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Fourier Analysis of PHMD (PhotoMedex, Inc.)


PHMD (PhotoMedex, Inc.) appears to have interesting cyclic behaviour every 109 weeks (123.4493*cosine), 99 weeks (109.5811*sine), and 38 weeks (56.3483*cosine).

PHMD (PhotoMedex, Inc.) has an average price of 434.54 (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 2/21/1996 to 1/9/2017 for PHMD (PhotoMedex, Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0434.5435   0 
199.28497 529.1394 (1*2π)/10901,090 weeks
2-160.8468 192.2408 (2*2π)/1090545 weeks
3-209.7618 -60.59858 (3*2π)/1090363 weeks
4122.1799 -193.1027 (4*2π)/1090273 weeks
5267.3852 78.45378 (5*2π)/1090218 weeks
633.34595 230.1044 (6*2π)/1090182 weeks
7-111.942 71.63476 (7*2π)/1090156 weeks
8-39.44724 -87.73438 (8*2π)/1090136 weeks
9112.6203 -58.91753 (9*2π)/1090121 weeks
10123.4493 53.88272 (10*2π)/1090109 weeks
1145.36182 109.5811 (11*2π)/109099 weeks
12-2.03592 56.76288 (12*2π)/109091 weeks
1325.45072 23.26156 (13*2π)/109084 weeks
1450.55783 48.29586 (14*2π)/109078 weeks
1536.27748 83.51691 (15*2π)/109073 weeks
16-8.14313 84.83579 (16*2π)/109068 weeks
17-35.44213 50.90535 (17*2π)/109064 weeks
18-30.64723 17.70589 (18*2π)/109061 weeks
19-5.80848 -1.22684 (19*2π)/109057 weeks
2027.32695 11.52752 (20*2π)/109055 weeks
217.8359 53.65008 (21*2π)/109052 weeks
22-11.30533 20.89266 (22*2π)/109050 weeks
23.40119 25.62485 (23*2π)/109047 weeks
24-4.41555 13.66711 (24*2π)/109045 weeks
257.28376 7.11752 (25*2π)/109044 weeks
2615.53163 13.68899 (26*2π)/109042 weeks
2734.35472 24.74701 (27*2π)/109040 weeks
2812.46003 72.6088 (28*2π)/109039 weeks
29-56.34832 48.01815 (29*2π)/109038 weeks
30-34.57741 -27.446 (30*2π)/109036 weeks
3134.37723 -15.65778 (31*2π)/109035 weeks
3230.00437 40.43077 (32*2π)/109034 weeks
33-9.67399 54.09196 (33*2π)/109033 weeks
34-51.0434 21.03156 (34*2π)/109032 weeks
35-17.52837 -35.27076 (35*2π)/109031 weeks
3628.29533 -16.2812 (36*2π)/109030 weeks
3743.13107 14.82333 (37*2π)/109029 weeks
3816.80293 49.46788 (38*2π)/109029 weeks
39-16.28332 35.94705 (39*2π)/109028 weeks
40-15.85455 14.38255 (40*2π)/109027 weeks
41-7.34725 3.70287 (41*2π)/109027 weeks
429.85349 8.24234 (42*2π)/109026 weeks
4311.03169 24.49377 (43*2π)/109025 weeks
44-14.7372 34.783 (44*2π)/109025 weeks
45-22.60474 1.69561 (45*2π)/109024 weeks
46-1.42178 -6.47391 (46*2π)/109024 weeks
4712.5801 .56391 (47*2π)/109023 weeks
4821.37817 21.38666 (48*2π)/109023 weeks
49-3.74242 39.66257 (49*2π)/109022 weeks
50-23.2107 16.35449 (50*2π)/109022 weeks
51-13.32783 .12803 (51*2π)/109021 weeks
524.84273 -5.64005 (52*2π)/109021 weeks
5324.04287 18.92229 (53*2π)/109021 weeks
54-8.33503 45.774 (54*2π)/109020 weeks
55-37.32356 16.89923 (55*2π)/109020 weeks
56-23.78747 -13.37145 (56*2π)/109019 weeks
579.5013 -11.94922 (57*2π)/109019 weeks
5813.61825 15.36783 (58*2π)/109019 weeks
59-10.4457 28.39053 (59*2π)/109018 weeks
60-32.41056 1.15725 (60*2π)/109018 weeks
61-2.07988 -20.96642 (61*2π)/109018 weeks
6218.91548 1.59683 (62*2π)/109018 weeks
635.2621 22.56935 (63*2π)/109017 weeks
64-17.98122 16.54416 (64*2π)/109017 weeks
65-19.25736 -5.92692 (65*2π)/109017 weeks
662.84682 -15.88745 (66*2π)/109017 weeks
6715.55609 4.8466 (67*2π)/109016 weeks
68-.20067 11.42546 (68*2π)/109016 weeks
69.98321 6.92719 (69*2π)/109016 weeks
70-4.91343 6.0151 (70*2π)/109016 weeks
713.33694 2.57349 (71*2π)/109015 weeks
72-2.06367 8.66705 (72*2π)/109015 weeks
731.50071 2.83426 (73*2π)/109015 weeks
74.61251 10.28239 (74*2π)/109015 weeks
75-1.71445 5.86534 (75*2π)/109015 weeks
76-1.62949 8.98893 (76*2π)/109014 weeks
77-4.9804 4.95535 (77*2π)/109014 weeks
78-3.02782 4.99506 (78*2π)/109014 weeks
79-3.32533 2.37382 (79*2π)/109014 weeks
801.08382 6.53725 (80*2π)/109014 weeks
81-7.76079 8.45085 (81*2π)/109013 weeks
82-5.78255 -4.32205 (82*2π)/109013 weeks
831.95509 3.4327 (83*2π)/109013 weeks
84-2.33685 -1.64673 (84*2π)/109013 weeks
852.45718 3.66546 (85*2π)/109013 weeks
86-1.76997 .2145 (86*2π)/109013 weeks
876.46001 1.52308 (87*2π)/109013 weeks
886.39553 8.48644 (88*2π)/109012 weeks
89-2.33375 16.19359 (89*2π)/109012 weeks
90-13.47655 4.60832 (90*2π)/109012 weeks
91-7.95922 -7.36506 (91*2π)/109012 weeks
9210.24893 -6.62371 (92*2π)/109012 weeks
939.21757 12.17074 (93*2π)/109012 weeks
94-8.73125 13.60599 (94*2π)/109012 weeks
95-11.66896 -5.88079 (95*2π)/109011 weeks
966.22063 -7.97691 (96*2π)/109011 weeks
9711.64988 5.60904 (97*2π)/109011 weeks
98-.44314 12.29287 (98*2π)/109011 weeks
99-4.06216 2.17471 (99*2π)/109011 weeks
1001.85083 -.0834 (100*2π)/109011 weeks
1016.52947 9.21436 (101*2π)/109011 weeks
102-3.14217 12.81273 (102*2π)/109011 weeks
103-11.8993 5.73929 (103*2π)/109011 weeks
104-5.81023 -7.23222 (104*2π)/109010 weeks
1055.64535 1.86178 (105*2π)/109010 weeks
106-3.24853 5.04412 (106*2π)/109010 weeks
107-3.29175 .64623 (107*2π)/109010 weeks
108-2.25943 -3.26353 (108*2π)/109010 weeks
1093.42971 -4.90415 (109*2π)/109010 weeks
11011.14323 3.6755 (110*2π)/109010 weeks
1111.45737 10.75435 (111*2π)/109010 weeks
112-4.80791 4.42082 (112*2π)/109010 weeks
113-.57239 -.86536 (113*2π)/109010 weeks
1144.80963 -.30974 (114*2π)/109010 weeks
1159.26214 9.49465 (115*2π)/10909 weeks
116-5.06535 16.62208 (116*2π)/10909 weeks
117-14.25976 4.27702 (117*2π)/10909 weeks
118-8.22965 -9.91542 (118*2π)/10909 weeks
1199.17111 -6.91652 (119*2π)/10909 weeks
1208.99952 9.59905 (120*2π)/10909 weeks
121-5.73346 10.77161 (121*2π)/10909 weeks
122-11.21025 -.86193 (122*2π)/10909 weeks
123.9668 -13.72617 (123*2π)/10909 weeks
12417.97729 1.2738 (124*2π)/10909 weeks
1256.07839 17.71255 (125*2π)/10909 weeks
126-10.82773 12.95626 (126*2π)/10909 weeks
127-12.09872 -5.90836 (127*2π)/10909 weeks
1287.43875 -5.67942 (128*2π)/10909 weeks
1296.43188 9.56665 (129*2π)/10908 weeks
130-6.61351 11.42016 (130*2π)/10908 weeks
131-13.13069 -.8413 (131*2π)/10908 weeks
132-.33051 -11.08226 (132*2π)/10908 weeks
1338.55043 .92633 (133*2π)/10908 weeks
134-.49057 7.81701 (134*2π)/10908 weeks
135-6.82077 .32516 (135*2π)/10908 weeks
136-.36322 -5.19799 (136*2π)/10908 weeks
1374.69218 -1.69542 (137*2π)/10908 weeks
1383.82322 3.64119 (138*2π)/10908 weeks
139.12428 2.9268 (139*2π)/10908 weeks
140-.82574 1.49261 (140*2π)/10908 weeks
1411.52455 -.07571 (141*2π)/10908 weeks
1421.15242 2.25356 (142*2π)/10908 weeks
143.13941 2.68821 (143*2π)/10908 weeks
1441.03879 -.87004 (144*2π)/10908 weeks
1452.46857 4.93781 (145*2π)/10908 weeks
146-3.7882 3.0841 (146*2π)/10907 weeks
147-1.79164 -2.05564 (147*2π)/10907 weeks
1481.41745 -3.07315 (148*2π)/10907 weeks
1496.35028 -1.0438 (149*2π)/10907 weeks
1504.16778 8.08546 (150*2π)/10907 weeks
151-4.64195 6.31772 (151*2π)/10907 weeks
152-6.64852 -2.51802 (152*2π)/10907 weeks
1532.57616 -9.19155 (153*2π)/10907 weeks
15411.75003 .00105 (154*2π)/10907 weeks
1556.163 10.11578 (155*2π)/10907 weeks
156-4.60328 9.98023 (156*2π)/10907 weeks
157-9.78507 -1.91415 (157*2π)/10907 weeks
1581.50939 -6.39758 (158*2π)/10907 weeks
1595.2644 -1.41689 (159*2π)/10907 weeks
1604.13661 3.28823 (160*2π)/10907 weeks
161-.78762 1.83488 (161*2π)/10907 weeks
162.97226 -2.13328 (162*2π)/10907 weeks
1635.51872 -1.53949 (163*2π)/10907 weeks
1646.79578 2.56838 (164*2π)/10907 weeks
1654.29567 6.92725 (165*2π)/10907 weeks
166-.43464 5.6207 (166*2π)/10907 weeks
167-1.10259 3.82298 (167*2π)/10907 weeks
168.57156 -1.33499 (168*2π)/10906 weeks
1697.42119 2.96549 (169*2π)/10906 weeks
170.60836 11.36914 (170*2π)/10906 weeks
171-7.38512 5.39002 (171*2π)/10906 weeks
172-6.32738 -2.20031 (172*2π)/10906 weeks
1733.37728 -5.79514 (173*2π)/10906 weeks
1746.9854 5.20339 (174*2π)/10906 weeks
175-3.52921 8.7882 (175*2π)/10906 weeks
176-8.98436 -.93535 (176*2π)/10906 weeks
177.19853 -8.7753 (177*2π)/10906 weeks
1789.28766 -2.02361 (178*2π)/10906 weeks
1795.95337 7.82669 (179*2π)/10906 weeks
180-3.12212 6.41283 (180*2π)/10906 weeks
181-4.22121 .3507 (181*2π)/10906 weeks
1821.86738 -2.68731 (182*2π)/10906 weeks
1833.15522 4.36233 (183*2π)/10906 weeks
184-3.07022 3.75683 (184*2π)/10906 weeks
185-4.56463 -.84629 (185*2π)/10906 weeks
1861.212 -5.64773 (186*2π)/10906 weeks
1875.8496 .77268 (187*2π)/10906 weeks
188.08273 3.61778 (188*2π)/10906 weeks
189-1.21164 -.42836 (189*2π)/10906 weeks
1901.47433 -1.47634 (190*2π)/10906 weeks
1914.7839 .2836 (191*2π)/10906 weeks
1922.36951 5.16153 (192*2π)/10906 weeks
193-3.81211 2.03386 (193*2π)/10906 weeks
194-.80816 -2.50173 (194*2π)/10906 weeks
1953.05683 -1.64026 (195*2π)/10906 weeks
1963.67058 2.71209 (196*2π)/10906 weeks
197-2.00032 3.09367 (197*2π)/10906 weeks
198-3.07407 -3.00854 (198*2π)/10906 weeks
1992.36418 -5.7389 (199*2π)/10905 weeks
2008.00839 -2.91447 (200*2π)/10905 weeks
2017.62775 5.09783 (201*2π)/10905 weeks
202-.60852 5.08309 (202*2π)/10905 weeks
203-.57489 -.17595 (203*2π)/10905 weeks
2042.03037 -1.39467 (204*2π)/10905 weeks
2055.5424 -.48145 (205*2π)/10905 weeks
2063.63149 4.98672 (206*2π)/10905 weeks
207.17748 1.7091 (207*2π)/10905 weeks
208.59308 1.32477 (208*2π)/10905 weeks
2092.00608 -2.45879 (209*2π)/10905 weeks
2106.23378 -.13136 (210*2π)/10905 weeks
2115.21647 5.35326 (211*2π)/10905 weeks
212-.01281 3.87866 (212*2π)/10905 weeks
213.4787 .53444 (213*2π)/10905 weeks
2144.62858 -1.9316 (214*2π)/10905 weeks
2157.87118 3.71873 (215*2π)/10905 weeks
2163.86184 7.76715 (216*2π)/10905 weeks
217-.80555 6.59625 (217*2π)/10905 weeks
218-1.52922 2.16699 (218*2π)/10905 weeks
2192.4246 1.75488 (219*2π)/10905 weeks
2201.78924 4.64195 (220*2π)/10905 weeks
221-.16846 4.17395 (221*2π)/10905 weeks
222-1.1659 4.07282 (222*2π)/10905 weeks
223-2.26476 .91583 (223*2π)/10905 weeks
224.7163 -.74067 (224*2π)/10905 weeks
2253.67995 .16135 (225*2π)/10905 weeks
2264.14963 5.55412 (226*2π)/10905 weeks
227-.63433 6.9536 (227*2π)/10905 weeks
228-3.60514 4.04806 (228*2π)/10905 weeks
229-3.89575 .53222 (229*2π)/10905 weeks
230.50312 -2.16465 (230*2π)/10905 weeks
2311.61793 2.58472 (231*2π)/10905 weeks
232-1.62329 2.15129 (232*2π)/10905 weeks
233-1.05112 -1.05562 (233*2π)/10905 weeks
2341.58445 -.21156 (234*2π)/10905 weeks
2352.21309 .3576 (235*2π)/10905 weeks
2362.36583 3.1606 (236*2π)/10905 weeks
237-1.26461 3.21335 (237*2π)/10905 weeks
238-.76436 -.72251 (238*2π)/10905 weeks
2391.2447 1.508 (239*2π)/10905 weeks
240-.25301 -.2946 (240*2π)/10905 weeks
2413.54053 1.07255 (241*2π)/10905 weeks
242.8341 4.38291 (242*2π)/10905 weeks
243-2.48922 2.05024 (243*2π)/10904 weeks
244-.87249 -.32883 (244*2π)/10904 weeks
245.99312 .34801 (245*2π)/10904 weeks
246-.72445 1.70569 (246*2π)/10904 weeks
247-2.95198 -1.23235 (247*2π)/10904 weeks
2481.65064 -6.00588 (248*2π)/10904 weeks
2497.11071 .19407 (249*2π)/10904 weeks
2504.2796 3.86374 (250*2π)/10904 weeks
251-.86113 5.11448 (251*2π)/10904 weeks
252-1.80674 -1.58791 (252*2π)/10904 weeks
2535.03004 -1.35302 (253*2π)/10904 weeks
2543.43131 6.24807 (254*2π)/10904 weeks
255-3.38977 4.15417 (255*2π)/10904 weeks
256-4.01507 -.88492 (256*2π)/10904 weeks
257.59874 -4.77536 (257*2π)/10904 weeks
2585.68804 -1.34854 (258*2π)/10904 weeks
2593.63107 4.40405 (259*2π)/10904 weeks
260-.93728 2.19459 (260*2π)/10904 weeks
261.21655 .74589 (261*2π)/10904 weeks
262.339 -.26824 (262*2π)/10904 weeks
2632.3115 -.75047 (263*2π)/10904 weeks
2642.46768 1.49679 (264*2π)/10904 weeks
265.89852 1.40472 (265*2π)/10904 weeks
266.80534 1.82319 (266*2π)/10904 weeks
267-1.36984 .39967 (267*2π)/10904 weeks
2681.18291 -3.73582 (268*2π)/10904 weeks
2695.69774 -1.0095 (269*2π)/10904 weeks
2704.53283 3.57203 (270*2π)/10904 weeks
2711.45552 3.87325 (271*2π)/10904 weeks
272-1.8064 1.80869 (272*2π)/10904 weeks
273.45304 -2.22437 (273*2π)/10904 weeks
2743.66499 -.88607 (274*2π)/10904 weeks
2753.87541 2.58252 (275*2π)/10904 weeks
2761.2121 2.20408 (276*2π)/10904 weeks
277.64701 .54919 (277*2π)/10904 weeks
2783.43404 -1.03237 (278*2π)/10904 weeks
2793.16948 2.2001 (279*2π)/10904 weeks
2803.12053 .70099 (280*2π)/10904 weeks
2813.68127 3.85151 (281*2π)/10904 weeks
282.42526 2.94462 (282*2π)/10904 weeks
283.77151 .86267 (283*2π)/10904 weeks
2842.48417 -.45721 (284*2π)/10904 weeks
2855.8102 1.44802 (285*2π)/10904 weeks
2864.34007 6.84113 (286*2π)/10904 weeks
287-1.94282 5.15048 (287*2π)/10904 weeks
288-1.01263 1.06644 (288*2π)/10904 weeks
2891.04246 -1.26169 (289*2π)/10904 weeks
2906.44931 .9396 (290*2π)/10904 weeks
2914.05691 8.21005 (291*2π)/10904 weeks
292-2.77997 6.44293 (292*2π)/10904 weeks
293-4.33267 1.50825 (293*2π)/10904 weeks
294.93171 -3.39308 (294*2π)/10904 weeks
2956.61218 2.37706 (295*2π)/10904 weeks
2961.63409 8.64807 (296*2π)/10904 weeks
297-5.94112 5.29682 (297*2π)/10904 weeks
298-5.11365 -2.83262 (298*2π)/10904 weeks
2993.36485 -4.46014 (299*2π)/10904 weeks
3006.10395 3.22059 (300*2π)/10904 weeks
3011.07308 7.11523 (301*2π)/10904 weeks
302-5.26574 3.37133 (302*2π)/10904 weeks
303-2.59591 -2.73925 (303*2π)/10904 weeks
3042.47215 -2.49948 (304*2π)/10904 weeks
3054.61758 1.79841 (305*2π)/10904 weeks
3061.34047 5.53772 (306*2π)/10904 weeks
307-3.68603 2.90574 (307*2π)/10904 weeks
308-1.85499 -2.32728 (308*2π)/10904 weeks
3092.5258 -1.35706 (309*2π)/10904 weeks
3102.25431 1.31168 (310*2π)/10904 weeks
311.61917 2.00759 (311*2π)/10904 weeks
312-.31477 .17073 (312*2π)/10903 weeks
3131.84811 -1.24928 (313*2π)/10903 weeks
3143.41994 .67469 (314*2π)/10903 weeks
3151.66139 2.15508 (315*2π)/10903 weeks
3161.31714 .6872 (316*2π)/10903 weeks
3172.94008 .60219 (317*2π)/10903 weeks
3183.27084 2.51621 (318*2π)/10903 weeks
3191.97072 2.68436 (319*2π)/10903 weeks
3201.62457 2.82978 (320*2π)/10903 weeks
3212.04192 2.55439 (321*2π)/10903 weeks
322.59826 3.66022 (322*2π)/10903 weeks
323.24715 2.4807 (323*2π)/10903 weeks
324-.55746 1.32231 (324*2π)/10903 weeks
3251.66712 -.34422 (325*2π)/10903 weeks
3264.40371 2.15983 (326*2π)/10903 weeks
3271.60296 4.77555 (327*2π)/10903 weeks
3281.73522 3.25831 (328*2π)/10903 weeks
329.21639 4.69201 (329*2π)/10903 weeks
330-.34423 2.76691 (330*2π)/10903 weeks
3311.14501 4.10072 (331*2π)/10903 weeks
332-1.91265 4.25748 (332*2π)/10903 weeks
333-1.28883 2.79195 (333*2π)/10903 weeks
334-3.36005 1.36846 (334*2π)/10903 weeks
335.11354 -.41247 (335*2π)/10903 weeks
3361.89075 1.38036 (336*2π)/10903 weeks
3371.49155 3.82021 (337*2π)/10903 weeks
338-2.12138 4.54492 (338*2π)/10903 weeks
339-3.15227 1.56094 (339*2π)/10903 weeks
340-1.71257 -.50661 (340*2π)/10903 weeks
3411.57203 .33518 (341*2π)/10903 weeks
342.25658 3.28279 (342*2π)/10903 weeks
343-1.55486 1.86314 (343*2π)/10903 weeks
344-1.24733 2.19273 (344*2π)/10903 weeks
345-2.44147 .84537 (345*2π)/10903 weeks
346-1.04812 -.41356 (346*2π)/10903 weeks
347-.17694 .92817 (347*2π)/10903 weeks
348-1.66762 -.27552 (348*2π)/10903 weeks
3491.0759 -.25577 (349*2π)/10903 weeks
350-1.05157 .92361 (350*2π)/10903 weeks
351.70809 -1.55679 (351*2π)/10903 weeks
3522.83485 1.26016 (352*2π)/10903 weeks
353.73131 3.51262 (353*2π)/10903 weeks
354-2.38135 2.96914 (354*2π)/10903 weeks
355-2.7401 -1.04632 (355*2π)/10903 weeks
3561.25286 -2.43215 (356*2π)/10903 weeks
3573.92192 2.56474 (357*2π)/10903 weeks
358-1.92973 4.89495 (358*2π)/10903 weeks
359-5.11186 .44177 (359*2π)/10903 weeks
360-.78344 -3.94766 (360*2π)/10903 weeks
3612.75816 -1.63452 (361*2π)/10903 weeks
3623.31518 2.46343 (362*2π)/10903 weeks
363-1.97308 3.56935 (363*2π)/10903 weeks
364-2.7342 -.66038 (364*2π)/10903 weeks
365.60334 -1.85931 (365*2π)/10903 weeks
3661.33428 .06234 (366*2π)/10903 weeks
367.69584 1.50627 (367*2π)/10903 weeks
368-1.93408 .65845 (368*2π)/10903 weeks
369-.00716 -1.88761 (369*2π)/10903 weeks
3702.22233 -1.58277 (370*2π)/10903 weeks
3712.56968 1.84838 (371*2π)/10903 weeks
372-1.11347 2.75645 (372*2π)/10903 weeks
373-2.71122 -1.94491 (373*2π)/10903 weeks
3742.74509 -3.92871 (374*2π)/10903 weeks
3754.93637 .61728 (375*2π)/10903 weeks
3762.17712 3.27123 (376*2π)/10903 weeks
377-.73246 2.43998 (377*2π)/10903 weeks
378.17425 -1.25794 (378*2π)/10903 weeks
3793.72949 .21986 (379*2π)/10903 weeks
3802.27938 3.98815 (380*2π)/10903 weeks
381-1.03138 3.34439 (381*2π)/10903 weeks
382-1.16605 .32296 (382*2π)/10903 weeks
3831.01256 -.07907 (383*2π)/10903 weeks
384.87635 1.96365 (384*2π)/10903 weeks
385.10054 1.73622 (385*2π)/10903 weeks
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