Feeds:
Posts

## FRACTIONAL POISSON NU PARAMETER SPECTRUM OF THE MARKET USING 250 STOCKS

The fractional Poisson process fits the waiting time distribution for volatility shocks extremely well with $R^2 = 0.991 +/- 0.008$ over 250 stocks.  Recall that two parameters $(\mu,\nu)$ determine the waiting time distribution.  A natural question is whether there are regularities in the spectrum of $\nu$ across the market.  We find that there are two pronounced peaks in the spectrum.

The quality of the fits is good in this sample of 250 stocks so I just post a few graphical fits and then the table of parameter values and R-squared.

TICKER,fpp-mu,fpp-nu,R^2
PRE,0.484615315727,0.450095870139,0.982286973909
IRBT,7.38612139328,0.362527889692,0.992238074736
G,-0.280012985448,0.0154009075977,0.973226769461
ICUI,0.993188443046,0.606584883385,0.996847077904
IGT,0.894871342214,0.333345132891,0.997763606632
SIAL,0.869638190565,0.333359763208,0.995292296602
KND,0.831284505449,0.411454639397,0.996104189894
ASH,0.864791549534,0.333336793691,0.990439240726
ABMD,0.999854446323,0.663013839986,0.996082894951
WSM,0.878824682339,0.558258979883,0.98474116516
RTEC,0.892470876328,0.333457885207,0.991479432972
LXU,0.772358732998,0.815470751741,0.999627434967
ELNK,0.869362387477,0.333343441265,0.997880874468
CVO,6.5701607992,0.371747143796,0.993158541941
GOV,-0.169002566217,0.0102511745133,0.974573290732
RRGB,7.55146137067,0.12779867799,0.996710837891
OEH,0.706955676744,0.500042117057,0.987122337549
GDP,0.783573607563,0.788282322461,0.999865329231
SIRO,0.496962689551,0.56140588038,0.97426141945
FFIN,0.931227686217,0.397013897098,0.998547783379
PBCT,0.928501665321,0.575113390102,0.991482133079
SRI,0.707087801075,0.50002497188,0.991828346536
MM,5.54759141977,0.329181210222,0.992456889065
SWKS,4.71607733076,0.42504306366,0.998524154227
TOL,0.999976556794,0.637509533547,0.988879791393
HBI,0.811900095067,0.333341199617,0.980427343746
MCRI,0.591090565204,0.885762790916,0.999531304748
WABC,0.706751079956,0.500043124331,0.99227636557
ITRI,0.898381659036,0.550259618804,0.991616726099
APH,0.949045276666,0.57233428286,0.987027579499
DF,0.800903490588,0.333348267437,0.989631683104
HTZ,0.706934766798,0.50002256032,0.987971638027
KNL,0.577255840837,0.50008926583,0.964982367406
ACGL,0.876370580913,0.333400743614,0.995182102729
SCSS,0.866751883654,0.333388529793,0.997777656575
MRK,0.577142880663,0.500020586199,0.985761935686
BKD,0.707046289765,0.500109819928,0.986608337799
TITN,0.706521195361,0.500077886099,0.991662140186
FNSR,0.886797435598,0.333365675023,0.994350843905
CR,0.865630743969,0.333443787873,0.997556404535
UEIC,0.999872761442,0.598394029025,0.998268635461
VOD,0.706996940306,0.500025150462,0.983072532083
OC,0.611133972634,0.500007120513,0.967925757184
NTRI,0.993580057637,0.592534095796,0.999360757075
CNA,0.707076711375,0.500030132586,0.985938932927
SYY,0.948213197927,0.575587112286,0.992475655601
CTL,0.834736823276,0.333364577516,0.996230051881
IIIN,0.999991469868,0.708312119767,0.998163639228
NJR,0.889749404304,0.333362223159,0.997547361826
UNFI,0.889149876068,0.33343888807,0.997284497858
VIAB,0.840659679724,0.333434393919,0.983301936723
EXLS,0.834658959814,0.333339668023,0.9987234194
YRCW,2.36425249844,0.322948402722,0.992277583517
STAR,0.689209293292,0.759759421926,0.999748674851
CHTR,0.707050215396,0.500085252312,0.997701231673
AFAM,0.805356022894,0.753622553653,0.99818303366
CDR,4.58198987075,0.438155531262,0.999150863342
PSEM,0.880997729335,0.545857309184,0.990236326832
PHH,5.81187717603,0.290349646782,0.976875793877
PVA,0.985925577374,0.588602473424,0.992859982669
WY,0.706996940306,0.500025150462,0.991997941404
GCI,0.868421132063,0.333499309268,0.98944112592
RGLD,0.999949894687,0.698318407795,0.998246800737
CRK,6.53746830442,0.43812138471,0.996900453759
SGMO,0.895593961388,0.333407005902,0.994333632954
S,0.890921346741,0.333379374569,0.990875834494
GFF,0.750320692019,0.8096340384,0.999747047864
ORCL,0.99998920853,0.47579699617,0.987792374049
ABM,0.861045667561,0.333336549882,0.997070761015
CBSH,0.870953725785,0.333377140911,0.997790696246
AHS,0.706981588144,0.500005330167,0.976702199117
VSH,8.35025289797,0.344037868201,0.992986096121
MLM,0.825746431242,0.546737352033,0.986369120542
OREX,0.938496866741,0.570215609544,0.975569214597
KKD,0.851335896766,0.456658969866,0.999206113821
FRP,0.855357158745,0.333337522393,0.997177852013
AGO,0.932799511285,0.333378044678,0.98726920864
SWN,7.01089705155,0.324906984506,0.992249416817
UAM,0.854868377594,0.73688311105,0.998975742417
PLCM,0.872055953456,0.333412620944,0.997713528781
MDC,0.92909361395,0.682638987618,0.998246838493
DD,0.821335319497,0.333340989701,0.988644483481
EZPW,0.989424517093,0.589031333305,0.98907912292
DOX,0.620468588871,0.434439367872,0.990983773991
CDI,0.999884976653,0.440772215866,0.99847280413
TRGT,0.761573067195,0.419293011709,0.993990195338
VICR,6.17340461587,0.322378772154,0.992465458082
TEG,0.706896011021,0.500051474613,0.993408626461
EOG,0.912639070765,0.333364617645,0.99686483706
HTH,0.494617071808,0.422330689707,0.989996959066
WSO,0.785909040985,0.744814572344,0.99932936732
NYNY,0.999970843418,0.695518870664,0.997333550549
WYN,0.707013865833,0.500073601149,0.982745612216
LANC,8.06760303967,0.103267752384,0.998345295141
AON,0.574110939914,0.500025658276,0.990294916268
SCHN,0.858354261226,0.368631010992,0.998382083184
DHI,11.2376301203,0.331075882065,0.995850783619
CRY,0.922522408058,0.560120703051,0.989938679445
VDSI,7.42164410707,0.358153839148,0.994452079888
ETR,0.999973125842,0.636105738648,0.997957174267
AVA,0.868921980892,0.374505445656,0.994508881791
MCO,1.74423718533,0.282078466743,0.99796590534
FELE,1.35096776894,0.498393907294,0.995052977298
RHT,0.876360237662,0.333563131514,0.993781775741
SAH,0.842967435017,0.333373316869,0.997974580842
RST,1.00631242801,0.0157321389223,0.970591825646
JACK,0.999982356145,0.686574384963,0.998551824141
LMT,0.70692596173,0.500250377467,0.992095651774
VSAT,0.832866427349,0.333347902125,0.998919921427
VVC,0.707018954654,0.500014476464,0.986707925792
SE,0.577251528106,0.500109301049,0.966128082318
GTS,0.829506944531,0.333346127165,0.994348988487
OB,0.976757091889,0.00221148783951,0.989089120518
AZPN,0.704905420901,0.500001358883,0.988682916586
HAS,0.706503991494,0.500079630099,0.979838995688
ALOG,0.99994327605,0.667990578253,0.997706335484
OMEX,6.50355210289,0.441864181014,0.997258967831
CNS,0.79370103426,0.33334426442,0.994662946367
MO,0.484256061275,0.450556404289,0.977232961651
ELY,0.891086164497,0.333369882811,0.992753489292
SFY,0.999998706128,0.652630159653,0.999227800441
FSTR,0.740576600969,0.756762579806,0.998871904357
RSH,0.707021851371,0.500078239067,0.987445902125
SNV,0.976755521422,0.416086275934,0.998511436661
IVR,0.087679381795,-0.070156997795,0.931719006918
CMC,7.28550601882,0.229938419695,0.993829067929
HIL,0.855525536077,0.334451387603,0.993879267324
UNH,0.565096343704,0.500152175641,0.983314997899
ZQK,5.35333522231,0.370091051906,0.995975311859
DRH,0.876603745441,0.333367845343,0.99453133052
REXI,0.973998605286,0.625247973955,0.997646544971
PH,0.838465219579,0.33335666064,0.998130118443
ARO,0.858099204918,0.333360903078,0.992715516555
SXT,0.707007557575,0.500003905654,0.993683364786
ZEP,0.707068497669,0.500015775612,0.983561589726
SBUX,0.871267820676,0.333403603565,0.996500585091
WRE,0.976072907601,0.41810290709,0.997734274765
WNC,0.999962982873,0.60289314558,0.984853052118
VSI,7.56354230723,0.127083336589,0.992693591993
CHK,6.16229577693,0.323381303462,0.992304784787
STI,0.706047378341,0.502028001938,0.985503127131
CLF,6.67754792459,0.278568665052,0.988721515396
TRAK,6.59690277645,0.36881809216,0.976396400175
AJG,0.88994863395,0.393197488006,0.998255706702
BDSI,0.999974090867,0.648984509537,0.991274003805
HRB,0.80602863292,0.333334217239,0.995216614427
WR,0.577235117225,0.500033176113,0.962557240474
TTEC,0.800409056413,0.333370649046,0.996597426045
BZH,7.35408416712,0.366497281145,0.995410368872
SNA,0.57729390448,0.500017661922,0.984308317588
OI,9.76107419431,0.37269763051,0.999124917776
INWK,0.577276664906,0.500054102387,0.977401651408
WRES,6.55072523842,0.266363168988,0.985401931906
PCLN,0.851858650091,0.333374317144,0.990729236845
SAFM,0.992770437547,0.625880779491,0.997734078636
GTXI,0.838099631646,0.333333522163,0.995780377913
TFX,0.707015784404,0.500022196756,0.989352023772
AMD,9.85569323095,0.366708478567,0.993269283698
CLW,0.707064858952,0.500002690343,0.948453535544
BEAV,0.988703173058,0.589814293648,0.995062356568
ALXN,0.934347212902,0.565510553517,0.992954838346
ROSE,0.854465474633,0.333340782405,0.997745018493
RJF,5.99716041964,0.311729327171,0.997029767388
BHE,0.833044117131,0.333363806073,0.996937725029
ANR,0.920217212337,0.565868250526,0.981201030519
TGT,0.827116861888,0.3333742288,0.994080831186
UMPQ,0.848437827009,0.333355796727,0.999140415453
EMR,0.839492141442,0.333460320959,0.995103174772
BKE,5.42173646638,0.283085469902,0.998495374059
HIBB,0.907660289787,0.333426798077,0.996656162405
AF,0.535140893771,0.451004733506,0.976763570785
MPW,0.812281310446,0.333378408157,0.995292950437
AMP,0.881400315519,0.333382571525,0.989602129631
EHTH,1.00008206971,0.503985927274,0.993066960846
BIO,0.999799529371,0.607164319966,0.998118526982
BSX,0.907728730298,0.555062691687,0.982838993501
AL,0.820890550391,0.284960777772,0.967021423562
WHR,0.707049680574,0.500056682607,0.991306130901
PAY,0.999966905986,0.4653660099,0.994870666268
BK,5.85296257481,0.287148721389,0.999173363442
AXP,0.70690238538,0.500071080014,0.98636918972
BRKL,0.706986663904,0.500026732928,0.993527347407
CYNO,0.706837556348,0.500544909557,0.995152315382
ROG,0.95084384055,0.448744967865,0.998890492682
HEES,0.901820825259,0.333427775507,0.996252825518
ONB,0.869817916505,0.561848479803,0.99176074633
ORN,0.934429658408,0.570757143581,0.991981066619
ECL,0.706904541548,0.500073274386,0.991374312951
IMMU,0.999942039096,0.644808165553,0.988166383997
TSS,0.858658970054,0.525882691507,0.969234877224
OSIR,0.999999661864,0.622926277689,0.990415735119
ZUMZ,0.707068371821,0.500022275281,0.991539258434
ARQL,0.876099287502,0.333457716605,0.99021871945
BBG,0.84245272987,0.333562700017,0.983973135051
IVC,0.959417139042,0.574489191858,0.986025052362
CREE,0.869731856592,0.333355685698,0.999052109004
CBT,0.706909855418,0.500032971263,0.995010384486
AXL,0.732533302381,0.575731087208,0.982663645811
GFIG,0.706949949155,0.500042113667,0.963367312738
AVP,0.85136766779,0.333348760433,0.996984415849
LTM,0.880153351184,0.333371166335,0.982825306462
SPW,6.14605793525,0.299131325648,0.993386379182
KOPN,8.95895202865,0.421615523114,0.994985003219
SWC,5.71597375297,0.314800525461,0.989944864987
PKD,0.999937416462,0.67003671733,0.997615034547
KFRC,0.830583195097,0.333368361703,0.998380412753
CCMP,0.70604659291,0.502061686106,0.991731513122
TPX,0.864938125352,0.333428524939,0.989961641868
WGL,0.707003945008,0.500001182336,0.989290013692
APP,8.57652293751,0.350664613915,0.993253904461
CRZO,6.64851350143,0.36318416906,0.998247148617
FSLR,0.867446011256,0.333409157215,0.995016189711
POWI,0.896281427461,0.546812076766,0.98179990258
CWST,0.707021478831,0.500105096344,0.984543067427
NTAP,10.3525154109,0.336154853609,0.992422017573
JDSU,6.44214322854,0.274941239506,0.993468408157
FOSL,0.889781130402,0.333371227336,0.999493239286
HPQ,0.707062348571,0.500005363445,0.98856764258
CRL,0.707054909965,0.500026740216,0.985660320274
HUM,0.89510613521,0.333391488173,0.998232636918
CLNE,0.920930951631,0.562526976663,0.986248294176
FMD,0.893793609822,0.333366311818,0.995041381238
PNM,0.99756844639,0.594545378177,0.999141739729
SYNA,0.875962610614,0.549149150832,0.98306683246
WAG,0.706230592862,0.501749215124,0.980492260013
FFBC,0.970879842635,0.60153900765,0.998220665777
ASPS,0.810170546488,0.333431385668,0.990943768629
MEG,0.925551198278,0.56092596513,0.994543499552
AMT,0.706996940306,0.500025150462,0.979326483233
RAIL,0.835689616776,0.333401442983,0.997564722666
SO,0.904241517544,0.556215742112,0.994250703653
ODFL,0.8931932048,0.729225635012,0.999346960949
INFA,1.98707620146,0.200402222368,0.996334949412
PLXS,0.964193707014,0.578785783861,0.992799523223
XNPT,0.707012918215,0.500063684613,0.973385297919
AKRX,4.73066615916,0.384036051172,0.997776385052
NWE,-0.491899230333,0.0230647665445,0.986704871715
MCY,7.4336637714,0.13497901221,0.99926222981
ANH,0.999979662618,0.600952038915,0.995548804438
WU,0.706988493219,0.500015993719,0.980038785028
BXC,6.32821132816,0.398792461091,0.993677597101
TE,0.577302334887,0.500027737308,0.982761446304
RGEN,0.999967239368,0.639911799331,0.995474636475
BMR,6.91383883996,0.334959178017,0.988105585893
ED,0.858803475298,0.333382582029,0.996811753594
ISRG,1.95655827866,0.0500017184414,0.99177271119
EBS,0.859803640772,0.333366296308,0.983933244225
AVID,0.843143137016,0.542782169892,0.983249322007
VRSN,0.706824750393,0.50001858312,0.992561099577