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Fourier Analysis of FLAG (WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF)


FLAG (WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF) appears to have interesting cyclic behaviour every 25 weeks (.7644*sine), 21 weeks (.6521*sine), and 19 weeks (.2813*cosine).

FLAG (WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF) has an average price of 30.98 (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 1/31/2013 to 11/6/2017 for FLAG (WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF WEATHERSTORM FORENSIC ACCOUNTING LONG-SHORT ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
030.9829   0 
1.51296 -3.55233 (1*2π)/250250 weeks
2-.31675 -4.15956 (2*2π)/250125 weeks
3-.82597 -1.58556 (3*2π)/25083 weeks
4.00616 -1.25736 (4*2π)/25063 weeks
5-.15558 -.83516 (5*2π)/25050 weeks
6.15064 -.8985 (6*2π)/25042 weeks
7.10009 -.8298 (7*2π)/25036 weeks
8-.24815 -.82935 (8*2π)/25031 weeks
9-.17836 -.54449 (9*2π)/25028 weeks
10.00481 -.76438 (10*2π)/25025 weeks
11-.14582 -.27327 (11*2π)/25023 weeks
12.23949 -.65207 (12*2π)/25021 weeks
13-.28131 -.52155 (13*2π)/25019 weeks
14-.02549 -.15256 (14*2π)/25018 weeks
15.04792 -.55159 (15*2π)/25017 weeks
16-.08186 -.42867 (16*2π)/25016 weeks
17-.07916 -.46471 (17*2π)/25015 weeks
18-.14553 -.34838 (18*2π)/25014 weeks
19-.09492 -.16328 (19*2π)/25013 weeks
20-.1056 -.26114 (20*2π)/25013 weeks
21.06378 -.32561 (21*2π)/25012 weeks
22-.26236 -.11276 (22*2π)/25011 weeks
23-.17463 -.29895 (23*2π)/25011 weeks
24-.19988 -.13642 (24*2π)/25010 weeks
25-.0729 -.10396 (25*2π)/25010 weeks
26-.04895 -.34417 (26*2π)/25010 weeks
27-.11406 -.19669 (27*2π)/2509 weeks
28-.10147 -.22241 (28*2π)/2509 weeks
29-.1611 -.18116 (29*2π)/2509 weeks
30.11408 -.1972 (30*2π)/2508 weeks
31-.0377 -.11603 (31*2π)/2508 weeks
32-.05254 -.15547 (32*2π)/2508 weeks
33-.00886 -.06706 (33*2π)/2508 weeks
34-.11253 -.17246 (34*2π)/2507 weeks
35-.00311 -.22581 (35*2π)/2507 weeks
36-.11842 -.10661 (36*2π)/2507 weeks
37-.05669 -.16617 (37*2π)/2507 weeks
38-.11636 -.1048 (38*2π)/2507 weeks
39-.07252 -.06507 (39*2π)/2506 weeks
40.01791 -.13879 (40*2π)/2506 weeks
41-.11724 -.12624 (41*2π)/2506 weeks
42-.09105 -.05287 (42*2π)/2506 weeks
43-.02551 -.09191 (43*2π)/2506 weeks
44-.07111 -.16225 (44*2π)/2506 weeks
45-.12106 -.08103 (45*2π)/2506 weeks
46.0484 -.11723 (46*2π)/2505 weeks
47-.1082 -.10081 (47*2π)/2505 weeks
48-.08532 -.05689 (48*2π)/2505 weeks
49-.07026 -.1315 (49*2π)/2505 weeks
50-.09612 -.04882 (50*2π)/2505 weeks
51-.06833 -.06987 (51*2π)/2505 weeks
52-.06925 -.12464 (52*2π)/2505 weeks
53.0168 -.09509 (53*2π)/2505 weeks
54-.08352 -.15503 (54*2π)/2505 weeks
55-.04969 -.03448 (55*2π)/2505 weeks
56-.06375 -.03945 (56*2π)/2504 weeks
57-.14515 -.11672 (57*2π)/2504 weeks
58-.03793 -.04795 (58*2π)/2504 weeks
59-.0684 -.05139 (59*2π)/2504 weeks
60-.12113 -.06386 (60*2π)/2504 weeks
61-.04071 .01403 (61*2π)/2504 weeks
62-.06821 -.10136 (62*2π)/2504 weeks
63-.07989 -.03265 (63*2π)/2504 weeks
64-.04061 -.0997 (64*2π)/2504 weeks
65-.12379 -.0492 (65*2π)/2504 weeks
66-.01261 -.05141 (66*2π)/2504 weeks
67-.09203 -.05965 (67*2π)/2504 weeks
68-.02528 -.08681 (68*2π)/2504 weeks
69-.05886 -.05916 (69*2π)/2504 weeks
70-.10412 -.04749 (70*2π)/2504 weeks
71-.03303 -.04428 (71*2π)/2504 weeks
72-.09314 -.04767 (72*2π)/2503 weeks
73-.05163 -.10514 (73*2π)/2503 weeks
74-.08272 -.08948 (74*2π)/2503 weeks
75-.0764 -.0318 (75*2π)/2503 weeks
76-.05624 -.00779 (76*2π)/2503 weeks
77-.04127 -.06997 (77*2π)/2503 weeks
78-.0835 -.0826 (78*2π)/2503 weeks
79-.07332 -.02215 (79*2π)/2503 weeks
80-.041 -.06267 (80*2π)/2503 weeks
81-.09118 -.036 (81*2π)/2503 weeks
82-.05931 -.06295 (82*2π)/2503 weeks
83-.06241 -.03745 (83*2π)/2503 weeks
84-.04329 -.02424 (84*2π)/2503 weeks
85-.07078 -.04375 (85*2π)/2503 weeks
86-.02769 -.02249 (86*2π)/2503 weeks
87-.07849 -.08183 (87*2π)/2503 weeks
88-.08979 -.00543 (88*2π)/2503 weeks
89-.05632 -.05184 (89*2π)/2503 weeks
90-.11635 -.04414 (90*2π)/2503 weeks
91-.05506 -.0615 (91*2π)/2503 weeks
92-.06588 -.05352 (92*2π)/2503 weeks
93-.08275 -.0364 (93*2π)/2503 weeks
94-.03223 -.07007 (94*2π)/2503 weeks
95-.09608 -.01661 (95*2π)/2503 weeks
96-.07848 -.05298 (96*2π)/2503 weeks
97-.03625 -.04518 (97*2π)/2503 weeks
98-.10206 -.01018 (98*2π)/2503 weeks
99-.07765 .02759 (99*2π)/2503 weeks
100-.06844 -.01426 (100*2π)/2503 weeks
101-.08539 -.03791 (101*2π)/2502 weeks
102-.04672 -.0319 (102*2π)/2502 weeks
103-.08014 .01618 (103*2π)/2502 weeks
104-.03382 -.00573 (104*2π)/2502 weeks
105-.09095 -.00195 (105*2π)/2502 weeks
106-.07024 -.00804 (106*2π)/2502 weeks
107-.04387 .01089 (107*2π)/2502 weeks
108-.07726 .02723 (108*2π)/2502 weeks
109-.07939 -.02816 (109*2π)/2502 weeks
110-.1082 .00654 (110*2π)/2502 weeks
111-.06985 -.01106 (111*2π)/2502 weeks
112-.06127 .02724 (112*2π)/2502 weeks
113-.0995 -.02896 (113*2π)/2502 weeks
114-.03152 -.06214 (114*2π)/2502 weeks
115-.07663 .00936 (115*2π)/2502 weeks
116-.08658 -.01438 (116*2π)/2502 weeks
117-.06443 -.01914 (117*2π)/2502 weeks
118-.03004 -.03764 (118*2π)/2502 weeks
119-.08484 -.05434 (119*2π)/2502 weeks
120-.0868 .05771 (120*2π)/2502 weeks
121-.02544 -.02947 (121*2π)/2502 weeks
122-.07812 .00372 (122*2π)/2502 weeks
123-.00865 -.00091 (123*2π)/2502 weeks
124-.09991 -.01041 (124*2π)/2502 weeks
125-.12502   (125*2π)/2502 weeks
126-.09991 .01041 (126*2π)/2502 weeks
127-.00865 .00091 (127*2π)/2502 weeks
128-.07812 -.00372 (128*2π)/2502 weeks
129-.02544 .02947 (129*2π)/2502 weeks
130-.0868 -.05771 (130*2π)/2502 weeks
131-.08484 .05434 (131*2π)/2502 weeks
132-.03004 .03764 (132*2π)/2502 weeks
133-.06443 .01914 (133*2π)/2502 weeks
134-.08658 .01438 (134*2π)/2502 weeks
135-.07663 -.00936 (135*2π)/2502 weeks
136-.03152 .06214 (136*2π)/2502 weeks
137-.0995 .02896 (137*2π)/2502 weeks
138-.06127 -.02724 (138*2π)/2502 weeks
139-.06985 .01106 (139*2π)/2502 weeks
140-.1082 -.00654 (140*2π)/2502 weeks
141-.07939 .02816 (141*2π)/2502 weeks
142-.07726 -.02723 (142*2π)/2502 weeks
143-.04387 -.01089 (143*2π)/2502 weeks
144-.07024 .00804 (144*2π)/2502 weeks
145-.09095 .00195 (145*2π)/2502 weeks
146-.03382 .00573 (146*2π)/2502 weeks
147-.08014 -.01618 (147*2π)/2502 weeks
148-.04672 .0319 (148*2π)/2502 weeks
149-.08539 .03791 (149*2π)/2502 weeks
150-.06844 .01426 (150*2π)/2502 weeks
151-.07765 -.02759 (151*2π)/2502 weeks
152-.10206 .01018 (152*2π)/2502 weeks
153-.03625 .04518 (153*2π)/2502 weeks
154-.07848 .05298 (154*2π)/2502 weeks
155-.09608 .01661 (155*2π)/2502 weeks
156-.03223 .07007 (156*2π)/2502 weeks
157-.08275 .0364 (157*2π)/2502 weeks
158-.06588 .05352 (158*2π)/2502 weeks
159-.05506 .0615 (159*2π)/2502 weeks
160-.11635 .04414 (160*2π)/2502 weeks
161-.05632 .05184 (161*2π)/2502 weeks
162-.08979 .00543 (162*2π)/2502 weeks
163-.07849 .08183 (163*2π)/2502 weeks
164-.02769 .02249 (164*2π)/2502 weeks
165-.07078 .04375 (165*2π)/2502 weeks
166-.04329 .02424 (166*2π)/2502 weeks
167-.06241 .03745 (167*2π)/2501 weeks
168-.05931 .06295 (168*2π)/2501 weeks
169-.09118 .036 (169*2π)/2501 weeks
170-.041 .06267 (170*2π)/2501 weeks
171-.07332 .02215 (171*2π)/2501 weeks
172-.0835 .0826 (172*2π)/2501 weeks
173-.04127 .06997 (173*2π)/2501 weeks
174-.05624 .00779 (174*2π)/2501 weeks
175-.0764 .0318 (175*2π)/2501 weeks
176-.08272 .08948 (176*2π)/2501 weeks
177-.05163 .10514 (177*2π)/2501 weeks
178-.09314 .04767 (178*2π)/2501 weeks
179-.03303 .04428 (179*2π)/2501 weeks
180-.10412 .04749 (180*2π)/2501 weeks
181-.05886 .05916 (181*2π)/2501 weeks
182-.02528 .08681 (182*2π)/2501 weeks
183-.09203 .05965 (183*2π)/2501 weeks
184-.01261 .05141 (184*2π)/2501 weeks
185-.12379 .0492 (185*2π)/2501 weeks
186-.04061 .0997 (186*2π)/2501 weeks
187-.07989 .03265 (187*2π)/2501 weeks
188-.06821 .10136 (188*2π)/2501 weeks
189-.04071 -.01403 (189*2π)/2501 weeks
190-.12113 .06386 (190*2π)/2501 weeks
191-.0684 .05139 (191*2π)/2501 weeks
192-.03793 .04795 (192*2π)/2501 weeks
193-.14515 .11672 (193*2π)/2501 weeks
194-.06375 .03945 (194*2π)/2501 weeks
195-.04969 .03448 (195*2π)/2501 weeks
196-.08352 .15503 (196*2π)/2501 weeks
197.0168 .09509 (197*2π)/2501 weeks
198-.06925 .12464 (198*2π)/2501 weeks
199-.06833 .06987 (199*2π)/2501 weeks
200-.09612 .04882 (200*2π)/2501 weeks
201-.07026 .1315 (201*2π)/2501 weeks
202-.08532 .05689 (202*2π)/2501 weeks
203-.1082 .10081 (203*2π)/2501 weeks
204.0484 .11723 (204*2π)/2501 weeks
205-.12106 .08103 (205*2π)/2501 weeks
206-.07111 .16225 (206*2π)/2501 weeks
207-.02551 .09191 (207*2π)/2501 weeks
208-.09105 .05287 (208*2π)/2501 weeks
209-.11724 .12624 (209*2π)/2501 weeks
210.01791 .13879 (210*2π)/2501 weeks
211-.07252 .06507 (211*2π)/2501 weeks
212-.11636 .1048 (212*2π)/2501 weeks
213-.05669 .16617 (213*2π)/2501 weeks
214-.11842 .10661 (214*2π)/2501 weeks
215-.00311 .22581 (215*2π)/2501 weeks
216-.11253 .17246 (216*2π)/2501 weeks
217-.00886 .06706 (217*2π)/2501 weeks
218-.05254 .15547 (218*2π)/2501 weeks
219-.0377 .11603 (219*2π)/2501 weeks
220.11408 .1972 (220*2π)/2501 weeks
221-.1611 .18116 (221*2π)/2501 weeks
222-.10147 .22241 (222*2π)/2501 weeks
223-.11406 .19669 (223*2π)/2501 weeks
224-.04895 .34417 (224*2π)/2501 weeks
225-.0729 .10396 (225*2π)/2501 weeks
226-.19988 .13642 (226*2π)/2501 weeks
227-.17463 .29895 (227*2π)/2501 weeks
228-.26236 .11276 (228*2π)/2501 weeks
229.06378 .32561 (229*2π)/2501 weeks
230-.1056 .26114 (230*2π)/2501 weeks
231-.09492 .16328 (231*2π)/2501 weeks
232-.14553 .34838 (232*2π)/2501 weeks
233-.07916 .46471 (233*2π)/2501 weeks
234-.08186 .42867 (234*2π)/2501 weeks
235.04792 .55159 (235*2π)/2501 weeks
236-.02549 .15256 (236*2π)/2501 weeks
237-.28131 .52155 (237*2π)/2501 weeks
238.23949 .65207 (238*2π)/2501 weeks
239-.14582 .27327 (239*2π)/2501 weeks
240.00481 .76438 (240*2π)/2501 weeks
241-.17836 .54449 (241*2π)/2501 weeks
242-.24815 .82935 (242*2π)/2501 weeks
243.10009 .8298 (243*2π)/2501 weeks
244.15064 .8985 (244*2π)/2501 weeks
245-.15558 .83516 (245*2π)/2501 weeks
246.00616 1.25736 (246*2π)/2501 weeks
247-.82597 1.58556 (247*2π)/2501 weeks
248-.31675 4.15956 (248*2π)/2501 weeks



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