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["You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."]
["Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr",null,null,null,null,null,null,"Version 0.6",null,"2019-10-23"]
["Linensed under Creative Commons - Attribution Alone (CC-BY)"]
["q",1024,"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."]
["Markov or not",0,"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"]
["H",0.8,"Hurst parameter (0 <= H <= 1)",null,null,null,null,null,null,null,"Original","Differenced"]
["M",0.7,"Fractal (Mandelbrot) parameter (0 <= M <= 1)",null,null,null,null,null,null,"var",{"$f":"SUM((K$13:K$2061)^2)","v":0.99574161502705627},{"$f":"SUM(($K$14:$K$2061-$K$13:$K$2060)^2)+$K$13^2","v":2.7302561482142558E-2}]
["α",20,"Time scale parameter",null,null,null,null,null,null,"m3",{"$f":"SUM(($K$13:$K$2061)^3)","v":0.18091312078155863},{"$f":"SUM(($K$14:$K$2061-$K$13:$K$2060)^3)+$K$13^3","v":1.6823254215121029E-3}]
["λ = γ(0)",1,"State scale parameter",null,null,null,null,null,null,"skew",{"$f":"K8/K7^1.5","v":0.18207489927988355},{"$f":"L8/L7^1.5","v":0.37291076190780642}]
["θ0",{"$f":"1/16","v":6.25E-2},"(0 for summetric, 1/4 for antisymmetric)",null,null,null,"Fun------->",0,null,"skew ratio",null,{"$f":"L9/K9","v":2.0481173592993294}]
[]
["κ, η","γ(κ)","cη","ω","s(ω)",null,null,"θ(ω)",null,"η","aη","cη convoluted"]
[{"$f":"IF(B5=1,markov_(B4,B8/2,B9),FHK_Cauchy_(B4,B7,B6,B8,B9))","v":0},1,0.99573119817040034,{"$f":"FFTPowSpec_(C13:C1037)","v":0},678.70055052840803,null,null,0,null,{"$f":"FFT_amaCoef_(E13:E1037,H13:H1037)","v":-1024},3.2481603073974963E-3,{"$f":"SUM($K$13:$K$2061*K13:K2061)","v":0.99574161502705627},{"$f":"K13","v":3.2481603073974963E-3}]
[1,0.99573119817040034,0.98208492532456704,4.8828125E-4,192.55042434575245,null,null,{"$f":"IF($H$10=1,RAND()/4,$B$10)","v":6.25E-2},null,-1023,3.3794014847919329E-3,{"$f":"SUM($K$13:$K$2061*K14:K2062)","v":0.98208505901329357},{"$f":"K14-K13","v":1.3124117739443664E-4}]
[2,0.98890806174748369,0.95580705961882639,9.765625E-4,113.68002355051581,null,null,{"$f":"IF($H$10=1,RAND()/4,$B$10)","v":6.25E-2},null,-1022,3.420211592016692E-3,{"$f":"SUM($K$13:$K$2061*K15:K2063)","v":0.95579508325522355},{"$f":"K15-K14","v":4.0810107224759085E-5}]
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[4,0.97186046476664623,0.89369569517482361,1.953125E-3,75.418491596000464,null,null,6.25E-2,null,-1020,3.4346304552155538E-3,{"$f":"SUM($K$13:$K$2061*K17:K2065)","v":0.89365983160086826},2.1100288566375247E-5]
[5,0.96239115391340824,0.86156585014455089,2.44140625E-3,66.868724554364377,null,null,6.25E-2,null,-1019,3.4254239489484861E-3,{"$f":"SUM($K$13:$K$2061*K18:K2066)","v":0.86151817672772169},-9.206506267067649E-6]
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[7,0.94257206743100241,0.79945692956244585,3.41796875E-3,53.212102307422562,null,null,6.25E-2,null,-1017,3.4294758202182002E-3,{"$f":"SUM($K$13:$K$2061*K20:K2068)","v":0.79938494089222878},-7.8588571423426901E-6]
[8,0.93246960168234305,0.77029152873635098,3.90625E-3,47.906505153658927,null,null,6.25E-2,null,-1016,3.437312821413685E-3,{"$f":"SUM($K$13:$K$2061*K21:K2069)","v":0.77020705014159929},7.8370011954848051E-6]
[9,0.92235383665053705,0.74265191348983706,4.39453125E-3,44.444891515177083,null,null,6.25E-2,null,-1015,3.4305602801786017E-3,{"$f":"SUM($K$13:$K$2061*K22:K2070)","v":0.74255543808267221},-6.752541235083287E-6]
[10,0.912285708566967,0.71660822523608658,4.8828125E-3,40.741574280453449,null,null,6.25E-2,null,-1014,3.4362739175931925E-3,{"$f":"SUM($K$13:$K$2061*K23:K2071)","v":0.71649918377304378},5.7136374145907998E-6]
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[12,0.89246636957430026,0.66929118147908184,5.859375E-3,35.371816968457296,null,null,6.25E-2,null,-1012,3.4347444263084712E-3,{"$f":"SUM($K$13:$K$2061*K25:K2073)","v":0.6691574366979165},4.4372867856953824E-6]
[13,0.88277632784132909,0.64791911536261182,6.34765625E-3,33.335506943476467,null,null,6.25E-2,null,-1011,3.4293384091109713E-3,{"$f":"SUM($K$13:$K$2061*K26:K2074)","v":0.64777323614667304},-5.406017197499835E-6]
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[15,0.86393290624171581,0.60936240784528195,7.32421875E-3,29.478427542895581,null,null,6.25E-2,null,-1009,3.4279312602570264E-3,{"$f":"SUM($K$13:$K$2061*K28:K2076)","v":0.60919163347409355},-4.9969109123040867E-6]
[16,0.85480255000807626,0.59200080716954062,7.8125E-3,27.68782905511156,null,null,6.25E-2,null,-1008,3.430920233411322E-3,{"$f":"SUM($K$13:$K$2061*K29:K2077)","v":0.59181727355700242},2.9889731542956377E-6]
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[22,0.80433494483889656,0.50926626151755272,1.07421875E-2,20.234439602720244,null,null,6.25E-2,null,-1002,3.4241807873845453E-3,{"$f":"SUM($K$13:$K$2061*K35:K2083)","v":0.50900718016507485},1.9412594810114259E-6]
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[24,0.78912783162890443,0.48808335271894521,1.171875E-2,18.390862304140107,null,null,6.25E-2,null,-1000,3.4217755526394986E-3,{"$f":"SUM($K$13:$K$2061*K37:K2085)","v":0.48779887529718452},1.7326563158115427E-6]
[25,0.78181104903810861,0.4784170619926158,1.220703125E-2,17.608290418670599,null,null,6.25E-2,null,-999,3.4177491798713829E-3,{"$f":"SUM($K$13:$K$2061*K38:K2086)","v":0.47812011506588803},-4.0263727681157102E-6]
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{"sheet":"Simulation","index":1,"n_rows":12061,"n_cols":10,"rows_kept":12061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
["The parameters and coefficients of this sheet are  given in sheet \"Model\""]
["Hit <F9> for another simulation"]
["Lognormal distribution shape parameter",null,null,null,1]
["Average",null,null,{"$f":"AVERAGE(D$13:D$10012)","v":1.6510049662521848},{"$f":"AVERAGE(E$13:E$10012)","v":30.57774149078594}]
["Std",null,null,{"$f":"STDEV(D$13:D$10012)","v":2.2138659469535251},{"$f":"STDEV(E$13:E$10012)","v":2.1815674876817215}]
["Skew",null,null,{"$f":"SKEW(D$13:D$10012)","v":5.3509520120723169},{"$f":"SKEW(E$13:E$10012)","v":0.99565473219676792}]
["Skew Differenced",null,null,{"$f":"SKEW(D14:D10012-D13:D10011)","v":-6.9173952210499615E-2},{"$f":"SKEW(E14:E10012-E13:E10011)","v":1.9015221731536667},{"$f":"E10/E9","v":1.9098208562301848}]
[]
["τ, η","a-η",null,"vη","xτ",null,"cη simulated"]
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{"sheet":"OBAMA-Markov","index":2,"n_rows":2061,"n_cols":12,"rows_kept":2061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
[{"$f":"Model!A4","v":"q"},{"$f":"Model!B4","v":1024},{"$f":"Model!C4","v":"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."}]
["Markov or not",1,"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"]
["H",null,"Hurst parameter (0 <= H <= 1)"]
["M",null,"Fractal (Mandelbrot) parameter (0 <= M <= 1)"]
["α",20,"Time scale parameter"]
["λ = γ(0)",1,"State scale parameter"]
["θ0",0.125,"(0 for summetric, 1/4 for antisymmetric)"]
[]
["κ, η","γ(κ)","cη","ω","s(ω)",null,null,"θ(ω)",null,"η","aη","cη convoluted"]
[{"$f":"IF(B5=1,markov_(B4,B8/2,B9),FHK_Cauchy_(B4,B7,B6,B8,B9))","v":0},1,0.96748360719190352,{"$f":"FFTPowSpec_(C13:C1037)","v":0},40.000000000050449,{"$f":"$E13^0.5/($E$13^0.5+$E$1037^0.5)","v":0.97195606361114673},{"$f":"$E13^-0.5/($E$13^-0.5+$E$1037^-0.5)","v":2.8043936388853222E-2},{"$f":"ACOS(F13+G13)/2/PI()","v":0},null,{"$f":"FFT_amaCoef_(E13:E1037,H13:H1037)","v":-1024},5.5511151231257827E-17,{"$f":"SUM($K$13:$K$2061*K13:K2061)","v":0.96748360719190363}]
[1,0.96748360719190352,0.90559170060627858,4.8828125E-4,39.962354511080193,{"$f":"$E14^0.5/($E$13^0.5+$E$1037^0.5)","v":0.97149858393211797},{"$f":"$E14^-0.5/($E$13^-0.5+$E$1037^-0.5)","v":2.805714230724576E-2},{"$f":"ACOS(F14+G14)/2/PI()","v":4.7443480478935518E-3},null,-1023,0,{"$f":"SUM($K$13:$K$2061*K14:K2062)","v":0.90559170060627847}]
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{"sheet":"OBAMA-FHK","index":3,"n_rows":2061,"n_cols":15,"rows_kept":2061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
[{"$f":"Model!A4","v":"q"},{"$f":"Model!B4","v":1024},{"$f":"Model!C4","v":"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."}]
[{"$f":"Model!A5","v":"Markov or not"},{"$f":"Model!B5","v":0},{"$f":"Model!C5","v":"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"}]
[{"$f":"Model!A6","v":"H"},{"$f":"Model!B6","v":0.8},{"$f":"Model!C6","v":"Hurst parameter (0 <= H <= 1)"},null,null,null,null,null,null,"Sum all",{"$f":"SUM(K13:K2061^2)","v":0.99574665759685455},null,null,{"$f":"SUM(N13:N2061^2)","v":0.99573119817040234}]
[{"$f":"Model!A7","v":"M"},{"$f":"Model!B7","v":0.7},{"$f":"Model!C7","v":"Fractal (Mandelbrot) parameter (0 <= M <= 1)"},null,null,"Minimize this by Solver to find θ(ω)--------------->",null,null,null,"Sum negative",{"$f":"SUM(K13:K1036^2)","v":6.2584008323125087E-3},null,null,{"$f":"SUM(N13:N1036^2)","v":0}]
[{"$f":"Model!A8","v":"α"},{"$f":"Model!B8","v":20},{"$f":"Model!C8","v":"Time scale parameter"},null,null,"θ parameters",null,null,null,null,{"$f":"K6-K7","v":0.989488256764542},null,null,{"$f":"N6-N7","v":0.99573119817040234}]
[{"$f":"Model!A9","v":"λ = γ(0)"},{"$f":"Model!B9","v":1},{"$f":"Model!C9","v":"State scale parameter"},null,null,0.10766286206401518,-2.5357308596122299E-2,null,null,null,{"$f":"$B$14/K8","v":1.006309262755954},null,null,{"$f":"$B$14/N8","v":0.999999999999998}]
[null,null,null,null,null,383.01687467551073,0.43604613044302715,null,null,"Adjustment factor",{"$f":"K9^0.5","v":1.0031496711637571}]
[null,null,null,null,null,53.975806889990253,0.23005350851198583]
["κ, η","γ(κ)","cη","ω","s(ω)",null,null,"θ(ω)",null,"η","aη","cη convoluted",null,"aη final","cη convoluted final"]
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{"sheet":"ToARMA(1,q')","index":4,"n_rows":2061,"n_cols":18,"rows_kept":2061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
[{"$f":"Model!A4","v":"q"},{"$f":"Model!B4","v":1024},{"$f":"Model!C4","v":"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."}]
[{"$f":"Model!A5","v":"Markov or not"},0,{"$f":"Model!C5","v":"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"}]
[{"$f":"Model!A6","v":"H"},{"$f":"Model!B6","v":0.8},{"$f":"Model!C6","v":"Hurst parameter (0 <= H <= 1)"},null,null,null,null,null,null,"Error in c",{"$f":"SUM((P13:P1037-C13:C1037)^2)","v":2.9302580798969182}]
[{"$f":"Model!A7","v":"M"},{"$f":"Model!B7","v":0.7},{"$f":"Model!C7","v":"Fractal (Mandelbrot) parameter (0 <= M <= 1)"},null,null,"Minimize this by Solver to find θ(ω)--------------->",null,null,null,"Error in a",{"$f":"SUM((K13:K2061-O13:O2061)^2)","v":1.0162108982510947E-2},{"$f":"K1037-MAX(K13:K2061)","v":-9.1690090125362833E-2},null,{"$f":"SUM(N13:N2061^2)","v":1.0128018749001944},{"$f":"SUM(O13:O2061^2)","v":0.99573119817040046}]
[{"$f":"Model!A8","v":"α"},{"$f":"Model!B8","v":20},{"$f":"Model!C8","v":"Time scale parameter"},null,null,"θ parameters",null,"β parameter",null,null,null,-0.1,null,null,null,null,null,{"$f":"MIN(R13:R1037)","v":-5.1437609727145173E-9}]
[{"$f":"Model!A9","v":"λ = γ(0)"},{"$f":"Model!B9","v":1},{"$f":"Model!C9","v":"State scale parameter"},null,null,0.10536875677643062,7.1197982430255533E-2,0.99731300958981783]
["ARMA size q'",100,null,null,null,384.64388475623366,0.66436026319960984,null,null,"Adjustment factor",{"$f":"($B$14/N7)^0.5","v":0.99153673538699783}]
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{"sheet":"ToAR(q')","index":5,"n_rows":2061,"n_cols":27,"rows_kept":2061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
[{"$f":"Model!A4","v":"q"},{"$f":"Model!B4","v":1024},{"$f":"Model!C4","v":"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."}]
[{"$f":"Model!A5","v":"Markov or not"},0,{"$f":"Model!C5","v":"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"}]
[{"$f":"Model!A6","v":"H"},{"$f":"Model!B6","v":0.8},{"$f":"Model!C6","v":"Hurst parameter (0 <= H <= 1)"},null,null,null,null,null,null,"Error in c",{"$f":"SUM((Y13:Y1037-C13:C1037)^2)","v":8.4242490113202706}]
[{"$f":"Model!A7","v":"M"},{"$f":"Model!B7","v":0.7},{"$f":"Model!C7","v":"Fractal (Mandelbrot) parameter (0 <= M <= 1)"},null,null,"Minimize this by Solver to find θ(ω)--------------->",null,null,null,"Error in a",{"$f":"SUM((K13:K2061-X13:X2061)^2)","v":2.5654158815542775E-2},{"$f":"K1037-MAX(K13:K2061)","v":-0.10000006723153568},null,100,null,null,null,null,null,null,null,null,{"$f":"SUM(W13:W2061^2)","v":0.97262197108354875},{"$f":"SUM(X13:X2061^2)","v":0.99573119817040245}]
[{"$f":"Model!A8","v":"α"},{"$f":"Model!B8","v":20},{"$f":"Model!C8","v":"Time scale parameter"},null,null,"θ parameters",null,null,null,null,null,-0.1,null,{"$f":"SUM(N13:N17)","v":0.98200168755082973}]
[{"$f":"Model!A9","v":"λ = γ(0)"},{"$f":"Model!B9","v":1},{"$f":"Model!C9","v":"State scale parameter"},null,null,7.6819533953270833E-2,8.2332230321314967E-2]
["AR size q'",100,null,null,null,0.20085099623182306,15.594608420616655,null,null,"Adjustment factor",{"$f":"($B$14/W7)^0.5","v":1.0118101212318102}]
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{"sheet":"To3AR(1)","index":6,"n_rows":2061,"n_cols":27,"rows_kept":2061,"cut":false,"hidden":false,"merged":[]}
[{"$f":"Model!A1","v":"You must have macros enabled in order for the program to work. You may see the code through the VBA Editor."}]
[{"$f":"Model!A2","v":"Program by Demetris Koutsoyiannis - Please report bugs to dk@itia.ntua.gr"},null,null,null,null,null,null,{"$f":"Model!H2","v":"Version 0.6"},null,{"$f":"Model!J2","v":"2019-10-23"}]
[{"$f":"Model!A3","v":"Linensed under Creative Commons - Attribution Alone (CC-BY)"}]
[{"$f":"Model!A4","v":"q"},{"$f":"Model!B4","v":1024},{"$f":"Model!C4","v":"The number of coefficients is 2q+1. If you change this number you must adapt the spreadsheet."}]
[{"$f":"Model!A5","v":"Markov or not"},0,{"$f":"Model!C5","v":"Set 1 for Markov, any other number for FHK (Cauchy climacogram)"},null,null,null,null,null,null,"Error in c",{"$f":"SUM((P13:P1037-C13:C1037)^2)","v":4.1036312901912946E-3}]
[{"$f":"Model!A6","v":"H"},{"$f":"Model!B6","v":0.8},{"$f":"Model!C6","v":"Hurst parameter (0 <= H <= 1)"},null,null,null,null,null,null,"Errorn in a",{"$f":"SUM((K13:K2061-X13:X2061)^2)","v":1.410610297371344E-2}]
[{"$f":"Model!A7","v":"M"},{"$f":"Model!B7","v":0.7},{"$f":"Model!C7","v":"Fractal (Mandelbrot) parameter (0 <= M <= 1)"},null,null,"Minimize this by Solver to find θ(ω)--------------->",null,null,null,"Totla error",{"$f":"K6+K5","v":1.8209734263904737E-2},{"$f":"K1037-MAX(K13:K2061)","v":-0.13774032587787055},null,100,null,{"$f":"EXP(-H9)","v":0.36808124323339775},null,null,null,null,null,null,{"$f":"SUM(W13:W2061^2)","v":0.97816600014103183},{"$f":"SUM(X13:X2061^2)","v":0.99573119817039968}]
[{"$f":"Model!A8","v":"α"},{"$f":"Model!B8","v":20},{"$f":"Model!C8","v":"Time scale parameter"},null,null,"θ parameters",null,"Three AR(1) parameters",null,null,null,-0.1,null,{"$f":"SUM(N13:N17)","v":0},null,{"$f":"EXP(-H10)","v":0.37106792513113968}]
[{"$f":"Model!A9","v":"λ = γ(0)"},{"$f":"Model!B9","v":1},{"$f":"Model!C9","v":"State scale parameter"},null,null,7.8287219642043146E-2,0.19313360217808423,0.99945159552326834,0.17088126819854108,null,null,null,null,null,null,0.39015905745280283]
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