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Fourier Analysis of KWEB (KraneShares CSI China Internet )


KWEB (KraneShares CSI China Internet ) appears to have interesting cyclic behaviour every 12 weeks (.871*sine), 17 weeks (.6983*sine), and 19 weeks (.6844*cosine).

KWEB (KraneShares CSI China Internet ) has an average price of 34.94 (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 8/1/2013 to 3/20/2017 for KWEB (KraneShares CSI China Internet ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
034.94075   0 
1-.62041 -.79744 (1*2π)/191191 weeks
2-.15923 -1.67502 (2*2π)/19196 weeks
3-1.08646 -1.80812 (3*2π)/19164 weeks
4.19634 -.81769 (4*2π)/19148 weeks
5-1.55944 -.17772 (5*2π)/19138 weeks
61.56131 -.98794 (6*2π)/19132 weeks
7-.26517 -.29215 (7*2π)/19127 weeks
81.523 -.24303 (8*2π)/19124 weeks
9-1.26821 -1.45996 (9*2π)/19121 weeks
10-.68438 -.57754 (10*2π)/19119 weeks
11.18675 -.69827 (11*2π)/19117 weeks
12-.17632 -.58706 (12*2π)/19116 weeks
13-.36228 -.40003 (13*2π)/19115 weeks
14-.00155 -.32148 (14*2π)/19114 weeks
15-.18116 -.25281 (15*2π)/19113 weeks
16-.4074 -.87096 (16*2π)/19112 weeks
17.29885 -.40385 (17*2π)/19111 weeks
18.12211 -.19407 (18*2π)/19111 weeks
19-.17154 -.41824 (19*2π)/19110 weeks
20.27051 -.04506 (20*2π)/19110 weeks
21-.20884 -.18772 (21*2π)/1919 weeks
22-.14431 -.14133 (22*2π)/1919 weeks
23.05639 -.46327 (23*2π)/1918 weeks
24.10403 -.235 (24*2π)/1918 weeks
25-.0936 -.40575 (25*2π)/1918 weeks
26.06622 .06732 (26*2π)/1917 weeks
27-.27397 -.1639 (27*2π)/1917 weeks
28-.24816 -.16437 (28*2π)/1917 weeks
29-.23933 -.24234 (29*2π)/1917 weeks
30-.16914 -.16161 (30*2π)/1916 weeks
31.15588 -.23909 (31*2π)/1916 weeks
32.01157 -.21916 (32*2π)/1916 weeks
33-.1335 -.09588 (33*2π)/1916 weeks
34-.10755 -.05688 (34*2π)/1916 weeks
35.14605 -.28075 (35*2π)/1915 weeks
36.0041 -.31204 (36*2π)/1915 weeks
37-.06928 -.09995 (37*2π)/1915 weeks
38-.20199 -.14769 (38*2π)/1915 weeks
39-.18168 -.14924 (39*2π)/1915 weeks
40-.11518 -.0722 (40*2π)/1915 weeks
41-.02969 -.15725 (41*2π)/1915 weeks
42-.21912 -.04333 (42*2π)/1915 weeks
43-.10582 -.03344 (43*2π)/1914 weeks
44-.10079 -.24266 (44*2π)/1914 weeks
45-.14938 -.13899 (45*2π)/1914 weeks
46-.24627 .02447 (46*2π)/1914 weeks
47-.00705 -.1796 (47*2π)/1914 weeks
48-.18815 -.14055 (48*2π)/1914 weeks
49.05029 -.01338 (49*2π)/1914 weeks
50-.01037 -.16461 (50*2π)/1914 weeks
51-.13057 -.02077 (51*2π)/1914 weeks
52-.04055 .01664 (52*2π)/1914 weeks
53-.02395 -.13868 (53*2π)/1914 weeks
54-.20919 -.12616 (54*2π)/1914 weeks
55-.13566 -.11145 (55*2π)/1913 weeks
56-.0785 -.025 (56*2π)/1913 weeks
57-.03109 .03293 (57*2π)/1913 weeks
58-.21575 -.02445 (58*2π)/1913 weeks
59-.12507 -.12317 (59*2π)/1913 weeks
60-.04169 -.04518 (60*2π)/1913 weeks
61-.11212 -.06123 (61*2π)/1913 weeks
62-.11263 -.04917 (62*2π)/1913 weeks
63.06554 -.21889 (63*2π)/1913 weeks
64-.06692 .05844 (64*2π)/1913 weeks
65-.02038 -.08291 (65*2π)/1913 weeks
66-.21495 -.06139 (66*2π)/1913 weeks
67-.0076 -.10233 (67*2π)/1913 weeks
68-.13947 .09394 (68*2π)/1913 weeks
69.06549 .03378 (69*2π)/1913 weeks
70-.22705 -.03239 (70*2π)/1913 weeks
71-.0644 -.15016 (71*2π)/1913 weeks
72-.10228 -.04109 (72*2π)/1913 weeks
73-.10176 -.0565 (73*2π)/1913 weeks
74.00037 -.0479 (74*2π)/1913 weeks
75-.14569 .11602 (75*2π)/1913 weeks
76-.04524 -.01071 (76*2π)/1913 weeks
77-.19327 .01366 (77*2π)/1912 weeks
78-.07547 -.03645 (78*2π)/1912 weeks
79-.13837 -.12651 (79*2π)/1912 weeks
80-.07628 .05644 (80*2π)/1912 weeks
81-.06068 .02496 (81*2π)/1912 weeks
82-.08394 .03583 (82*2π)/1912 weeks
83.00564 .0573 (83*2π)/1912 weeks
84-.14948 -.09874 (84*2π)/1912 weeks
85-.05171 -.01295 (85*2π)/1912 weeks
86-.0236 -.16023 (86*2π)/1912 weeks
87-.02173 -.08078 (87*2π)/1912 weeks
88-.02537 .10503 (88*2π)/1912 weeks
89-.03439 -.03943 (89*2π)/1912 weeks
90-.19636 .0663 (90*2π)/1912 weeks
91-.10756 .04176 (91*2π)/1912 weeks
92-.03737 .06696 (92*2π)/1912 weeks
93-.17092 -.02884 (93*2π)/1912 weeks
94-.00735 .12044 (94*2π)/1912 weeks
95-.20393 .06264 (95*2π)/1912 weeks
96-.20393 -.06264 (96*2π)/1912 weeks
97-.00735 -.12044 (97*2π)/1912 weeks
98-.17092 .02884 (98*2π)/1912 weeks
99-.03737 -.06696 (99*2π)/1912 weeks
100-.10756 -.04176 (100*2π)/1912 weeks
101-.19636 -.0663 (101*2π)/1912 weeks
102-.03439 .03943 (102*2π)/1912 weeks
103-.02537 -.10503 (103*2π)/1912 weeks
104-.02173 .08078 (104*2π)/1912 weeks
105-.0236 .16023 (105*2π)/1912 weeks
106-.05171 .01295 (106*2π)/1912 weeks
107-.14948 .09874 (107*2π)/1912 weeks
108.00564 -.0573 (108*2π)/1912 weeks
109-.08394 -.03583 (109*2π)/1912 weeks
110-.06068 -.02496 (110*2π)/1912 weeks
111-.07628 -.05644 (111*2π)/1912 weeks
112-.13837 .12651 (112*2π)/1912 weeks
113-.07547 .03645 (113*2π)/1912 weeks
114-.19327 -.01366 (114*2π)/1912 weeks
115-.04524 .01071 (115*2π)/1912 weeks
116-.14569 -.11602 (116*2π)/1912 weeks
117.00037 .0479 (117*2π)/1912 weeks
118-.10176 .0565 (118*2π)/1912 weeks
119-.10228 .04109 (119*2π)/1912 weeks
120-.0644 .15016 (120*2π)/1912 weeks
121-.22705 .03239 (121*2π)/1912 weeks
122.06549 -.03378 (122*2π)/1912 weeks
123-.13947 -.09394 (123*2π)/1912 weeks
124-.0076 .10233 (124*2π)/1912 weeks
125-.21495 .06139 (125*2π)/1912 weeks
126-.02038 .08291 (126*2π)/1912 weeks
127-.06692 -.05844 (127*2π)/1912 weeks
128.06554 .21889 (128*2π)/1911 weeks
129-.11263 .04917 (129*2π)/1911 weeks
130-.11212 .06123 (130*2π)/1911 weeks
131-.04169 .04518 (131*2π)/1911 weeks
132-.12507 .12317 (132*2π)/1911 weeks
133-.21575 .02445 (133*2π)/1911 weeks
134-.03109 -.03293 (134*2π)/1911 weeks
135-.0785 .025 (135*2π)/1911 weeks
136-.13566 .11145 (136*2π)/1911 weeks
137-.20919 .12616 (137*2π)/1911 weeks
138-.02395 .13868 (138*2π)/1911 weeks
139-.04055 -.01664 (139*2π)/1911 weeks
140-.13057 .02077 (140*2π)/1911 weeks
141-.01037 .16461 (141*2π)/1911 weeks
142.05029 .01338 (142*2π)/1911 weeks
143-.18815 .14055 (143*2π)/1911 weeks
144-.00705 .1796 (144*2π)/1911 weeks
145-.24627 -.02447 (145*2π)/1911 weeks
146-.14938 .13899 (146*2π)/1911 weeks
147-.10079 .24266 (147*2π)/1911 weeks
148-.10582 .03344 (148*2π)/1911 weeks
149-.21912 .04333 (149*2π)/1911 weeks
150-.02969 .15725 (150*2π)/1911 weeks
151-.11518 .0722 (151*2π)/1911 weeks
152-.18168 .14924 (152*2π)/1911 weeks
153-.20199 .14769 (153*2π)/1911 weeks
154-.06928 .09995 (154*2π)/1911 weeks
155.0041 .31204 (155*2π)/1911 weeks
156.14605 .28075 (156*2π)/1911 weeks
157-.10755 .05688 (157*2π)/1911 weeks
158-.1335 .09588 (158*2π)/1911 weeks
159.01157 .21916 (159*2π)/1911 weeks
160.15588 .23909 (160*2π)/1911 weeks
161-.16914 .16161 (161*2π)/1911 weeks
162-.23933 .24234 (162*2π)/1911 weeks
163-.24816 .16437 (163*2π)/1911 weeks
164-.27397 .1639 (164*2π)/1911 weeks
165.06622 -.06732 (165*2π)/1911 weeks
166-.0936 .40575 (166*2π)/1911 weeks
167.10403 .235 (167*2π)/1911 weeks
168.05639 .46327 (168*2π)/1911 weeks
169-.14431 .14133 (169*2π)/1911 weeks
170-.20884 .18772 (170*2π)/1911 weeks
171.27051 .04506 (171*2π)/1911 weeks
172-.17154 .41824 (172*2π)/1911 weeks
173.12211 .19407 (173*2π)/1911 weeks
174.29885 .40385 (174*2π)/1911 weeks
175-.4074 .87096 (175*2π)/1911 weeks
176-.18116 .25281 (176*2π)/1911 weeks
177-.00155 .32148 (177*2π)/1911 weeks
178-.36228 .40003 (178*2π)/1911 weeks
179-.17632 .58706 (179*2π)/1911 weeks
180.18675 .69827 (180*2π)/1911 weeks
181-.68438 .57754 (181*2π)/1911 weeks
182-1.26821 1.45996 (182*2π)/1911 weeks
1831.523 .24303 (183*2π)/1911 weeks
184-.26517 .29215 (184*2π)/1911 weeks
1851.56131 .98794 (185*2π)/1911 weeks
186-1.55944 .17772 (186*2π)/1911 weeks
187.19634 .81769 (187*2π)/1911 weeks
188-1.08646 1.80812 (188*2π)/1911 weeks
189-.15923 1.67502 (189*2π)/1911 weeks

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