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# Fourier Analysis of SII (SMITH INTL INC)

SII (SMITH INTL INC) appears to have interesting cyclic behaviour every 58 weeks (1252.548*cosine), 38 weeks (1131.591*sine), and 53 weeks (1080.775*sine).

SII (SMITH INTL INC) has an average price of 6,481.19 (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 12/28/2004 to 3/20/2017 for SII (SMITH INTL INC), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06,481.188   0
14,367.184 -10,071.78 (1*2π)/639639 weeks
2-4,160.037 -4,867.022 (2*2π)/639320 weeks
3-2,197.771 -221.2028 (3*2π)/639213 weeks
4-1,725.108 -427.3783 (4*2π)/639160 weeks
5-1,638.944 1,639.051 (5*2π)/639128 weeks
6676.2991 1,840.183 (6*2π)/639107 weeks
7939.2463 809.5362 (7*2π)/63991 weeks
81,363.045 885.0417 (8*2π)/63980 weeks
91,776.087 -161.3456 (9*2π)/63971 weeks
101,037.677 -472.3383 (10*2π)/63964 weeks
111,252.548 -392.0145 (11*2π)/63958 weeks
12896.3655 -1,080.775 (12*2π)/63953 weeks
13185.616 -617.5874 (13*2π)/63949 weeks
14611.351 -232.5174 (14*2π)/63946 weeks
15747.5938 -540.5873 (15*2π)/63943 weeks
16730.5944 -724.1652 (16*2π)/63940 weeks
17366.3716 -1,131.591 (17*2π)/63938 weeks
18-325.3744 -694.183 (18*2π)/63936 weeks
1935.92341 -90.84972 (19*2π)/63934 weeks
20238.4203 -337.0569 (20*2π)/63932 weeks
2166.21786 -109.424 (21*2π)/63930 weeks
22480.9865 27.63711 (22*2π)/63929 weeks
23575.4608 -241.4989 (23*2π)/63928 weeks
24652.2535 -236.7265 (24*2π)/63927 weeks
25787.1428 -578.7688 (25*2π)/63926 weeks
26465.3529 -743.2997 (26*2π)/63925 weeks
27469.3161 -658.5845 (27*2π)/63924 weeks
28346.1758 -908.3578 (28*2π)/63923 weeks
2928.83934 -725.0601 (29*2π)/63922 weeks
30230.5557 -598.8676 (30*2π)/63921 weeks
31121.5017 -874.2869 (31*2π)/63921 weeks
32-195.3139 -735.0129 (32*2π)/63920 weeks
33-230.8701 -538.9156 (33*2π)/63919 weeks
34-268.7776 -314.8772 (34*2π)/63919 weeks
3518.48842 -112.4536 (35*2π)/63918 weeks
36205.4715 -344.8419 (36*2π)/63918 weeks
3776.18884 -380.2319 (37*2π)/63917 weeks
38204.6347 -333.1116 (38*2π)/63917 weeks
39238.4805 -514.2376 (39*2π)/63916 weeks
40176.2149 -589.0483 (40*2π)/63916 weeks
4178.46642 -740.5109 (41*2π)/63916 weeks
42-192.3038 -664.9909 (42*2π)/63915 weeks
43-110.9562 -481.2429 (43*2π)/63915 weeks
44-125.4509 -644.532 (44*2π)/63915 weeks
45-348.2698 -494.1475 (45*2π)/63914 weeks
46-165.9637 -369.8714 (46*2π)/63914 weeks
47-268.639 -560.085 (47*2π)/63914 weeks
48-470.6785 -282.4349 (48*2π)/63913 weeks
49-187.0367 -126.1631 (49*2π)/63913 weeks
50-149.3457 -294.3336 (50*2π)/63913 weeks
51-180.8154 -230.5759 (51*2π)/63913 weeks
52-118.0922 -312.3046 (52*2π)/63912 weeks
53-273.5612 -279.8999 (53*2π)/63912 weeks
54-117.2867 -112.8713 (54*2π)/63912 weeks
553.32478 -364.4176 (55*2π)/63912 weeks
56-267.7823 -421.1715 (56*2π)/63911 weeks
57-266.3303 -222.872 (57*2π)/63911 weeks
58-179.1732 -276.9636 (58*2π)/63911 weeks
59-250.9013 -299.9157 (59*2π)/63911 weeks
60-264.0643 -288.0978 (60*2π)/63911 weeks
61-346.4124 -304.5273 (61*2π)/63910 weeks
62-435.3832 -214.6048 (62*2π)/63910 weeks
63-468.0618 -95.5664 (63*2π)/63910 weeks
64-429.3645 72.64211 (64*2π)/63910 weeks
65-255.916 158.0001 (65*2π)/63910 weeks
66-125.5556 108.1419 (66*2π)/63910 weeks
67-49.15326 35.71633 (67*2π)/63910 weeks
68-46.21797 -69.88315 (68*2π)/6399 weeks
69-82.77975 -87.12985 (69*2π)/6399 weeks
70-49.76434 -163.3657 (70*2π)/6399 weeks
71-222.249 -265.8805 (71*2π)/6399 weeks
72-357.0457 -61.47567 (72*2π)/6399 weeks
73-191.2773 31.8129 (73*2π)/6399 weeks
74-188.6419 -66.64697 (74*2π)/6399 weeks
75-223.1748 -17.00149 (75*2π)/6399 weeks
76-216.1925 -65.34987 (76*2π)/6398 weeks
77-382.3857 11.29151 (77*2π)/6398 weeks
78-281.9625 259.9966 (78*2π)/6398 weeks
79-88.75656 208.632 (79*2π)/6398 weeks
80-102.6196 203.5211 (80*2π)/6398 weeks
8176.67568 246.9238 (81*2π)/6398 weeks
82168.1324 17.33376 (82*2π)/6398 weeks
8326.722 -64.48763 (83*2π)/6398 weeks
8420.37678 -58.48391 (84*2π)/6398 weeks
85-69.70356 -140.5528 (85*2π)/6398 weeks
86-203.8112 -28.63938 (86*2π)/6397 weeks
87-138.2273 105.4171 (87*2π)/6397 weeks
88-46.29122 117.8687 (88*2π)/6397 weeks
8931.12678 80.01139 (89*2π)/6397 weeks
9028.48793 -30.87123 (90*2π)/6397 weeks
91-96.86368 -48.29445 (91*2π)/6397 weeks
92-151.9928 73.48013 (92*2π)/6397 weeks
93-74.09933 184.6702 (93*2π)/6397 weeks
9454.22437 185.1789 (94*2π)/6397 weeks
95103.2607 123.0155 (95*2π)/6397 weeks
96148.8196 112.0249 (96*2π)/6397 weeks
97227.6574 5.68923 (97*2π)/6397 weeks
98139.7807 -115.436 (98*2π)/6397 weeks
9975.52285 -76.69667 (99*2π)/6396 weeks
10087.73373 -120.4697 (100*2π)/6396 weeks
101-29.1162 -126.7216 (101*2π)/6396 weeks
102-19.4495 -14.10052 (102*2π)/6396 weeks
10327.77108 -58.1667 (103*2π)/6396 weeks
104-47.12387 -22.30663 (104*2π)/6396 weeks
10546.1847 51.49004 (105*2π)/6396 weeks
10669.88016 -50.03954 (106*2π)/6396 weeks
107-1.2845 13.29363 (107*2π)/6396 weeks
108139.0389 45.7237 (108*2π)/6396 weeks
109135.7268 -108.7407 (109*2π)/6396 weeks
11033.19971 -64.15472 (110*2π)/6396 weeks
111113.916 -26.87743 (111*2π)/6396 weeks
112116.7266 -96.50117 (112*2π)/6396 weeks
113124.286 -82.41476 (113*2π)/6396 weeks
114170.8603 -183.9692 (114*2π)/6396 weeks
11532.62317 -269.1248 (115*2π)/6396 weeks
116-54.81597 -167.016 (116*2π)/6396 weeks
117-10.01496 -124.4493 (117*2π)/6395 weeks
118-18.69032 -140.0572 (118*2π)/6395 weeks
119-31.70844 -114.0844 (119*2π)/6395 weeks
120-18.43729 -106.4822 (120*2π)/6395 weeks
121-34.37764 -108.0562 (121*2π)/6395 weeks
122-44.64241 -57.90011 (122*2π)/6395 weeks
12332.43518 -24.16179 (123*2π)/6395 weeks
12480.2659 -102.6133 (124*2π)/6395 weeks
12530.01566 -126.2053 (125*2π)/6395 weeks
12672.90149 -111.2319 (126*2π)/6395 weeks
12773.711 -217.7291 (127*2π)/6395 weeks
128-29.61884 -218.2012 (128*2π)/6395 weeks
129-6.34818 -197.555 (129*2π)/6395 weeks
130-88.04538 -275.7151 (130*2π)/6395 weeks
131-201.6891 -139.2301 (131*2π)/6395 weeks
132-68.04694 -60.71783 (132*2π)/6395 weeks
133-78.92177 -165.6478 (133*2π)/6395 weeks
134-142.0364 -78.88411 (134*2π)/6395 weeks
135-38.60159 -82.79768 (135*2π)/6395 weeks
136-129.2511 -153.1089 (136*2π)/6395 weeks
137-149.0898 4.44195 (137*2π)/6395 weeks
13817.65777 -21.17295 (138*2π)/6395 weeks
139-37.43988 -134.4799 (139*2π)/6395 weeks
140-61.08106 -71.16155 (140*2π)/6395 weeks
141-7.06563 -131.9181 (141*2π)/6395 weeks
142-105.279 -163.1836 (142*2π)/6395 weeks
143-95.40405 -88.23793 (143*2π)/6394 weeks
144-71.98906 -156.8592 (144*2π)/6394 weeks
145-187.5744 -146.8774 (145*2π)/6394 weeks
146-170.7175 -33.07669 (146*2π)/6394 weeks
147-102.2125 -59.90447 (147*2π)/6394 weeks
148-155.075 -87.89613 (148*2π)/6394 weeks
149-176.4079 -22.55841 (149*2π)/6394 weeks
150-137.9715 -1.55139 (150*2π)/6394 weeks
151-151.7331 4.68972 (151*2π)/6394 weeks
152-125.5365 82.02184 (152*2π)/6394 weeks
153-3.21347 68.69355 (153*2π)/6394 weeks
154-1.15187 -44.93369 (154*2π)/6394 weeks
155-58.67078 -36.91482 (155*2π)/6394 weeks
156-17.27489 -50.83904 (156*2π)/6394 weeks
157-82.48974 -122.9963 (157*2π)/6394 weeks
158-150.1029 -50.34786 (158*2π)/6394 weeks
159-109.2788 -40.96592 (159*2π)/6394 weeks
160-191.1066 -42.44818 (160*2π)/6394 weeks
161-172.0029 104.4973 (161*2π)/6394 weeks
162-35.31592 76.7639 (162*2π)/6394 weeks
163-78.38588 17.20605 (163*2π)/6394 weeks
164-44.91603 73.23061 (164*2π)/6394 weeks
165-7.24995 -31.25454 (165*2π)/6394 weeks
166-155.4028 -18.44076 (166*2π)/6394 weeks
167-97.65464 142.238 (167*2π)/6394 weeks
16826.90655 75.54649 (168*2π)/6394 weeks
169-24.596 36.47467 (169*2π)/6394 weeks
17031.14734 77.43267 (170*2π)/6394 weeks
17172.72888 -30.4362 (171*2π)/6394 weeks
172-26.17255 -68.01682 (172*2π)/6394 weeks
173-44.86551 -16.72726 (173*2π)/6394 weeks
174-44.06692 -26.53749 (174*2π)/6394 weeks
175-78.30379 1.3841 (175*2π)/6394 weeks
176-48.61638 41.79517 (176*2π)/6394 weeks
177-27.14165 20.89293 (177*2π)/6394 weeks
178-51.33921 31.33448 (178*2π)/6394 weeks
179-21.36886 70.09608 (179*2π)/6394 weeks
18013.24078 40.42823 (180*2π)/6394 weeks
181-20.96855 49.01102 (181*2π)/6394 weeks
18245.18615 113.4667 (182*2π)/6394 weeks
183141.1635 20.94853 (183*2π)/6393 weeks
18463.95538 -57.13155 (184*2π)/6393 weeks
18565.72375 -3.49906 (185*2π)/6393 weeks
186115.0193 -97.37622 (186*2π)/6393 weeks
187-18.19802 -147.6256 (187*2π)/6393 weeks
188-42.82448 -49.39285 (188*2π)/6393 weeks
189-25.33207 -82.52818 (189*2π)/6393 weeks
190-120.5499 -19.61945 (190*2π)/6393 weeks
191-12.52926 104.0689 (191*2π)/6393 weeks
19283.59567 -1.54767 (192*2π)/6393 weeks
19314.64187 -21.22916 (193*2π)/6393 weeks
19481.40997 2.78241 (194*2π)/6393 weeks
19566.90294 -112.4172 (195*2π)/6393 weeks
196-39.50599 -63.29335 (196*2π)/6393 weeks
19738.18195 -.68744 (197*2π)/6393 weeks
19852.30315 -81.79313 (198*2π)/6393 weeks
1991.73129 -50.18761 (199*2π)/6393 weeks
20078.82361 -37.86576 (200*2π)/6393 weeks
20180.96114 -142.2729 (201*2π)/6393 weeks
202-5.04744 -161.1855 (202*2π)/6393 weeks
203-30.26473 -134.8762 (203*2π)/6393 weeks
204-62.92267 -137.8611 (204*2π)/6393 weeks
205-109.9814 -82.48754 (205*2π)/6393 weeks
206-63.42704 -11.54697 (206*2π)/6393 weeks
207-4.02311 -46.54255 (207*2π)/6393 weeks
208-41.98681 -69.15492 (208*2π)/6393 weeks
209-23.37773 -19.44371 (209*2π)/6393 weeks
21027.62115 -64.22581 (210*2π)/6393 weeks
211-17.89433 -86.44487 (211*2π)/6393 weeks
21220.09011 -58.16162 (212*2π)/6393 weeks
21328.8304 -157.2833 (213*2π)/6393 weeks
214-87.64618 -145.0424 (214*2π)/6393 weeks
215-39.9369 -68.99383 (215*2π)/6393 weeks
216-29.78258 -159.069 (216*2π)/6393 weeks
217-128.8845 -117.4914 (217*2π)/6393 weeks
218-56.09357 -73.4094 (218*2π)/6393 weeks
219-107.3596 -169.4063 (219*2π)/6393 weeks
220-211.5239 -42.59538 (220*2π)/6393 weeks
221-67.17295 31.85718 (221*2π)/6393 weeks
222-59.26801 -79.52116 (222*2π)/6393 weeks
223-112.8234 -19.85807 (223*2π)/6393 weeks
224-22.4878 -30.06091 (224*2π)/6393 weeks
225-87.71378 -104.0671 (225*2π)/6393 weeks
226-112.2587 -8.46367 (226*2π)/6393 weeks
227-18.06528 -42.63316 (227*2π)/6393 weeks
228-95.49081 -108.9893 (228*2π)/6393 weeks
229-117.2219 -18.11281 (229*2π)/6393 weeks
230-35.34982 -43.41497 (230*2π)/6393 weeks
231-86.8754 -109.4476 (231*2π)/6393 weeks
232-128.4575 -67.84109 (232*2π)/6393 weeks
233-114.508 -71.93839 (233*2π)/6393 weeks
234-174.2587 -79.63982 (234*2π)/6393 weeks
235-206.1284 7.403 (235*2π)/6393 weeks
236-139.3896 54.25996 (236*2π)/6393 weeks
237-125.9843 25.54404 (237*2π)/6393 weeks
238-141.8107 80.27274 (238*2π)/6393 weeks
239-36.99074 109.9741 (239*2π)/6393 weeks
240-4.36533 7.44883 (240*2π)/6393 weeks
241-61.96916 10.31355 (241*2π)/6393 weeks
242.6275 11.28172 (242*2π)/6393 weeks
243-43.82906 -94.37766 (243*2π)/6393 weeks
244-140.8863 -21.84558 (244*2π)/6393 weeks
245-50.68925 11.16901 (245*2π)/6393 weeks
246-100.8615 -93.06795 (246*2π)/6393 weeks
247-203.365 3.52819 (247*2π)/6393 weeks
248-124.4953 60.57034 (248*2π)/6393 weeks
249-160.7635 34.55256 (249*2π)/6393 weeks
250-148.9534 162.4197 (250*2π)/6393 weeks
251.57798 140.4956 (251*2π)/6393 weeks
252-32.71254 54.93258 (252*2π)/6393 weeks
253-23.45053 117.7706 (253*2π)/6393 weeks
25460.28346 49.12313 (254*2π)/6393 weeks
255-14.90079 -10.29158 (255*2π)/6393 weeks
256-6.50733 45.49203 (256*2π)/6392 weeks
25732.38527 -33.58118 (257*2π)/6392 weeks
258-80.11485 -64.56107 (258*2π)/6392 weeks
259-102.9649 32.09875 (259*2π)/6392 weeks
260-54.21984 36.20232 (260*2π)/6392 weeks
261-80.04472 34.86283 (261*2π)/6392 weeks
262-60.19485 85.75484 (262*2π)/6392 weeks
263-10.32557 67.72079 (263*2π)/6392 weeks
264-29.54255 46.48912 (264*2π)/6392 weeks
265-18.26557 82.7879 (265*2π)/6392 weeks
26631.16913 53.39634 (266*2π)/6392 weeks
267-13.18984 19.19066 (267*2π)/6392 weeks
268-11.25775 93.44488 (268*2π)/6392 weeks
26993.74207 64.76949 (269*2π)/6392 weeks
27058.78914 -33.94141 (270*2π)/6392 weeks
27117.27402 4.78898 (271*2π)/6392 weeks
27269.56905 -29.53909 (272*2π)/6392 weeks
273-13.35399 -88.0183 (273*2π)/6392 weeks
274-45.65024 -2.20003 (274*2π)/6392 weeks
27510.37849 -27.31771 (275*2π)/6392 weeks
276-73.20569 -43.06196 (276*2π)/6392 weeks
277-53.59234 64.48418 (277*2π)/6392 weeks
27825.76758 19.33004 (278*2π)/6392 weeks
279-37.64713 8.19065 (279*2π)/6392 weeks
28020.09285 82.27348 (280*2π)/6392 weeks
28183.49693 -5.71176 (281*2π)/6392 weeks
2828.60737 -22.08314 (282*2π)/6392 weeks
28361.89109 27.79414 (283*2π)/6392 weeks
284100.6509 -72.08812 (284*2π)/6392 weeks
28511.36777 -102.79 (285*2π)/6392 weeks
28610.41201 -64.40977 (286*2π)/6392 weeks
2876.75421 -109.1657 (287*2π)/6392 weeks
288-63.5932 -98.04568 (288*2π)/6392 weeks
289-61.12216 -45.03595 (289*2π)/6392 weeks
290-53.23946 -53.94373 (290*2π)/6392 weeks
291-90.41057 -21.43675 (291*2π)/6392 weeks
292-41.36618 47.55663 (292*2π)/6392 weeks
29339.27617 4.35909 (293*2π)/6392 weeks
29411.58392 -53.04527 (294*2π)/6392 weeks
29510.06355 -35.65281 (295*2π)/6392 weeks
29628.58695 -99.00783 (296*2π)/6392 weeks
297-77.14304 -119.6086 (297*2π)/6392 weeks
298-85.19674 -9.62645 (298*2π)/6392 weeks
299-3.53425 -25.7544 (299*2π)/6392 weeks
300-32.7926 -54.39892 (300*2π)/6392 weeks
30112.18714 -35.93873 (301*2π)/6392 weeks
3029.4581 -155.1137 (302*2π)/6392 weeks
303-141.7048 -137.0724 (303*2π)/6392 weeks
304-107.8095 -26.25844 (304*2π)/6392 weeks
305-89.62865 -89.97318 (305*2π)/6392 weeks
306-185.1531 -19.64618 (306*2π)/6392 weeks
307-72.39384 77.05682 (307*2π)/6392 weeks
308-21.16782 -30.21032 (308*2π)/6392 weeks
309-95.60402 -9.83136 (309*2π)/6392 weeks
310-15.88937 24.46459 (310*2π)/6392 weeks
311-15.46372 -73.12566 (311*2π)/6392 weeks
312-81.19468 -51.33439 (312*2π)/6392 weeks
313-44.26844 -51.09869 (313*2π)/6392 weeks
314-106.3838 -100.5053 (314*2π)/6392 weeks
315-156.8545 -12.17324 (315*2π)/6392 weeks
316-79.76602 14.25414 (316*2π)/6392 weeks
317-96.88596 -39.86596 (317*2π)/6392 weeks
318-134.3034 15.15028 (318*2π)/6392 weeks
319-62.76863 37.10086 (319*2π)/6392 weeks
320-62.76863 -37.10086 (320*2π)/6392 weeks
321-134.3034 -15.15028 (321*2π)/6392 weeks
322-96.88596 39.86596 (322*2π)/6392 weeks
323-79.76602 -14.25414 (323*2π)/6392 weeks
324-156.8545 12.17324 (324*2π)/6392 weeks
325-106.3838 100.5053 (325*2π)/6392 weeks
326-44.26844 51.09869 (326*2π)/6392 weeks
327-81.19468 51.33439 (327*2π)/6392 weeks
328-15.46372 73.12566 (328*2π)/6392 weeks
329-15.88937 -24.46459 (329*2π)/6392 weeks
330-95.60402 9.83136 (330*2π)/6392 weeks
331-21.16782 30.21032 (331*2π)/6392 weeks
332-72.39384 -77.05682 (332*2π)/6392 weeks
333-185.1531 19.64618 (333*2π)/6392 weeks
334-89.62865 89.97318 (334*2π)/6392 weeks
335-107.8095 26.25844 (335*2π)/6392 weeks
336-141.7048 137.0724 (336*2π)/6392 weeks
3379.4581 155.1137 (337*2π)/6392 weeks
33812.18714 35.93873 (338*2π)/6392 weeks
339-32.7926 54.39892 (339*2π)/6392 weeks
340-3.53425 25.7544 (340*2π)/6392 weeks
341-85.19674 9.62645 (341*2π)/6392 weeks
342-77.14304 119.6086 (342*2π)/6392 weeks
34328.58695 99.00783 (343*2π)/6392 weeks
34410.06355 35.65281 (344*2π)/6392 weeks
34511.58392 53.04527 (345*2π)/6392 weeks
34639.27617 -4.35909 (346*2π)/6392 weeks
347-41.36618 -47.55663 (347*2π)/6392 weeks
348-90.41057 21.43675 (348*2π)/6392 weeks
349-53.23946 53.94373 (349*2π)/6392 weeks
350-61.12216 45.03595 (350*2π)/6392 weeks
351-63.5932 98.04568 (351*2π)/6392 weeks
3526.75421 109.1657 (352*2π)/6392 weeks
35310.41201 64.40977 (353*2π)/6392 weeks
35411.36777 102.79 (354*2π)/6392 weeks
355100.6509 72.08812 (355*2π)/6392 weeks
35661.89109 -27.79414 (356*2π)/6392 weeks
3578.60737 22.08314 (357*2π)/6392 weeks
35883.49693 5.71176 (358*2π)/6392 weeks
35920.09285 -82.27348 (359*2π)/6392 weeks
360-37.64713 -8.19065 (360*2π)/6392 weeks
36125.76758 -19.33004 (361*2π)/6392 weeks
362-53.59234 -64.48418 (362*2π)/6392 weeks
363-73.20569 43.06196 (363*2π)/6392 weeks
36410.37849 27.31771 (364*2π)/6392 weeks
365-45.65024 2.20003 (365*2π)/6392 weeks
366-13.35399 88.0183 (366*2π)/6392 weeks
36769.56905 29.53909 (367*2π)/6392 weeks
36817.27402 -4.78898 (368*2π)/6392 weeks
36958.78914 33.94141 (369*2π)/6392 weeks
37093.74207 -64.76949 (370*2π)/6392 weeks
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