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# Fourier Analysis of PAFSX (PARNASSUS ASIA FUND INVESTOR SHARES)

PAFSX (PARNASSUS ASIA FUND INVESTOR SHARES) appears to have interesting cyclic behaviour every 20 weeks (.2059*sine), 17 weeks (.1766*sine), and 22 weeks (.1577*cosine).

PAFSX (PARNASSUS ASIA FUND INVESTOR SHARES) has an average price of 12.77 (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 1/2/2014 to 3/26/2018 for PAFSX (PARNASSUS ASIA FUND INVESTOR SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
012.7665   0
11.3823 -.60931 (1*2π)/222222 weeks
2-.59508 -.57257 (2*2π)/222111 weeks
3.28114 -.50183 (3*2π)/22274 weeks
4-.22106 -.16331 (4*2π)/22256 weeks
5-.16326 -.25327 (5*2π)/22244 weeks
6-.00163 -.45126 (6*2π)/22237 weeks
7-.04558 -.11046 (7*2π)/22232 weeks
8-.14927 -.18993 (8*2π)/22228 weeks
9.04525 -.18661 (9*2π)/22225 weeks
10-.15767 .05375 (10*2π)/22222 weeks
11.04177 -.20587 (11*2π)/22220 weeks
12-.10163 -.06263 (12*2π)/22219 weeks
13-.04179 -.17664 (13*2π)/22217 weeks
14-.02795 -.01729 (14*2π)/22216 weeks
15-.02048 -.05625 (15*2π)/22215 weeks
16-.0181 -.05869 (16*2π)/22214 weeks
17-.00247 -.05627 (17*2π)/22213 weeks
18-.02458 -.08036 (18*2π)/22212 weeks
19.07345 -.07965 (19*2π)/22212 weeks
20.00103 .01324 (20*2π)/22211 weeks
21-.01361 -.07706 (21*2π)/22211 weeks
22-.01575 -.03021 (22*2π)/22210 weeks
23.00283 -.0812 (23*2π)/22210 weeks
24.00407 -.05433 (24*2π)/2229 weeks
25-.00491 -.06542 (25*2π)/2229 weeks
26.01456 -.06643 (26*2π)/2229 weeks
27-.07214 -.04265 (27*2π)/2228 weeks
28-.01874 -.0338 (28*2π)/2228 weeks
29-.03061 -.07091 (29*2π)/2228 weeks
30-.00886 -.02719 (30*2π)/2227 weeks
31-.02432 -.03469 (31*2π)/2227 weeks
32-.02974 -.02609 (32*2π)/2227 weeks
33-.02178 -.02086 (33*2π)/2227 weeks
34-.02363 .01187 (34*2π)/2227 weeks
35-.00508 -.00913 (35*2π)/2226 weeks
36-.03064 -.00051 (36*2π)/2226 weeks
37.00483 -.02275 (37*2π)/2226 weeks
38-.04018 -.03769 (38*2π)/2226 weeks
39-.01913 -.02728 (39*2π)/2226 weeks
40-.02379 -.05018 (40*2π)/2226 weeks
41.00848 .02965 (41*2π)/2225 weeks
42-.01645 -.05148 (42*2π)/2225 weeks
43.00068 .00789 (43*2π)/2225 weeks
44-.04064 -.01127 (44*2π)/2225 weeks
45.01195 -.03756 (45*2π)/2225 weeks
46-.02094 -.02566 (46*2π)/2225 weeks
47-.00718 -.03904 (47*2π)/2225 weeks
48-.01728 -.01142 (48*2π)/2225 weeks
49-.01658 -.04013 (49*2π)/2225 weeks
50-.03284 -.01706 (50*2π)/2224 weeks
51-.03162 -.05758 (51*2π)/2224 weeks
52-.02329 -.0198 (52*2π)/2224 weeks
53-.02374 -.02616 (53*2π)/2224 weeks
54-.03681 .00675 (54*2π)/2224 weeks
55-.02772 -.04352 (55*2π)/2224 weeks
56-.0186 -.01108 (56*2π)/2224 weeks
57-.03782 -.03073 (57*2π)/2224 weeks
58-.02359 .00746 (58*2π)/2224 weeks
59-.04382 .00209 (59*2π)/2224 weeks
60-.02479 -.0136 (60*2π)/2224 weeks
61-.03175 -.00076 (61*2π)/2224 weeks
62-.00948 -.01332 (62*2π)/2224 weeks
63-.04483 -.00578 (63*2π)/2224 weeks
64-.01481 -.0036 (64*2π)/2223 weeks
65-.00429 -.00582 (65*2π)/2223 weeks
66-.02124 -.02285 (66*2π)/2223 weeks
67-.0179 -.01246 (67*2π)/2223 weeks
68-.00168 -.01005 (68*2π)/2223 weeks
69-.00525 -.0132 (69*2π)/2223 weeks
70.01331 -.0118 (70*2π)/2223 weeks
71-.01291 -.01656 (71*2π)/2223 weeks
72.0006 -.0245 (72*2π)/2223 weeks
73-.01526 -.02698 (73*2π)/2223 weeks
74-.01468 -.03312 (74*2π)/2223 weeks
75-.01247 -.00382 (75*2π)/2223 weeks
76-.03003 -.02168 (76*2π)/2223 weeks
77-.00551 -.03017 (77*2π)/2223 weeks
78-.01757 -.00325 (78*2π)/2223 weeks
79-.05024 -.01684 (79*2π)/2223 weeks
80-.01343 -.00481 (80*2π)/2223 weeks
81-.02516 -.00367 (81*2π)/2223 weeks
82-.00988 -.01118 (82*2π)/2223 weeks
83-.02537 -.00409 (83*2π)/2223 weeks
84-.01645 -.00531 (84*2π)/2223 weeks
85-.01644 .00398 (85*2π)/2223 weeks
86-.02521 .01236 (86*2π)/2223 weeks
87-.01961 -.02797 (87*2π)/2223 weeks
88-.00504 -.00346 (88*2π)/2223 weeks
89-.01859 -.00638 (89*2π)/2222 weeks
90-.01356 -.00567 (90*2π)/2222 weeks
91-.01946 .00134 (91*2π)/2222 weeks
92-.01762 -.01472 (92*2π)/2222 weeks
93-.01445 .00978 (93*2π)/2222 weeks
94-.01733 -.01282 (94*2π)/2222 weeks
95-.02077 -.00443 (95*2π)/2222 weeks
96-.02123 .00139 (96*2π)/2222 weeks
97-.01648 -.0219 (97*2π)/2222 weeks
98-.01988 .00193 (98*2π)/2222 weeks
99-.02505 .00662 (99*2π)/2222 weeks
100.00186 -.02084 (100*2π)/2222 weeks
101-.01922 -.01033 (101*2π)/2222 weeks
102-.00051 -.01324 (102*2π)/2222 weeks
103-.01131 -.00088 (103*2π)/2222 weeks
104-.0072 .00198 (104*2π)/2222 weeks
105-.02361 .00317 (105*2π)/2222 weeks
106.00454 .00404 (106*2π)/2222 weeks
107-.02808 -.00093 (107*2π)/2222 weeks
108-.00545 -.01434 (108*2π)/2222 weeks
109-.00992 .01947 (109*2π)/2222 weeks
110-.03576 -.00901 (110*2π)/2222 weeks
111-.01595   (111*2π)/2222 weeks
112-.03576 .00901 (112*2π)/2222 weeks
113-.00992 -.01947 (113*2π)/2222 weeks
114-.00545 .01434 (114*2π)/2222 weeks
115-.02808 .00093 (115*2π)/2222 weeks
116.00454 -.00404 (116*2π)/2222 weeks
117-.02361 -.00317 (117*2π)/2222 weeks
118-.0072 -.00198 (118*2π)/2222 weeks
119-.01131 .00088 (119*2π)/2222 weeks
120-.00051 .01324 (120*2π)/2222 weeks
121-.01922 .01033 (121*2π)/2222 weeks
122.00186 .02084 (122*2π)/2222 weeks
123-.02505 -.00662 (123*2π)/2222 weeks
124-.01988 -.00193 (124*2π)/2222 weeks
125-.01648 .0219 (125*2π)/2222 weeks
126-.02123 -.00139 (126*2π)/2222 weeks
127-.02077 .00443 (127*2π)/2222 weeks
128-.01733 .01282 (128*2π)/2222 weeks
129-.01445 -.00978 (129*2π)/2222 weeks
130-.01762 .01472 (130*2π)/2222 weeks
131-.01946 -.00134 (131*2π)/2222 weeks
132-.01356 .00567 (132*2π)/2222 weeks
133-.01859 .00638 (133*2π)/2222 weeks
134-.00504 .00346 (134*2π)/2222 weeks
135-.01961 .02797 (135*2π)/2222 weeks
136-.02521 -.01236 (136*2π)/2222 weeks
137-.01644 -.00398 (137*2π)/2222 weeks
138-.01645 .00531 (138*2π)/2222 weeks
139-.02537 .00409 (139*2π)/2222 weeks
140-.00988 .01118 (140*2π)/2222 weeks
141-.02516 .00367 (141*2π)/2222 weeks
142-.01343 .00481 (142*2π)/2222 weeks
143-.05024 .01684 (143*2π)/2222 weeks
144-.01757 .00325 (144*2π)/2222 weeks
145-.00551 .03017 (145*2π)/2222 weeks
146-.03003 .02168 (146*2π)/2222 weeks
147-.01247 .00382 (147*2π)/2222 weeks
148-.01468 .03312 (148*2π)/2222 weeks
149-.01526 .02698 (149*2π)/2221 weeks
150.0006 .0245 (150*2π)/2221 weeks
151-.01291 .01656 (151*2π)/2221 weeks
152.01331 .0118 (152*2π)/2221 weeks
153-.00525 .0132 (153*2π)/2221 weeks
154-.00168 .01005 (154*2π)/2221 weeks
155-.0179 .01246 (155*2π)/2221 weeks
156-.02124 .02285 (156*2π)/2221 weeks
157-.00429 .00582 (157*2π)/2221 weeks
158-.01481 .0036 (158*2π)/2221 weeks
159-.04483 .00578 (159*2π)/2221 weeks
160-.00948 .01332 (160*2π)/2221 weeks
161-.03175 .00076 (161*2π)/2221 weeks
162-.02479 .0136 (162*2π)/2221 weeks
163-.04382 -.00209 (163*2π)/2221 weeks
164-.02359 -.00746 (164*2π)/2221 weeks
165-.03782 .03073 (165*2π)/2221 weeks
166-.0186 .01108 (166*2π)/2221 weeks
167-.02772 .04352 (167*2π)/2221 weeks
168-.03681 -.00675 (168*2π)/2221 weeks
169-.02374 .02616 (169*2π)/2221 weeks
170-.02329 .0198 (170*2π)/2221 weeks
171-.03162 .05758 (171*2π)/2221 weeks
172-.03284 .01706 (172*2π)/2221 weeks
173-.01658 .04013 (173*2π)/2221 weeks
174-.01728 .01142 (174*2π)/2221 weeks
175-.00718 .03904 (175*2π)/2221 weeks
176-.02094 .02566 (176*2π)/2221 weeks
177.01195 .03756 (177*2π)/2221 weeks
178-.04064 .01127 (178*2π)/2221 weeks
179.00068 -.00789 (179*2π)/2221 weeks
180-.01645 .05148 (180*2π)/2221 weeks
181.00848 -.02965 (181*2π)/2221 weeks
182-.02379 .05018 (182*2π)/2221 weeks
183-.01913 .02728 (183*2π)/2221 weeks
184-.04018 .03769 (184*2π)/2221 weeks
185.00483 .02275 (185*2π)/2221 weeks
186-.03064 .00051 (186*2π)/2221 weeks
187-.00508 .00913 (187*2π)/2221 weeks
188-.02363 -.01187 (188*2π)/2221 weeks
189-.02178 .02086 (189*2π)/2221 weeks
190-.02974 .02609 (190*2π)/2221 weeks
191-.02432 .03469 (191*2π)/2221 weeks
192-.00886 .02719 (192*2π)/2221 weeks
193-.03061 .07091 (193*2π)/2221 weeks
194-.01874 .0338 (194*2π)/2221 weeks
195-.07214 .04265 (195*2π)/2221 weeks
196.01456 .06643 (196*2π)/2221 weeks
197-.00491 .06542 (197*2π)/2221 weeks
198.00407 .05433 (198*2π)/2221 weeks
199.00283 .0812 (199*2π)/2221 weeks
200-.01575 .03021 (200*2π)/2221 weeks
201-.01361 .07706 (201*2π)/2221 weeks
202.00103 -.01324 (202*2π)/2221 weeks
203.07345 .07965 (203*2π)/2221 weeks
204-.02458 .08036 (204*2π)/2221 weeks
205-.00247 .05627 (205*2π)/2221 weeks
206-.0181 .05869 (206*2π)/2221 weeks
207-.02048 .05625 (207*2π)/2221 weeks
208-.02795 .01729 (208*2π)/2221 weeks
209-.04179 .17664 (209*2π)/2221 weeks
210-.10163 .06263 (210*2π)/2221 weeks
211.04177 .20587 (211*2π)/2221 weeks
212-.15767 -.05375 (212*2π)/2221 weeks
213.04525 .18661 (213*2π)/2221 weeks
214-.14927 .18993 (214*2π)/2221 weeks
215-.04558 .11046 (215*2π)/2221 weeks
216-.00163 .45126 (216*2π)/2221 weeks
217-.16326 .25327 (217*2π)/2221 weeks
218-.22106 .16331 (218*2π)/2221 weeks
219.28114 .50183 (219*2π)/2221 weeks
220-.59508 .57257 (220*2π)/2221 weeks