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# Fourier Analysis of HBC (HSBC Holdings, plc. Common Stoc)

HBC (HSBC Holdings, plc. Common Stoc) appears to have interesting cyclic behaviour every 31 weeks (1289.544*sine), 26 weeks (1188.97*sine), and 28 weeks (1037.195*sine).

HBC (HSBC Holdings, plc. Common Stoc) has an average price of 10,514.01 (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 2/22/2010 to 3/13/2017 for HBC (HSBC Holdings, plc. Common Stoc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
010,514.01   0
14,945.191 -5,185.25 (1*2π)/367367 weeks
22,939.102 -4,081.28 (2*2π)/367184 weeks
31,558.102 -3,005.584 (3*2π)/367122 weeks
41,026.808 -2,405.619 (4*2π)/36792 weeks
5693.9773 -2,725.509 (5*2π)/36773 weeks
6261.8981 -2,393.523 (6*2π)/36761 weeks
7239.7811 -1,270.586 (7*2π)/36752 weeks
8-192.7957 -1,404.873 (8*2π)/36746 weeks
9517.1656 -1,020.37 (9*2π)/36741 weeks
10269.1919 -727.2143 (10*2π)/36737 weeks
11570.9877 -641.2821 (11*2π)/36733 weeks
12872.9362 -1,289.544 (12*2π)/36731 weeks
13374.6677 -1,037.195 (13*2π)/36728 weeks
14453.1012 -1,188.97 (14*2π)/36726 weeks
15261.3588 -1,101.313 (15*2π)/36724 weeks
16225.1029 -986.2545 (16*2π)/36723 weeks
1794.58797 -1,040.574 (17*2π)/36722 weeks
1838.79319 -831.5743 (18*2π)/36720 weeks
19233.6292 -899.4629 (19*2π)/36719 weeks
2072.89753 -747.3004 (20*2π)/36718 weeks
21211.5713 -994.4476 (21*2π)/36717 weeks
22-97.04865 -923.6118 (22*2π)/36717 weeks
2310.12047 -734.2817 (23*2π)/36716 weeks
24-34.39883 -735.2306 (24*2π)/36715 weeks
25-51.30706 -739.6332 (25*2π)/36715 weeks
263.42569 -771.8179 (26*2π)/36714 weeks
27-134.9345 -673.3958 (27*2π)/36714 weeks
28-83.12125 -632.8573 (28*2π)/36713 weeks
29-69.74271 -665.7624 (29*2π)/36713 weeks
3032.37056 -561.4962 (30*2π)/36712 weeks
31-.8502 -644.6469 (31*2π)/36712 weeks
32-62.16127 -675.4611 (32*2π)/36711 weeks
33-125.245 -569.3188 (33*2π)/36711 weeks
34-187.8635 -521.1163 (34*2π)/36711 weeks
35-103.1819 -496.5377 (35*2π)/36710 weeks
36-115.3851 -474.3908 (36*2π)/36710 weeks
37-157.5 -494.1597 (37*2π)/36710 weeks
38-157.2947 -413.015 (38*2π)/36710 weeks
39-50.75807 -489.6593 (39*2π)/3679 weeks
40-140.567 -512.2479 (40*2π)/3679 weeks
41-201.3504 -493.1693 (41*2π)/3679 weeks
42-222.9996 -432.8435 (42*2π)/3679 weeks
43-152.1422 -466.86 (43*2π)/3679 weeks
44-202.9048 -390.072 (44*2π)/3678 weeks
45-270.9108 -370.7575 (45*2π)/3678 weeks
46-141.0671 -268.5755 (46*2π)/3678 weeks
47-106.4971 -284.5342 (47*2π)/3678 weeks
48-160.3258 -343.6219 (48*2π)/3678 weeks
49-160.532 -351.8649 (49*2π)/3677 weeks
50-195.6377 -303.2054 (50*2π)/3677 weeks
51-192.1976 -350.7874 (51*2π)/3677 weeks
52-197.6454 -355.7314 (52*2π)/3677 weeks
53-245.309 -284.1392 (53*2π)/3677 weeks
54-312.8058 -155.4969 (54*2π)/3677 weeks
55-197.7405 -183.967 (55*2π)/3677 weeks
56-164.6582 -227.7959 (56*2π)/3677 weeks
57-237.0547 -115.5631 (57*2π)/3676 weeks
58-227.5048 -159.0577 (58*2π)/3676 weeks
59-129.5128 -174.7598 (59*2π)/3676 weeks
60-64.66866 -137.754 (60*2π)/3676 weeks
61-129.7458 -194.3397 (61*2π)/3676 weeks
62-94.51275 -232.6162 (62*2π)/3676 weeks
63-85.74333 -215.4261 (63*2π)/3676 weeks
64-195.0481 -224.813 (64*2π)/3676 weeks
65-147.1574 -208.6943 (65*2π)/3676 weeks
66-147.5177 -149.1595 (66*2π)/3676 weeks
67-150.3727 -145.7018 (67*2π)/3675 weeks
68-120.763 -150.052 (68*2π)/3675 weeks
69-130.6538 -157.5953 (69*2π)/3675 weeks
70-140.0008 -64.62211 (70*2π)/3675 weeks
71-101.5419 -131.2494 (71*2π)/3675 weeks
72-52.0568 -157.5804 (72*2π)/3675 weeks
73-52.64692 -164.0511 (73*2π)/3675 weeks
74-171.2768 -198.8747 (74*2π)/3675 weeks
75-77.24338 -123.1413 (75*2π)/3675 weeks
76-82.03396 -154.8934 (76*2π)/3675 weeks
77-87.64725 -175.4704 (77*2π)/3675 weeks
78-121.6721 -218.5773 (78*2π)/3675 weeks
79-168.7736 -108.1432 (79*2π)/3675 weeks
80-55.51004 -131.592 (80*2π)/3675 weeks
81-103.9788 -205.1984 (81*2π)/3675 weeks
82-91.28847 -127.473 (82*2π)/3674 weeks
83-120.0714 -117.3016 (83*2π)/3674 weeks
84-86.95335 -105.5743 (84*2π)/3674 weeks
85-78.92966 -90.13781 (85*2π)/3674 weeks
86-77.50708 -150.6058 (86*2π)/3674 weeks
87-75.74347 -120.6656 (87*2π)/3674 weeks
88-75.23326 -147.4583 (88*2π)/3674 weeks
89-16.45811 -170.7532 (89*2π)/3674 weeks
90-85.86867 -183.4496 (90*2π)/3674 weeks
91-105.4777 -147.7236 (91*2π)/3674 weeks
92-81.1243 -147.6276 (92*2π)/3674 weeks
93-129.3137 -171.9198 (93*2π)/3674 weeks
94-138.3686 -147.8327 (94*2π)/3674 weeks
95-141.0391 -131.2415 (95*2π)/3674 weeks
96-108.8341 -120.2483 (96*2π)/3674 weeks
97-71.3754 -136.8185 (97*2π)/3674 weeks
98-85.05959 -187.4735 (98*2π)/3674 weeks
99-106.6316 -144.8682 (99*2π)/3674 weeks
100-108.0375 -154.4575 (100*2π)/3674 weeks
101-88.58881 -173.333 (101*2π)/3674 weeks
102-82.30927 -149.7205 (102*2π)/3674 weeks
103-134.5297 -145.5264 (103*2π)/3674 weeks
104-103.8375 -120.5058 (104*2π)/3674 weeks
105-82.38479 -127.364 (105*2π)/3673 weeks
106-120.8034 -126.0314 (106*2π)/3673 weeks
107-125.3414 -137.8629 (107*2π)/3673 weeks
108-122.2035 -131.6489 (108*2π)/3673 weeks
109-96.103 -141.5379 (109*2π)/3673 weeks
110-106.9346 -165.2422 (110*2π)/3673 weeks
111-114.9387 -146.606 (111*2π)/3673 weeks
112-106.1901 -142.427 (112*2π)/3673 weeks
113-146.707 -160.8252 (113*2π)/3673 weeks
114-144.061 -126.4577 (114*2π)/3673 weeks
115-158.8426 -110.9087 (115*2π)/3673 weeks
116-154.0281 -90.22288 (116*2π)/3673 weeks
117-99.32455 -123.766 (117*2π)/3673 weeks
118-132.2686 -151.1108 (118*2π)/3673 weeks
119-123.4892 -115.2111 (119*2π)/3673 weeks
120-154.6111 -137.3275 (120*2π)/3673 weeks
121-121.8545 -100.9883 (121*2π)/3673 weeks
122-127.6359 -147.1618 (122*2π)/3673 weeks
123-167.068 -126.5095 (123*2π)/3673 weeks
124-148.5996 -111.1 (124*2π)/3673 weeks
125-184.9693 -111.4805 (125*2π)/3673 weeks
126-147.3137 -98.53916 (126*2π)/3673 weeks
127-162.7975 -124.2677 (127*2π)/3673 weeks
128-169.4613 -77.38351 (128*2π)/3673 weeks
129-180.4652 -82.63443 (129*2π)/3673 weeks
130-128.9995 -100.1876 (130*2π)/3673 weeks
131-132.9615 -113.9326 (131*2π)/3673 weeks
132-189.5199 -104.091 (132*2π)/3673 weeks
133-151.9227 -59.77096 (133*2π)/3673 weeks
134-110.9646 -107.1697 (134*2π)/3673 weeks
135-160.0513 -111.7275 (135*2π)/3673 weeks
136-176.2304 -69.0277 (136*2π)/3673 weeks
137-172.3574 -50.44926 (137*2π)/3673 weeks
138-140.3836 -71.90344 (138*2π)/3673 weeks
139-164.3577 -80.31969 (139*2π)/3673 weeks
140-150.2295 -63.48675 (140*2π)/3673 weeks
141-150.1768 -59.13675 (141*2π)/3673 weeks
142-142.5349 -86.03149 (142*2π)/3673 weeks
143-168.4214 -102.3601 (143*2π)/3673 weeks
144-186.689 -69.73473 (144*2π)/3673 weeks
145-177.8318 -25.84284 (145*2π)/3673 weeks
146-175.8437 -59.89223 (146*2π)/3673 weeks
147-155.187 -26.86245 (147*2π)/3672 weeks
148-191.1721 -61.25936 (148*2π)/3672 weeks
149-189.6709 -6.38512 (149*2π)/3672 weeks
150-151.3951 -5.40601 (150*2π)/3672 weeks
151-149.1191 -79.46026 (151*2π)/3672 weeks
152-201.4846 -58.75585 (152*2π)/3672 weeks
153-220.1307 -25.29092 (153*2π)/3672 weeks
154-172.5727 11.77663 (154*2π)/3672 weeks
155-160.638 -28.36541 (155*2π)/3672 weeks
156-172.9164 -27.71135 (156*2π)/3672 weeks
157-163.153 21.17609 (157*2π)/3672 weeks
158-133.4572 -9.18978 (158*2π)/3672 weeks
159-124.7641 -27.26546 (159*2π)/3672 weeks
160-124.9199 -51.54875 (160*2π)/3672 weeks
161-168.4077 -52.81807 (161*2π)/3672 weeks
162-148.9007 -52.89655 (162*2π)/3672 weeks
163-187.067 -56.54016 (163*2π)/3672 weeks
164-196.8625 7.48894 (164*2π)/3672 weeks
165-176.8414 -.13265 (165*2π)/3672 weeks
166-152.7401 37.86651 (166*2π)/3672 weeks
167-167.3275 26.53432 (167*2π)/3672 weeks
168-174.3408 14.45367 (168*2π)/3672 weeks
169-155.7986 78.15376 (169*2π)/3672 weeks
170-121.8525 68.33954 (170*2π)/3672 weeks
171-99.19556 19.73049 (171*2π)/3672 weeks
172-99.96301 -13.94881 (172*2π)/3672 weeks
173-125.5489 -4.02278 (173*2π)/3672 weeks
174-131.2129 24.05209 (174*2π)/3672 weeks
175-112.4655 1.72162 (175*2π)/3672 weeks
176-105.1455 28.85641 (176*2π)/3672 weeks
177-108.7006 1.47639 (177*2π)/3672 weeks
178-113.2855 .39679 (178*2π)/3672 weeks
179-95.54694 .09977 (179*2π)/3672 weeks
180-136.4928 6.81759 (180*2π)/3672 weeks
181-130.0278 4.38572 (181*2π)/3672 weeks
182-106.5199 -16.02562 (182*2π)/3672 weeks
183-116.7518 41.83594 (183*2π)/3672 weeks
184-116.7518 -41.83594 (184*2π)/3672 weeks
185-106.5199 16.02562 (185*2π)/3672 weeks
186-130.0278 -4.38572 (186*2π)/3672 weeks
187-136.4928 -6.81759 (187*2π)/3672 weeks
188-95.54694 -.09977 (188*2π)/3672 weeks
189-113.2855 -.39679 (189*2π)/3672 weeks
190-108.7006 -1.47639 (190*2π)/3672 weeks
191-105.1455 -28.85641 (191*2π)/3672 weeks
192-112.4655 -1.72162 (192*2π)/3672 weeks
193-131.2129 -24.05209 (193*2π)/3672 weeks
194-125.5489 4.02278 (194*2π)/3672 weeks
195-99.96301 13.94881 (195*2π)/3672 weeks
196-99.19556 -19.73049 (196*2π)/3672 weeks
197-121.8525 -68.33954 (197*2π)/3672 weeks
198-155.7986 -78.15376 (198*2π)/3672 weeks
199-174.3408 -14.45367 (199*2π)/3672 weeks
200-167.3275 -26.53432 (200*2π)/3672 weeks
201-152.7401 -37.86651 (201*2π)/3672 weeks
202-176.8414 .13265 (202*2π)/3672 weeks
203-196.8625 -7.48894 (203*2π)/3672 weeks
204-187.067 56.54016 (204*2π)/3672 weeks
205-148.9007 52.89655 (205*2π)/3672 weeks
206-168.4077 52.81807 (206*2π)/3672 weeks
207-124.9199 51.54875 (207*2π)/3672 weeks
208-124.7641 27.26546 (208*2π)/3672 weeks
209-133.4572 9.18978 (209*2π)/3672 weeks
210-163.153 -21.17609 (210*2π)/3672 weeks
211-172.9164 27.71135 (211*2π)/3672 weeks
212-160.638 28.36541 (212*2π)/3672 weeks
213-172.5727 -11.77663 (213*2π)/3672 weeks
214-220.1307 25.29092 (214*2π)/3672 weeks
215-201.4846 58.75585 (215*2π)/3672 weeks
216-149.1191 79.46026 (216*2π)/3672 weeks
217-151.3951 5.40601 (217*2π)/3672 weeks
218-189.6709 6.38512 (218*2π)/3672 weeks
219-191.1721 61.25936 (219*2π)/3672 weeks
220-155.187 26.86245 (220*2π)/3672 weeks
221-175.8437 59.89223 (221*2π)/3672 weeks
222-177.8318 25.84284 (222*2π)/3672 weeks
223-186.689 69.73473 (223*2π)/3672 weeks
224-168.4214 102.3601 (224*2π)/3672 weeks
225-142.5349 86.03149 (225*2π)/3672 weeks
226-150.1768 59.13675 (226*2π)/3672 weeks
227-150.2295 63.48675 (227*2π)/3672 weeks
228-164.3577 80.31969 (228*2π)/3672 weeks
229-140.3836 71.90344 (229*2π)/3672 weeks
230-172.3574 50.44926 (230*2π)/3672 weeks
231-176.2304 69.0277 (231*2π)/3672 weeks
232-160.0513 111.7275 (232*2π)/3672 weeks
233-110.9646 107.1697 (233*2π)/3672 weeks
234-151.9227 59.77096 (234*2π)/3672 weeks
235-189.5199 104.091 (235*2π)/3672 weeks
236-132.9615 113.9326 (236*2π)/3672 weeks
237-128.9995 100.1876 (237*2π)/3672 weeks
238-180.4652 82.63443 (238*2π)/3672 weeks
239-169.4613 77.38351 (239*2π)/3672 weeks
240-162.7975 124.2677 (240*2π)/3672 weeks
241-147.3137 98.53916 (241*2π)/3672 weeks
242-184.9693 111.4805 (242*2π)/3672 weeks
243-148.5996 111.1 (243*2π)/3672 weeks
244-167.068 126.5095 (244*2π)/3672 weeks
245-127.6359 147.1618 (245*2π)/3671 weeks
246-121.8545 100.9883 (246*2π)/3671 weeks
247-154.6111 137.3275 (247*2π)/3671 weeks
248-123.4892 115.2111 (248*2π)/3671 weeks
249-132.2686 151.1108 (249*2π)/3671 weeks
250-99.32455 123.766 (250*2π)/3671 weeks
251-154.0281 90.22288 (251*2π)/3671 weeks
252-158.8426 110.9087 (252*2π)/3671 weeks
253-144.061 126.4577 (253*2π)/3671 weeks
254-146.707 160.8252 (254*2π)/3671 weeks
255-106.1901 142.427 (255*2π)/3671 weeks
256-114.9387 146.606 (256*2π)/3671 weeks
257-106.9346 165.2422 (257*2π)/3671 weeks
258-96.103 141.5379 (258*2π)/3671 weeks
259-122.2035 131.6489 (259*2π)/3671 weeks
260-125.3414 137.8629 (260*2π)/3671 weeks
261-120.8034 126.0314 (261*2π)/3671 weeks
262-82.38479 127.364 (262*2π)/3671 weeks
263-103.8375 120.5058 (263*2π)/3671 weeks
264-134.5297 145.5264 (264*2π)/3671 weeks
265-82.30927 149.7205 (265*2π)/3671 weeks
266-88.58881 173.333 (266*2π)/3671 weeks
267-108.0375 154.4575 (267*2π)/3671 weeks
268-106.6316 144.8682 (268*2π)/3671 weeks
269-85.05959 187.4735 (269*2π)/3671 weeks
270-71.3754 136.8185 (270*2π)/3671 weeks
271-108.8341 120.2483 (271*2π)/3671 weeks
272-141.0391 131.2415 (272*2π)/3671 weeks
273-138.3686 147.8327 (273*2π)/3671 weeks
274-129.3137 171.9198 (274*2π)/3671 weeks
275-81.1243 147.6276 (275*2π)/3671 weeks
276-105.4777 147.7236 (276*2π)/3671 weeks
277-85.86867 183.4496 (277*2π)/3671 weeks
278-16.45811 170.7532 (278*2π)/3671 weeks
279-75.23326 147.4583 (279*2π)/3671 weeks
280-75.74347 120.6656 (280*2π)/3671 weeks
281-77.50708 150.6058 (281*2π)/3671 weeks
282-78.92966 90.13781 (282*2π)/3671 weeks
283-86.95335 105.5743 (283*2π)/3671 weeks
284-120.0714 117.3016 (284*2π)/3671 weeks
285-91.28847 127.473 (285*2π)/3671 weeks
286-103.9788 205.1984 (286*2π)/3671 weeks
287-55.51004 131.592 (287*2π)/3671 weeks
288-168.7736 108.1432 (288*2π)/3671 weeks
289-121.6721 218.5773 (289*2π)/3671 weeks
290-87.64725 175.4704 (290*2π)/3671 weeks
291-82.03396 154.8934 (291*2π)/3671 weeks
292-77.24338 123.1413 (292*2π)/3671 weeks
293-171.2768 198.8747 (293*2π)/3671 weeks
294-52.64692 164.0511 (294*2π)/3671 weeks
295-52.0568 157.5804 (295*2π)/3671 weeks
296-101.5419 131.2494 (296*2π)/3671 weeks
297-140.0008 64.62211 (297*2π)/3671 weeks
298-130.6538 157.5953 (298*2π)/3671 weeks
299-120.763 150.052 (299*2π)/3671 weeks
300-150.3727 145.7018 (300*2π)/3671 weeks
301-147.5177 149.1595 (301*2π)/3671 weeks
302-147.1574 208.6943 (302*2π)/3671 weeks
303-195.0481 224.813 (303*2π)/3671 weeks
304-85.74333 215.4261 (304*2π)/3671 weeks
305-94.51275 232.6162 (305*2π)/3671 weeks
306-129.7458 194.3397 (306*2π)/3671 weeks
307-64.66866 137.754 (307*2π)/3671 weeks
308-129.5128 174.7598 (308*2π)/3671 weeks
309-227.5048 159.0577 (309*2π)/3671 weeks
310-237.0547 115.5631 (310*2π)/3671 weeks
311-164.6582 227.7959 (311*2π)/3671 weeks
312-197.7405 183.967 (312*2π)/3671 weeks
313-312.8058 155.4969 (313*2π)/3671 weeks
314-245.309 284.1392 (314*2π)/3671 weeks
315-197.6454 355.7314 (315*2π)/3671 weeks
316-192.1976 350.7874 (316*2π)/3671 weeks
317-195.6377 303.2054 (317*2π)/3671 weeks
318-160.532 351.8649 (318*2π)/3671 weeks
319-160.3258 343.6219 (319*2π)/3671 weeks
320-106.4971 284.5342 (320*2π)/3671 weeks
321-141.0671 268.5755 (321*2π)/3671 weeks
322-270.9108 370.7575 (322*2π)/3671 weeks
323-202.9048 390.072 (323*2π)/3671 weeks
324-152.1422 466.86 (324*2π)/3671 weeks
325-222.9996 432.8435 (325*2π)/3671 weeks
326-201.3504 493.1693 (326*2π)/3671 weeks
327-140.567 512.2479 (327*2π)/3671 weeks
328-50.75807 489.6593 (328*2π)/3671 weeks
329-157.2947 413.015 (329*2π)/3671 weeks
330-157.5 494.1597 (330*2π)/3671 weeks
331-115.3851 474.3908 (331*2π)/3671 weeks
332-103.1819 496.5377 (332*2π)/3671 weeks
333-187.8635 521.1163 (333*2π)/3671 weeks
334-125.245 569.3188 (334*2π)/3671 weeks
335-62.16127 675.4611 (335*2π)/3671 weeks
336-.8502 644.6469 (336*2π)/3671 weeks
33732.37056 561.4962 (337*2π)/3671 weeks
338-69.74271 665.7624 (338*2π)/3671 weeks
339-83.12125 632.8573 (339*2π)/3671 weeks
340-134.9345 673.3958 (340*2π)/3671 weeks
3413.42569 771.8179 (341*2π)/3671 weeks
342-51.30706 739.6332 (342*2π)/3671 weeks
343-34.39883 735.2306 (343*2π)/3671 weeks
34410.12047 734.2817 (344*2π)/3671 weeks
345-97.04865 923.6118 (345*2π)/3671 weeks
346211.5713 994.4476 (346*2π)/3671 weeks
34772.89753 747.3004 (347*2π)/3671 weeks
348233.6292 899.4629 (348*2π)/3671 weeks
34938.79319 831.5743 (349*2π)/3671 weeks
35094.58797 1,040.574 (350*2π)/3671 weeks
351225.1029 986.2545 (351*2π)/3671 weeks
352261.3588 1,101.313 (352*2π)/3671 weeks
353453.1012 1,188.97 (353*2π)/3671 weeks
354374.6677 1,037.195 (354*2π)/3671 weeks
355872.9362 1,289.544 (355*2π)/3671 weeks
356570.9877 641.2821 (356*2π)/3671 weeks
357269.1919 727.2143 (357*2π)/3671 weeks
358517.1656 1,020.37 (358*2π)/3671 weeks
359-192.7957 1,404.873 (359*2π)/3671 weeks
360239.7811 1,270.586 (360*2π)/3671 weeks
361261.8981 2,393.523 (361*2π)/3671 weeks
362693.9773 2,725.509 (362*2π)/3671 weeks
3631,026.808 2,405.619 (363*2π)/3671 weeks
3641,558.102 3,005.584 (364*2π)/3671 weeks
3652,939.102 4,081.28 (365*2π)/3671 weeks

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