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Fourier Analysis of HSI


HSI appears to have interesting cyclic behaviour every 182 weeks (1351.347*sine), 200 weeks (1009.17*cosine), and 182 weeks (741.6483*cosine).

HSI has an average price of 9,138.77 (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 1/16/2017 for HSI, this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09,138.772   0 
1-391.5992 -8,071.598 (1*2π)/20032,003 weeks
2-350.5672 -4,015.139 (2*2π)/20031,002 weeks
3-2,155.508 -1,487.009 (3*2π)/2003668 weeks
4-563.1182 -1,159.269 (4*2π)/2003501 weeks
5-1,085.925 -1,314.194 (5*2π)/2003401 weeks
6-2,027.599 -124.6692 (6*2π)/2003334 weeks
7-769.855 171.5215 (7*2π)/2003286 weeks
8-879.914 -192.75 (8*2π)/2003250 weeks
9-689.5761 291.6593 (9*2π)/2003223 weeks
10-1,009.17 -148.0807 (10*2π)/2003200 weeks
11-741.6483 1,351.347 (11*2π)/2003182 weeks
12260.1519 255.9686 (12*2π)/2003167 weeks
13-59.87405 465.3771 (13*2π)/2003154 weeks
14-292.9687 9.06998 (14*2π)/2003143 weeks
15-344.2883 924.4779 (15*2π)/2003134 weeks
16277.354 672.2733 (16*2π)/2003125 weeks
17483.8792 441.9838 (17*2π)/2003118 weeks
18457.1111 156.2269 (18*2π)/2003111 weeks
1944.77943 220.589 (19*2π)/2003105 weeks
20454.9252 363.744 (20*2π)/2003100 weeks
21564.3376 94.30015 (21*2π)/200395 weeks
22478.0482 -409.7814 (22*2π)/200391 weeks
2399.67803 1.61132 (23*2π)/200387 weeks
2479.59332 -108.9625 (24*2π)/200383 weeks
25296.4798 172.3689 (25*2π)/200380 weeks
26537.9958 -193.4565 (26*2π)/200377 weeks
27287.9301 -499.673 (27*2π)/200374 weeks
28-60.47219 -376.8133 (28*2π)/200372 weeks
29-64.72928 -222.6652 (29*2π)/200369 weeks
3014.00013 -221.4856 (30*2π)/200367 weeks
318.19399 -133.2585 (31*2π)/200365 weeks
32-39.27473 -331.9951 (32*2π)/200363 weeks
33-179.78 -267.2571 (33*2π)/200361 weeks
34-258.7526 -140.2163 (34*2π)/200359 weeks
35-237.9513 -67.97791 (35*2π)/200357 weeks
36-212.8248 18.72948 (36*2π)/200356 weeks
37-172.9329 15.31062 (37*2π)/200354 weeks
38-195.9815 4.50526 (38*2π)/200353 weeks
39-208.7566 11.06606 (39*2π)/200351 weeks
40-252.5567 195.6376 (40*2π)/200350 weeks
41-51.18225 241.5895 (41*2π)/200349 weeks
42-128.7893 82.43033 (42*2π)/200348 weeks
43-93.94382 327.3677 (43*2π)/200347 weeks
44-34.79447 354.4185 (44*2π)/200346 weeks
45213.0315 353.1086 (45*2π)/200345 weeks
46243.3303 172.6274 (46*2π)/200344 weeks
47308.67 25.91598 (47*2π)/200343 weeks
48211.7291 29.41481 (48*2π)/200342 weeks
49267.4791 68.68372 (49*2π)/200341 weeks
50291.2591 -235.0743 (50*2π)/200340 weeks
51141.386 -151.6088 (51*2π)/200339 weeks
52-4.67565 -187.5046 (52*2π)/200339 weeks
53128.3715 53.00072 (53*2π)/200338 weeks
5461.50287 -190.2275 (54*2π)/200337 weeks
55159.6541 -207.4726 (55*2π)/200336 weeks
56-111.5084 -90.37062 (56*2π)/200336 weeks
5766.15138 -126.8085 (57*2π)/200335 weeks
58-70.67128 -87.99162 (58*2π)/200335 weeks
5924.89439 -158.4335 (59*2π)/200334 weeks
60-166.4157 -108.7344 (60*2π)/200333 weeks
61-60.61713 15.24928 (61*2π)/200333 weeks
62-111.2351 -31.48719 (62*2π)/200332 weeks
6361.05154 16.13144 (63*2π)/200332 weeks
64-166.2651 -141.415 (64*2π)/200331 weeks
65-29.71781 86.37507 (65*2π)/200331 weeks
66-127.485 -.06918 (66*2π)/200330 weeks
671.09068 61.95275 (67*2π)/200330 weeks
68-43.51741 -38.85279 (68*2π)/200329 weeks
69-75.82266 95.84689 (69*2π)/200329 weeks
70-5.74969 99.17201 (70*2π)/200329 weeks
7144.22966 98.12167 (71*2π)/200328 weeks
7227.02338 -26.81254 (72*2π)/200328 weeks
73-26.04657 95.32349 (73*2π)/200327 weeks
7460.46339 110.2766 (74*2π)/200327 weeks
7589.94718 26.97688 (75*2π)/200327 weeks
76120.6188 9.45288 (76*2π)/200326 weeks
7799.1363 -87.16981 (77*2π)/200326 weeks
7815.95064 -4.44367 (78*2π)/200326 weeks
7994.73592 -28.81655 (79*2π)/200325 weeks
8033.03559 -88.46442 (80*2π)/200325 weeks
8135.01361 -29.5662 (81*2π)/200325 weeks
82-11.25276 -36.70335 (82*2π)/200324 weeks
8313.34219 43.61716 (83*2π)/200324 weeks
84120.2905 -20.78664 (84*2π)/200324 weeks
8521.55892 -62.53637 (85*2π)/200324 weeks
86104.1622 3.25323 (86*2π)/200323 weeks
8749.38876 -131.7438 (87*2π)/200323 weeks
8814.82854 -78.13864 (88*2π)/200323 weeks
89-4.50065 -155.9586 (89*2π)/200323 weeks
90-84.25992 -60.49215 (90*2π)/200322 weeks
91-4.69058 -14.0651 (91*2π)/200322 weeks
92-53.56374 -98.79598 (92*2π)/200322 weeks
93-45.08878 -13.37782 (93*2π)/200322 weeks
94-63.30424 -31.30744 (94*2π)/200321 weeks
955.5847 63.41395 (95*2π)/200321 weeks
9618.17628 -37.73799 (96*2π)/200321 weeks
97-40.44434 -78.99491 (97*2π)/200321 weeks
98-53.40266 3.97777 (98*2π)/200320 weeks
99-66.54128 17.79015 (99*2π)/200320 weeks
1001.79676 6.20765 (100*2π)/200320 weeks
101-10.43125 -40.93219 (101*2π)/200320 weeks
102-101.8385 -17.49377 (102*2π)/200320 weeks
103-61.86662 102.4064 (103*2π)/200319 weeks
10412.98566 87.83274 (104*2π)/200319 weeks
10549.8585 58.58698 (105*2π)/200319 weeks
10651.77926 37.56878 (106*2π)/200319 weeks
10759.75634 44.89049 (107*2π)/200319 weeks
10877.70865 9.1336 (108*2π)/200319 weeks
10975.67366 15.59258 (109*2π)/200318 weeks
110136.5408 -59.33588 (110*2π)/200318 weeks
11128.23801 -53.06174 (111*2π)/200318 weeks
11256.8339 -69.9847 (112*2π)/200318 weeks
113-4.50811 -28.14471 (113*2π)/200318 weeks
11478.45531 -57.88897 (114*2π)/200318 weeks
11517.13058 -65.25183 (115*2π)/200317 weeks
1169.10102 -53.61374 (116*2π)/200317 weeks
11719.85135 -51.13717 (117*2π)/200317 weeks
11838.27384 -33.74917 (118*2π)/200317 weeks
11953.65823 -150.2582 (119*2π)/200317 weeks
120-43.00269 -97.9613 (120*2π)/200317 weeks
121-77.3516 -106.5508 (121*2π)/200317 weeks
122-79.87006 -34.46495 (122*2π)/200316 weeks
123-4.82843 -33.13711 (123*2π)/200316 weeks
124-57.85441 -60.27254 (124*2π)/200316 weeks
125-59.7821 -102.7732 (125*2π)/200316 weeks
126-164.5931 -20.37943 (126*2π)/200316 weeks
127-98.84142 58.01971 (127*2π)/200316 weeks
128-47.66128 70.54759 (128*2π)/200316 weeks
129-68.35531 65.73401 (129*2π)/200316 weeks
130-3.39595 74.34693 (130*2π)/200315 weeks
131-19.13915 93.28912 (131*2π)/200315 weeks
13290.908 85.97993 (132*2π)/200315 weeks
13371.29688 8.80382 (133*2π)/200315 weeks
13449.28325 31.32491 (134*2π)/200315 weeks
13589.37503 -30.21174 (135*2π)/200315 weeks
13661.76137 -11.5881 (136*2π)/200315 weeks
13770.01128 -94.52624 (137*2π)/200315 weeks
138-34.97744 -36.94323 (138*2π)/200315 weeks
13923.52549 -57.29175 (139*2π)/200314 weeks
1408.84382 1.23687 (140*2π)/200314 weeks
14161.02027 -17.72441 (141*2π)/200314 weeks
14242.33255 -62.86024 (142*2π)/200314 weeks
1437.71897 -86.1853 (143*2π)/200314 weeks
14415.74814 -60.4637 (144*2π)/200314 weeks
145-12.99726 -51.52828 (145*2π)/200314 weeks
146-2.25247 -47.82187 (146*2π)/200314 weeks
147-12.56539 -86.37596 (147*2π)/200314 weeks
148-37.18771 -51.95484 (148*2π)/200314 weeks
149-13.41297 -86.30578 (149*2π)/200313 weeks
150-105.1787 -66.99715 (150*2π)/200313 weeks
151-114.493 -32.84226 (151*2π)/200313 weeks
152-84.68108 45.04029 (152*2π)/200313 weeks
153-53.38902 66.41457 (153*2π)/200313 weeks
15417.40026 39.20437 (154*2π)/200313 weeks
15526.21704 -2.5053 (155*2π)/200313 weeks
156.75687 -5.83114 (156*2π)/200313 weeks
15737.13702 -24.58437 (157*2π)/200313 weeks
158-37.94654 -36.17775 (158*2π)/200313 weeks
159-28.32219 -7.72609 (159*2π)/200313 weeks
160-20.49216 16.60466 (160*2π)/200313 weeks
16135.27009 22.52524 (161*2π)/200312 weeks
16224.94436 -54.97093 (162*2π)/200312 weeks
163-22.31702 -13.24453 (163*2π)/200312 weeks
164-4.96797 -43.52974 (164*2π)/200312 weeks
165-23.5151 -37.49099 (165*2π)/200312 weeks
166-41.32053 -28.79832 (166*2π)/200312 weeks
167-82.87984 21.86184 (167*2π)/200312 weeks
168-10.43606 56.84533 (168*2π)/200312 weeks
1696.9317 23.09441 (169*2π)/200312 weeks
17029.23732 53.21605 (170*2π)/200312 weeks
17144.69246 -8.11441 (171*2π)/200312 weeks
17230.40071 9.3272 (172*2π)/200312 weeks
17377.23669 -23.67304 (173*2π)/200312 weeks
17440.58592 -26.43634 (174*2π)/200312 weeks
17569.68155 -72.16914 (175*2π)/200311 weeks
17625.3427 -91.93267 (176*2π)/200311 weeks
17736.58537 -123.56 (177*2π)/200311 weeks
178-51.05091 -123.2856 (178*2π)/200311 weeks
179-66.71954 -103.2951 (179*2π)/200311 weeks
180-94.62759 -60.88507 (180*2π)/200311 weeks
181-85.07505 -53.54404 (181*2π)/200311 weeks
182-124.8948 -2.21639 (182*2π)/200311 weeks
183-70.64395 36.6855 (183*2π)/200311 weeks
184-68.23547 29.89669 (184*2π)/200311 weeks
185-15.10454 36.75947 (185*2π)/200311 weeks
186-37.20381 16.05616 (186*2π)/200311 weeks
187-24.27028 19.43312 (187*2π)/200311 weeks
188-13.48893 48.2579 (188*2π)/200311 weeks
18921.4387 -.64104 (189*2π)/200311 weeks
19012.13527 -24.54459 (190*2π)/200311 weeks
191-15.06017 -28.78207 (191*2π)/200310 weeks
192-50.54177 1.85543 (192*2π)/200310 weeks
193-27.92955 -.2438 (193*2π)/200310 weeks
194-36.05246 55.68055 (194*2π)/200310 weeks
19531.54742 41.5618 (195*2π)/200310 weeks
19631.65437 49.8543 (196*2π)/200310 weeks
19766.41548 -47.52426 (197*2π)/200310 weeks
1988.25664 -29.59884 (198*2π)/200310 weeks
19914.24571 -40.93659 (199*2π)/200310 weeks
200-23.6908 -17.39129 (200*2π)/200310 weeks
20115.2143 -7.21992 (201*2π)/200310 weeks
20211.65492 -8.46003 (202*2π)/200310 weeks
20367.65458 -53.22142 (203*2π)/200310 weeks
2042.24083 -104.2422 (204*2π)/200310 weeks
205-40.40672 -122.0852 (205*2π)/200310 weeks
206-109.9087 -61.06335 (206*2π)/200310 weeks
207-94.49649 -20.75041 (207*2π)/200310 weeks
208-72.15884 42.60086 (208*2π)/200310 weeks
209-27.59927 23.70926 (209*2π)/200310 weeks
210-13.93165 47.97598 (210*2π)/200310 weeks
21135.11642 -22.76992 (211*2π)/20039 weeks
2124.74394 -24.48279 (212*2π)/20039 weeks
213-24.58128 -68.52086 (213*2π)/20039 weeks
214-54.15179 -13.21849 (214*2π)/20039 weeks
215-32.61497 -23.71015 (215*2π)/20039 weeks
216-13.80312 -16.64793 (216*2π)/20039 weeks
217-50.67789 -86.66415 (217*2π)/20039 weeks
218-139.3282 -29.39958 (218*2π)/20039 weeks
219-117.8919 33.95132 (219*2π)/20039 weeks
220-103.1772 104.1142 (220*2π)/20039 weeks
221-13.80176 101.9139 (221*2π)/20039 weeks
222-4.63954 92.28104 (222*2π)/20039 weeks
22345.08947 61.84991 (223*2π)/20039 weeks
22446.5206 57.09347 (224*2π)/20039 weeks
22577.72392 -.53606 (225*2π)/20039 weeks
22635.41803 -6.01721 (226*2π)/20039 weeks
22768.98357 -30.00999 (227*2π)/20039 weeks
22840.58644 -45.29797 (228*2π)/20039 weeks
22939.63189 -83.66146 (229*2π)/20039 weeks
230-36.53702 -87.56746 (230*2π)/20039 weeks
231-43.79186 -38.07832 (231*2π)/20039 weeks
232-39.05592 -26.04418 (232*2π)/20039 weeks
233-25.53918 -15.85148 (233*2π)/20039 weeks
234-17.13964 -15.13338 (234*2π)/20039 weeks
235-32.28723 -36.94647 (235*2π)/20039 weeks
2363.94214 -44.89756 (236*2π)/20038 weeks
237-47.8105 -78.01861 (237*2π)/20038 weeks
238-85.5648 -71.56396 (238*2π)/20038 weeks
239-140.7367 -19.16082 (239*2π)/20038 weeks
240-109.5869 54.60938 (240*2π)/20038 weeks
241-71.41487 47.98367 (241*2π)/20038 weeks
242-49.12808 104.9871 (242*2π)/20038 weeks
243-9.15276 74.715 (243*2π)/20038 weeks
24454.92351 62.98562 (244*2π)/20038 weeks
24548.57447 -21.26687 (245*2π)/20038 weeks
2466.23125 -49.72351 (246*2π)/20038 weeks
247-45.61512 -30.97657 (247*2π)/20038 weeks
248-57.69614 29.333 (248*2π)/20038 weeks
2494.09792 20.74501 (249*2π)/20038 weeks
250.23223 19.54474 (250*2π)/20038 weeks
25111.04409 -34.86617 (251*2π)/20038 weeks
252-34.47159 -6.5205 (252*2π)/20038 weeks
253-28.23138 -15.16373 (253*2π)/20038 weeks
254-38.67619 1.88632 (254*2π)/20038 weeks
255-36.05224 27.20889 (255*2π)/20038 weeks
256-6.37571 26.5697 (256*2π)/20038 weeks
25720.31639 5.29901 (257*2π)/20038 weeks
2585.04675 -49.90649 (258*2π)/20038 weeks
259-67.58015 -44.42372 (259*2π)/20038 weeks
260-84.21156 52.26398 (260*2π)/20038 weeks
261-17.86704 38.3744 (261*2π)/20038 weeks
262-4.02093 44.26441 (262*2π)/20038 weeks
263-12.78928 25.17892 (263*2π)/20038 weeks
26419.03757 62.00597 (264*2π)/20038 weeks
26546.73921 21.78776 (265*2π)/20038 weeks
26695.54442 -22.69534 (266*2π)/20038 weeks
26735.17735 -81.2599 (267*2π)/20038 weeks
268-16.3954 -91.78783 (268*2π)/20037 weeks
269-42.64998 -56.73869 (269*2π)/20037 weeks
270-52.86726 -49.82178 (270*2π)/20037 weeks
271-44.99913 -66.14822 (271*2π)/20037 weeks
272-115.5958 -40.99888 (272*2π)/20037 weeks
273-110.9503 -3.68146 (273*2π)/20037 weeks
274-86.75137 39.53792 (274*2π)/20037 weeks
275-84.81196 23.6474 (275*2π)/20037 weeks
276-54.14379 67.70101 (276*2π)/20037 weeks
277-54.61536 40.46054 (277*2π)/20037 weeks
278-30.14936 34.27219 (278*2π)/20037 weeks
279-62.38517 37.25814 (279*2π)/20037 weeks
280-82.38149 68.32272 (280*2π)/20037 weeks
281-42.68866 131.0913 (281*2π)/20037 weeks
28219.23867 126.6319 (282*2π)/20037 weeks
28372.0624 111.7976 (283*2π)/20037 weeks
284107.4719 52.39883 (284*2π)/20037 weeks
285117.6411 16.61193 (285*2π)/20037 weeks
28688.93929 -69.57521 (286*2π)/20037 weeks
28723.30334 -61.89581 (287*2π)/20037 weeks
28816.31641 -40.62195 (288*2π)/20037 weeks
28911.47086 -36.69752 (289*2π)/20037 weeks
29020.07509 -75.00826 (290*2π)/20037 weeks
291-29.19456 -89.91487 (291*2π)/20037 weeks
292-49.71543 -60.22082 (292*2π)/20037 weeks
293-78.61912 -34.16043 (293*2π)/20037 weeks
294-46.60003 -38.33847 (294*2π)/20037 weeks
295-91.62949 -38.48154 (295*2π)/20037 weeks
296-106.2715 -6.52338 (296*2π)/20037 weeks
297-109.2366 39.47473 (297*2π)/20037 weeks
298-71.53842 55.50132 (298*2π)/20037 weeks
299-69.27857 56.32336 (299*2π)/20037 weeks
300-47.57711 89.36658 (300*2π)/20037 weeks
301-24.54842 67.97709 (301*2π)/20037 weeks
302-19.72123 75.4062 (302*2π)/20037 weeks
303-12.94723 64.54237 (303*2π)/20037 weeks
30411.48645 85.57837 (304*2π)/20037 weeks
30538.77589 79.29556 (305*2π)/20037 weeks
30694.00426 38.85026 (306*2π)/20037 weeks
30768.83202 -40.6368 (307*2π)/20037 weeks
30825.69279 -68.72633 (308*2π)/20037 weeks
309-38.4623 -57.79449 (309*2π)/20036 weeks
310-71.96841 -19.32945 (310*2π)/20036 weeks
311-67.06132 34.50832 (311*2π)/20036 weeks
312-19.64138 50.5191 (312*2π)/20036 weeks
3131.25224 47.60859 (313*2π)/20036 weeks
31439.99047 27.24828 (314*2π)/20036 weeks
31516.15798 -12.82657 (315*2π)/20036 weeks
3169.47407 -28.78669 (316*2π)/20036 weeks
317-22.24365 -24.80109 (317*2π)/20036 weeks
318-34.18517 -28.81721 (318*2π)/20036 weeks
319-62.02554 -25.98921 (319*2π)/20036 weeks
320-105.6766 5.91216 (320*2π)/20036 weeks
321-89.17607 81.71103 (321*2π)/20036 weeks
322-50.79753 117.9076 (322*2π)/20036 weeks
32335.53139 124.7049 (323*2π)/20036 weeks
32472.52666 51.71243 (324*2π)/20036 weeks
32549.651 30.13815 (325*2π)/20036 weeks
32671.0011 9.56317 (326*2π)/20036 weeks
32775.18279 -16.33142 (327*2π)/20036 weeks
32849.3342 -85.84966 (328*2π)/20036 weeks
329-16.22995 -98.11689 (329*2π)/20036 weeks
330-54.93209 -69.69653 (330*2π)/20036 weeks
331-92.62627 -61.67886 (331*2π)/20036 weeks
332-114.6207 -19.5286 (332*2π)/20036 weeks
333-139.8167 28.29322 (333*2π)/20036 weeks
334-103.7594 97.71363 (334*2π)/20036 weeks
335-56.68016 130.3977