)/2011670 weeks
4-650.9262 -1,076.881 (4*2π)/2011503 weeks
5-1,206.599 -1,161.697 (5*2π)/2011402 weeks
6-2,025.647 123.6779 (6*2π)/2011335 weeks
7-712.0026 311.3848 (7*2π)/2011287 weeks
8-853.0438 -28.29935 (8*2π)/2011251 weeks
9-600.5532 444.6967 (9*2π)/2011223 weeks
10-934.5315 76.53763 (10*2π)/2011201 weeks
11-412.6043 1,490.995 (11*2π)/2011183 weeks
12411.395 211.0566 (12*2π)/2011168 weeks
1390.59328 478.5746 (13*2π)/2011155 weeks
14-193.5734 92.6023 (14*2π)/2011144 weeks
15-25.71651 981.8428 (15*2π)/2011134 weeks
16544.2112 536.7503 (16*2π)/2011126 weeks
17653.342 241.5809 (17*2π)/2011118 weeks
18519.9198 -23.51104 (18*2π)/2011112 weeks
19147.117 138.5005 (19*2π)/2011106 weeks
20584.9203 140.6282 (20*2π)/2011101 weeks
21563.3026 -176.4087 (21*2π)/201196 weeks
22302.5984 -581.3505 (22*2π)/201191 weeks
2358.95704 -44.23192 (23*2π)/201187 weeks
2444.84729 -162.0842 (24*2π)/201184 weeks
25332.5476 5.52204 (25*2π)/201180 weeks
26374.2538 -434.0283 (26*2π)/201177 weeks
27-11.66465 -566.8275 (27*2π)/201174 weeks
28-266.554 -273.0246 (28*2π)/201172 weeks
29-171.8807 -125.0988 (29*2π)/201169 weeks
30-90.08913 -152.0053 (30*2π)/201167 weeks
31-77.38708 -69.81853 (31*2π)/201165 weeks
32-202.0124 -212.0512 (32*2π)/201163 weeks
33-277.8191 -52.63585 (33*2π)/201161 weeks
34-256.3959 99.94931 (34*2π)/201159 weeks
35-174.2425 143.5649 (35*2π)/201157 weeks
36-98.26701 191.4942 (36*2π)/201156 weeks
37-59.05147 154.8785 (37*2π)/201154 weeks
38-72.30294 154.362 (38*2π)/201153 weeks
39-51.67572 173.0409 (39*2π)/201152 weeks
4031.15647 325.289 (40*2π)/201150 weeks
41216.3302 216.2506 (41*2π)/201149 weeks
4270.23917 118.2588 (42*2π)/201148 weeks
43246.6052 284.323 (43*2π)/201147 weeks
44299.7339 196.078 (44*2π)/201146 weeks
45452.1667 11.12 (45*2π)/201145 weeks
46308.023 -161.4547 (46*2π)/201144 weeks
47244.5155 -273.4924 (47*2π)/201143 weeks
48148.97 -180.3002 (48*2π)/201142 weeks
49183.5988 -190.8826 (49*2π)/201141 weeks
50-1.6217 -392.3395 (50*2π)/201140 weeks
51-57.23192 -161.3887 (51*2π)/201139 weeks
52-138.5905 -96.02068 (52*2π)/201139 weeks
53109.0727 -18.07969 (53*2π)/201138 weeks
54-117.249 -172.8181 (54*2π)/201137 weeks
55-35.53514 -173.5795 (55*2π)/201137 weeks
56-144.9796 90.34014 (56*2π)/201136 weeks
57-14.51619 -72.18709 (57*2π)/201135 weeks
58-91.79538 53.81229 (58*2π)/201135 weeks
59-52.30842 -47.98471 (59*2π)/201134 weeks
60-116.6608 127.926 (60*2π)/201134 weeks
6164.01765 101.1094 (61*2π)/201133 weeks
62-9.30813 72.6361 (62*2π)/201132 weeks
63117.6297 -7.3578 (63*2π)/201132 weeks
64-124.7202 64.64529 (64*2π)/201131 weeks
65162.9776 100.8285 (65*2π)/201131 weeks
6615.28526 76.00963 (66*2π)/201130 weeks
67147.1622 9.01184 (67*2π)/201130 weeks
6837.87817 -4.11537 (68*2π)/201130 weeks
69137.6441 87.05103 (69*2π)/201129 weeks
70157.4358 -7.00573 (70*2π)/201129 weeks
71144.7818 -49.49124 (71*2π)/201128 weeks
7238.87114 -85.50433 (72*2π)/201128 weeks
73121.5923 19.79122 (73*2π)/201128 weeks
74144.9563 -80.9249 (74*2π)/201127 weeks
7562.29678 -139.3161 (75*2π)/201127 weeks
7650.32627 -138.5357 (76*2π)/201126 weeks
77-30.23086 -127.2587 (77*2π)/201126 weeks
7816.93215 -11.99982 (78*2π)/201126 weeks
7927.27024 -99.56047 (79*2π)/201125 weeks
80-40.48093 -51.7009 (80*2π)/201125 weeks
8131.62441 -20.51375 (81*2π)/201125 weeks
829.15923 -3.93746 (82*2π)/201125 weeks
8379.425 -22.01824 (83*2π)/201124 weeks
8433.06516 -127.0147 (84*2π)/201124 weeks
85-40.43706 -30.62901 (85*2π)/201124 weeks
8642.44521 -68.02053 (86*2π)/201123 weeks
87-101.4793 -46.39103 (87*2π)/201123 weeks
88-28.38511 19.65254 (88*2π)/201123 weeks
89-67.81922 8.89233 (89*2π)/201123 weeks
9027.68825 94.49323 (90*2π)/201122 weeks
9175.40454 5.93725 (91*2π)/201122 weeks
92-13.09633 21.52409 (92*2π)/201122 weeks
9389.21895 32.30209 (93*2π)/201122 weeks
9459.91964 14.39707 (94*2π)/201121 weeks
95133.965 -26.27847 (95*2π)/201121 weeks
968.59013 -48.3536 (96*2π)/201121 weeks
973.26253 10.83581 (97*2π)/201121 weeks
9896.2368 25.07003 (98*2π)/201121 weeks
9980.8878 -.02804 (99*2π)/201120 weeks
10074.45766 -68.31365 (100*2π)/201120 weeks
10137.59494 -36.55152 (101*2π)/201120 weeks
10276.20633 25.95687 (102*2π)/201120 weeks
103172.1529 -47.49186 (103*2π)/201120 weeks
104102.9104 -130.8964 (104*2π)/201119 weeks
10552.27065 -136 (105*2π)/201119 weeks
10624.79627 -113.2593 (106*2π)/201119 weeks
10721.30561 -105.2651 (107*2π)/201119 weeks
108-17.04359 -109.4858 (108*2π)/201119 weeks
109-16.67655 -86.91701 (109*2π)/201118 weeks
110-65.50166 -106.312 (110*2π)/201118 weeks
111-42.15961 18.86507 (111*2π)/201118 weeks
112-26.62196 -31.70211 (112*2π)/201118 weeks
1137.38828 15.88254 (113*2π)/201118 weeks
114-15.83719 -63.69034 (114*2π)/201118 weeks
115-14.55711 19.90236 (115*2π)/201117 weeks
1166.28945 3.92217 (116*2π)/201117 weeks
1177.10712 -11.48778 (117*2π)/201117 weeks
1186.59451 -12.83973 (118*2π)/201117 weeks
119-63.67563 3.54451 (119*2π)/201117 weeks
12042.99277 92.44725 (120*2π)/201117 weeks
12150.29633 55.47756 (121*2π)/201117 weeks
122111.3106 10.29208 (122*2π)/201116 weeks
12375.70392 -49.41637 (123*2π)/201116 weeks
12451.61883 19.16924 (124*2π)/201116 weeks
12562.25233 -1.10339 (125*2π)/201116 weeks
126159.1564 28.98578 (126*2π)/201116 weeks
127163.0164 -104.6911 (127*2π)/201116 weeks
128101.8763 -129.1325 (128*2π)/201116 weeks
12963.03393 -104.0367 (129*2π)/201116 weeks
13043.82912 -156.9286 (130*2π)/201115 weeks
13124.71927 -123.0324 (131*2π)/201115 weeks
132-28.32579 -175.715 (132*2π)/201115 weeks
133-79.30856 -75.62514 (133*2π)/201115 weeks
134-33.71939 -53.14708 (134*2π)/201115 weeks
135-78.33202 -62.78643 (135*2π)/201115 weeks
136-29.43525 -12.04049 (136*2π)/201115 weeks
137-64.53751 -1.30793 (137*2π)/201115 weeks
13836.90385 43.40901 (138*2π)/201115 weeks
139-2.893 -50.90487 (139*2π)/201114 weeks
14039.99126 -30.88784 (140*2π)/201114 weeks
141-18.32343 -47.06464 (141*2π)/201114 weeks
142-26.67555 11.01872 (142*2π)/201114 weeks
1434.27677 24.01529 (143*2π)/201114 weeks
14442.76217 -5.83948 (144*2π)/201114 weeks
14545.20135 10.47951 (145*2π)/201114 weeks
14635.83112 -10.93557 (146*2π)/201114 weeks
14725.65587 3.4686 (147*2π)/201114 weeks
14873.52737 -6.07118 (148*2π)/201114 weeks
14945.58174 -22.96617 (149*2π)/201113 weeks
150104.5119 8.61526 (150*2π)/201113 weeks
151100.6659 -74.4866 (151*2π)/201113 weeks
15291.02023 -131.8184 (152*2π)/201113 weeks
15320.28932 -128.7702 (153*2π)/201113 weeks
154-41.23733 -120.231 (154*2π)/201113 weeks
155-38.44 -58.87804 (155*2π)/201113 weeks
156-4.85698 -34.94239 (156*2π)/201113 weeks
157-12.04602 -49.17976 (157*2π)/201113 weeks
15826.51093 -.01447 (158*2π)/201113 weeks
15928.67787 -65.24049 (159*2π)/201113 weeks
16013.06584 -71.54446 (160*2π)/201113 weeks
161-20.92204 -72.86301 (161*2π)/201112 weeks
162-32.29281 -4.32285 (162*2π)/201112 weeks
16343.78578 -16.74217 (163*2π)/201112 weeks
164.02856 -37.89173 (164*2π)/201112 weeks
16534.44267 -38.34445 (165*2π)/201112 weeks
16639.9981 -52.87157 (166*2π)/201112 weeks
16745.4511 -74.80965 (167*2π)/201112 weeks
168-24.12436 -121.0899 (168*2π)/201112 weeks
169-54.06042 -59.00318 (169*2π)/201112 weeks
170-34.5861 -54.67046 (170*2π)/201112 weeks
171-67.4444 -6.47972 (171*2π)/201112 weeks
172-16.92503 -6.40223 (172*2π)/201112 weeks
173-43.37778 -2.58778 (173*2π)/201112 weeks
1747.82272 36.41999 (174*2π)/201112 weeks
175-8.80715 26.84055 (175*2π)/201111 weeks
17651.17606 43.93387 (176*2π)/201111 weeks
17760.26845 11.08767 (177*2π)/201111 weeks
178123.8658 10.99244 (178*2π)/201111 weeks
179106.6899 -64.54037 (179*2π)/201111 weeks
180101.0259 -93.44476 (180*2π)/201111 weeks
18155.86942 -112.8601 (181*2π)/201111 weeks
18259.7134 -121.7969 (182*2π)/201111 weeks
183-12.99395 -146.4437 (183*2π)/201111 weeks
184-33.64964 -92.93987 (184*2π)/201111 weeks
185-49.59085 -95.37142 (185*2π)/201111 weeks
186-30.61308 -43.73837 (186*2π)/201111 weeks
187-34.08715 -64.09553 (187*2π)/201111 weeks
188-31.71742 -57.14223 (188*2π)/201111 weeks
189-59.21428 -21.10844 (189*2π)/201111 weeks
190-6.83428 -14.50139 (190*2π)/201111 weeks
19119.61937 -29.3204 (191*2π)/201111 weeks
19220.40763 -54.53806 (192*2π)/201110 weeks
193-27.47646 -67.31586 (193*2π)/201110 weeks
194-15.31315 -66.94237 (194*2π)/201110 weeks
195-73.43285 -35.10885 (195*2π)/201110 weeks
196-28.66134 9.19661 (196*2π)/201110 weeks
197-41.79961 41.68948 (197*2π)/201110 weeks
19857.57607 3.99349 (198*2π)/201110 weeks
19921.32666 -19.90243 (199*2π)/201110 weeks
20039.81428 -30.57533 (200*2π)/201110 weeks
201-5.18881 -41.86897 (201*2π)/201110 weeks
20212.64174 -10.66345 (202*2π)/201110 weeks
2034.46914 -3.17561 (203*2π)/201110 weeks
20485.82814 7.81478 (204*2π)/201110 weeks
20585.52278 -66.84083 (205*2π)/201110 weeks
20679.69917 -126.8633 (206*2π)/201110 weeks
207-11.35257 -139.9358 (207*2π)/201110 weeks
208-37.01783 -117.1396 (208*2π)/201110 weeks
209-69.90617 -51.91624 (209*2π)/201110 weeks
210-34.80132 -36.6473 (210*2π)/201110 weeks
211-42.50286 5.10295 (211*2π)/201110 weeks
21239.12387 -20.42854 (212*2π)/20119 weeks
21328.37124 -31.55883 (213*2π)/20119 weeks
21431.10871 -91.35824 (214*2π)/20119 weeks
215-21.48392 -64.52302 (215*2π)/20119 weeks
216-3.90442 -64.67231 (216*2π)/20119 weeks
21714.7129 -44.87396 (217*2π)/20119 weeks
21822.72279 -129.8578 (218*2π)/20119 weeks
219-83.92092 -134.8838 (219*2π)/20119 weeks
220-107.3909 -80.08985 (220*2π)/20119 weeks
221-140.8325 -4.94132 (221*2π)/20119 weeks
222-68.46558 40.5829 (222*2π)/20119 weeks
223-57.69244 48.95162 (223*2π)/20119 weeks
2241.75278 46.97687 (224*2π)/20119 weeks
22510.28606 52.06668 (225*2π)/20119 weeks
22667.06522 12.37579 (226*2π)/20119 weeks
22735.53033 -6.59219 (227*2π)/20119 weeks
22879.57668 -20.14889 (228*2π)/20119 weeks
22964.22649 -43.80965 (229*2π)/20119 weeks
23081.00304 -85.82484 (230*2π)/20119 weeks
23111.09381 -119.7571 (231*2π)/20119 weeks
232-13.93949 -80.32612 (232*2π)/20119 weeks
233-16.94686 -67.89913 (233*2π)/20119 weeks
234-8.37178 -54.17198 (234*2π)/20119 weeks
235-.33595 -49.65454 (235*2π)/20119 weeks
236-11.71826 -73.71595 (236*2π)/20119 weeks
23727.27118 -75.72227 (237*2π)/20118 weeks
238-15.12812 -120.4591 (238*2π)/20118 weeks
239-55.28892 -126.2987 (239*2π)/20118 weeks
240-124.018 -86.30299 (240*2π)/20118 weeks
241-110.3806 -6.41957 (241*2π)/20118 weeks
242-74.28059 -4.35617 (242*2π)/20118 weeks
243-58.93647 58.92599 (243*2π)/20118 weeks
244-15.61746 37.278 (244*2π)/20118 weeks
24552.5163 33.23082 (245*2π)/20118 weeks
24656.27244 -51.9197 (246*2π)/20118 weeks
24716.90829 -86.11546 (247*2π)/20118 weeks
248-36.92544 -71.92432 (248*2π)/20118 weeks
249-52.65978 -11.92469 (249*2π)/20118 weeks
2509.11882 -18.57282 (250*2π)/20118 weeks
2515.58318 -20.24625 (251*2π)/20118 weeks
25215.79239 -75.15092 (252*2π)/20118 weeks
253-29.94572 -46.37861 (253*2π)/20118 weeks
254-24.27234 -54.95316 (254*2π)/20118 weeks
255-34.12642 -37.12804 (255*2π)/20118 weeks
256-29.55559 -12.38938 (256*2π)/20118 weeks
257.2183 -16.3748 (257*2π)/20118 weeks
25823.34205 -41.17755 (258*2π)/20118 weeks
259-.0646 -93.45707 (259*2π)/20118 weeks
260-71.62179 -75.98226 (260*2π)/20118 weeks
261-72.22829 21.82647 (261*2π)/20118 weeks
262-5.8694 -3.94429 (262*2π)/20118 weeks
2637.12635 -2.3925 (263*2π)/20118 weeks
264-4.18356 -21.54153 (264*2π)/20118 weeks
26533.00038 5.26478 (265*2π)/20118 weeks
26649.49524 -45.10696 (266*2π)/20118 weeks
26779.02039 -98.68526 (267*2π)/20118 weeks
268-1.4399 -138.3354 (268*2π)/20118 weeks
269-54.87227 -128.3873 (269*2π)/20117 weeks
270-70.29237 -83.01813 (270*2π)/20117 weeks
271-76.58833 -72.33413 (271*2π)/20117 weeks
272-73.8071 -84.19084 (272*2π)/20117 weeks
273-130.1781 -35.04068 (273*2π)/20117 weeks
274-104.3619 .20654 (274*2π)/20117 weeks
275-64.15614 29.93717 (275*2π)/20117 weeks
276-63.40448 10.76523 (276*2π)/20117 weeks
277-19.63912 38.62012 (277*2π)/20117 weeks
278-29.87495 7.71103 (278*2π)/20117 weeks
279-9.91479 -4.38119 (279*2π)/20117 weeks
280-37.32852 12.20659 (280*2π)/20117 weeks
281-33.06617 44.98338 (281*2π)/20117 weeks
28234.3096 72.6974 (282*2π)/20117 weeks
28383.75736 25.71893 (283*2π)/20117 weeks
284110.4075 -21.59857 (284*2π)/20117 weeks
28598.16099 -92.93903 (285*2π)/20117 weeks
28670.76636 -123.4042 (286*2π)/20117 weeks
287-5.23832 -170.6538 (287*2π)/20117 weeks
288-57.01647 -115.9152 (288*2π)/20117 weeks
289-48.02038 -89.4783 (289*2π)/20117 weeks
290-52.25118 -84.06521 (290*2π)/20117 weeks
291-67.1377 -112.7206 (291*2π)/20117 weeks
292-112.7569 -84.7746 (292*2π)/20117 weeks
293-104.5365 -40.04912 (293*2π)/20117 weeks
294-105.8217 -6.39702 (294*2π)/20117 weeks
295-76.4704 -25.72418 (295*2π)/20117 weeks
296-107.5714 4.89585 (296*2π)/20117 weeks
297-85.21134 37.94394 (297*2π)/20117 weeks
298-50.30571 64.04752 (298*2π)/20117 weeks
299-9.11912 41.22065 (299*2π)/20117 weeks
300-8.06957 32.53636 (300*2π)/20117 weeks
30124.96616 34.06689 (301*2π)/20117 weeks
30221.92997 -5.46614 (302*2π)/20117 weeks
30323.80381 -5.95907 (303*2π)/20117 weeks
30419.39747 -24.40432 (304*2π)/20117 weeks
30543.20144 -30.70642 (305*2π)/20117 weeks
30640.88114 -62.73816 (306*2π)/20117 weeks
30727.85855 -120.8451 (307*2π)/20117 weeks
308-59.04369 -133.018 (308*2π)/20117 weeks
309-97.9825 -91.09371 (309*2π)/20117 weeks
310-112.3326 -24.73321 (310*2π)/20116 weeks
311-81.65462 17.70957 (311*2π)/20116 weeks
312-27.99193 28.39627 (312*2π)/20116 weeks
3137.49944 -13.37626 (313*2π)/20116 weeks
3141.65904 -36.80535 (314*2π)/20116 weeks
315-7.06631 -71.02983 (315*2π)/20116 weeks
316-61.08621 -63.39262 (316*2π)/20116 weeks
317-69.36468 -51.17875 (317*2π)/20116 weeks
318-77.59629 -15.08893 (318*2π)/20116 weeks
319-74.72917 -5.28182 (319*2π)/20116 weeks
320-71.21674 20.82887 (320*2π)/20116 weeks
321-46.09733 58.7024 (321*2π)/20116 weeks
32231.82804 55.20586 (322*2π)/20116 weeks
32361.13422 6.37436 (323*2π)/20116 weeks
32472.61971 -73.00834 (324*2π)/20116 weeks
325-3.10299 -121.4629 (325*2π)/20116 weeks
326-42.69567 -88.79523 (326*2π)/2011