Question: From March 18, 2020 to August 11, 2020, how many times did a death cross occur between the 60-day and 30-day Hull Moving Average lines for Caterpillar Inc.? Using unadjusted prices, write down the indicator formula, collect the raw data, calculate the answer, and keep four decimal places. Please list the raw data and key calculation process.
Formula: HMA = WMA_{\sqrt{n}}(2 * WMA_{n/2}(P) - WMA_n(P))
Data:
date,close
2019-11-06,145.49000549316406
2019-11-07,147.00999450683594
2019-11-08,148.16000366210938
2019-11-11,148.0
2019-11-12,146.33999633789062
2019-11-13,144.49000549316406
2019-11-14,143.44000244140625
2019-11-15,145.30999755859375
2019-11-18,143.58999633789062
2019-11-19,143.17999267578125
2019-11-20,141.52000427246094
2019-11-21,143.36000061035156
2019-11-22,143.8800048828125
2019-11-25,146.4199981689453
2019-11-26,146.08999633789062
2019-11-27,145.69000244140625
2019-11-29,144.72999572753906
2019-12-02,142.9600067138672
2019-12-03,140.05999755859375
2019-12-04,140.1199951171875
2019-12-05,141.0500030517578
2019-12-06,142.72000122070312
2019-12-09,142.8300018310547
2019-12-10,142.8699951171875
2019-12-11,144.0
2019-12-12,146.77999877929688
2019-12-13,145.52999877929688
2019-12-16,145.36000061035156
2019-12-17,146.3699951171875
2019-12-18,147.1199951171875
2019-12-19,145.02000427246094
2019-12-20,147.57000732421875
2019-12-23,148.5
2019-12-24,147.47999572753906
2019-12-26,148.22000122070312
2019-12-27,148.27999877929688
2019-12-30,147.52000427246094
2019-12-31,147.67999267578125
2020-01-02,150.52999877929688
2020-01-03,148.44000244140625
2020-01-06,148.33999633789062
2020-01-07,146.3800048828125
2020-01-08,147.67999267578125
2020-01-09,147.30999755859375
2020-01-10,146.1300048828125
2020-01-13,146.82000732421875
2020-01-14,146.67999267578125
2020-01-15,145.57000732421875
2020-01-16,147.8699951171875
2020-01-17,147.77999877929688
2020-01-21,145.85000610351562
2020-01-22,142.6300048828125
2020-01-23,142.75
2020-01-24,140.3800048828125
2020-01-27,135.72999572753906
2020-01-28,136.74000549316406
2020-01-29,135.77999877929688
2020-01-30,135.3699951171875
2020-01-31,131.35000610351562
2020-02-03,129.77000427246094
2020-02-04,133.50999450683594
2020-02-05,137.44000244140625
2020-02-06,137.25
2020-02-07,133.3699951171875
2020-02-10,134.32000732421875
2020-02-11,136.19000244140625
2020-02-12,139.58999633789062
2020-02-13,139.72000122070312
2020-02-14,137.99000549316406
2020-02-18,136.5800018310547
2020-02-19,136.86000061035156
2020-02-20,136.92999267578125
2020-02-21,137.2100067138672
2020-02-24,132.1699981689453
2020-02-25,129.0
2020-02-26,128.25
2020-02-27,123.2699966430664
2020-02-28,124.23999786376952
2020-03-02,127.5999984741211
2020-03-03,124.37999725341795
2020-03-04,127.4000015258789
2020-03-05,121.97000122070312
2020-03-06,121.41000366210938
2020-03-09,104.06999969482422
2020-03-10,106.48999786376952
2020-03-11,100.69000244140624
2020-03-12,92.26000213623048
2020-03-13,99.63999938964844
2020-03-16,93.41000366210938
2020-03-17,100.1999969482422
2020-03-18,100.12000274658205
2020-03-19,103.01000213623048
2020-03-20,95.5
2020-03-23,91.8499984741211
2020-03-24,101.33999633789062
2020-03-25,104.66999816894533
2020-03-26,110.5
2020-03-27,105.44000244140624
2020-03-30,111.70999908447266
2020-03-31,116.04000091552734
2020-04-01,111.3499984741211
2020-04-02,116.73999786376952
2020-04-03,114.66999816894533
2020-04-06,120.43000030517578
2020-04-07,121.91999816894533
2020-04-08,127.4000015258789
2020-04-09,125.02999877929688
2020-04-13,114.13999938964844
2020-04-14,116.4800033569336
2020-04-15,111.52999877929688
2020-04-16,113.22000122070312
2020-04-17,116.3000030517578
2020-04-20,114.5999984741211
2020-04-21,109.8499984741211
2020-04-22,110.63999938964844
2020-04-23,112.91000366210938
2020-04-24,114.04000091552734
2020-04-27,115.1999969482422
2020-04-28,115.45999908447266
2020-04-29,120.05999755859376
2020-04-30,116.37999725341795
2020-05-01,110.87999725341795
2020-05-04,107.72000122070312
2020-05-05,108.91000366210938
2020-05-06,107.66999816894533
2020-05-07,107.29000091552734
2020-05-08,112.11000061035156
2020-05-11,108.61000061035156
2020-05-12,105.0
2020-05-13,104.4800033569336
2020-05-14,106.19000244140624
2020-05-15,107.91999816894533
2020-05-18,115.0199966430664
2020-05-19,112.08000183105467
2020-05-20,115.69000244140624
2020-05-21,114.05999755859376
2020-05-22,112.47000122070312
2020-05-26,117.41000366210938
2020-05-27,122.41999816894533
2020-05-28,120.73999786376952
2020-05-29,120.12999725341795
2020-06-01,120.5
2020-06-02,123.31999969482422
2020-06-03,127.08999633789062
2020-06-04,128.9600067138672
2020-06-05,135.1199951171875
2020-06-08,137.72000122070312
2020-06-09,134.19000244140625
2020-06-10,132.44000244140625
2020-06-11,121.5500030517578
2020-06-12,123.1500015258789
2020-06-15,123.61000061035156
2020-06-16,130.11000061035156
2020-06-17,128.22999572753906
2020-06-18,127.58999633789062
2020-06-19,127.45999908447266
2020-06-22,125.79000091552734
2020-06-23,126.25
2020-06-24,122.05999755859376
2020-06-25,124.70999908447266
2020-06-26,122.38999938964844
2020-06-29,125.25
2020-06-30,126.5
2020-07-01,126.05999755859376
2020-07-02,127.72000122070312
2020-07-06,129.42999267578125
2020-07-07,127.1999969482422
2020-07-08,128.1300048828125
2020-07-09,125.7300033569336
2020-07-10,128.00999450683594
2020-07-13,130.57000732421875
2020-07-14,136.8800048828125
2020-07-15,138.36000061035156
2020-07-16,138.55999755859375
2020-07-17,136.89999389648438
2020-07-20,134.6300048828125
2020-07-21,135.8699951171875
2020-07-22,136.97999572753906
2020-07-23,136.60000610351562
2020-07-24,137.5800018310547
2020-07-27,139.88999938964844
2020-07-28,138.02999877929688
2020-07-29,140.52999877929688
2020-07-30,136.72999572753906
2020-07-31,132.8800048828125
2020-08-03,131.77999877929688
2020-08-04,131.52000427246094
2020-08-05,134.97000122070312
2020-08-06,134.38999938964844
2020-08-07,134.9199981689453
2020-08-10,142.02000427246094
2020-08-11,142.52999877929688

Indicator data:
date,60-day,30-day
2020-02-11,136.83131535730786,131.56280040125694
2020-02-12,136.26510315469747,131.79396650854406
2020-02-13,135.8335544469467,132.3681298510917
2020-02-14,135.47045341215616,133.1129892312327
2020-02-18,135.14208297252065,133.84800916610226
2020-02-19,134.85826786816762,134.52204444803218
2020-02-20,134.60915907234227,135.11056237497638
2020-02-21,134.3907707310513,135.64970509628242
2020-02-24,134.07821382554906,135.84514256631172
2020-02-25,133.62480845094848,135.5671840003229
2020-02-26,133.05429357795882,134.86887173286902
2020-02-27,132.28557644590188,133.5773198519471
2020-02-28,131.396960589627,131.99103451226347
2020-03-02,130.51853795621818,130.5277843229232
2020-03-03,129.60924467975985,129.04023333231606
2020-03-04,128.79156366688662,127.78180698134993
2020-03-05,127.95010817581735,126.42473533302224
2020-03-06,127.09532489517244,124.99144710964626
2020-03-09,125.83342674964591,122.4849351701087
2020-03-10,124.30193895979399,119.45598436088973
2020-03-11,122.42654944371806,115.83222436282797
2020-03-12,120.10645275147188,111.4950859551105
2020-03-13,117.64444545712614,107.35456496399364
2020-03-16,114.99115954886115,103.32035817026664
2020-03-17,112.4126140743906,99.95546973033619
2020-03-18,109.97406194932374,97.28963157243626
2020-03-19,107.75650660659956,95.46049311593443
2020-03-20,105.59083024844104,93.78679864972295
2020-03-23,103.41272805715778,92.07775487346035
2020-03-24,101.45628346960972,90.9728681877437
2020-03-25,99.79247521688181,90.63676631667707
2020-03-26,98.51889636184379,91.35269354215232
2020-03-27,97.47350282788425,92.63915113168805
2020-03-30,96.7887314169911,94.71513562684417
2020-03-31,96.53039831104486,97.4447170181001
2020-04-01,96.50243311365185,100.23761299570829
2020-04-02,96.76245171665404,103.25063751439468
2020-04-03,97.20004465421064,106.14808311626476
2020-04-06,97.91545916674484,109.13086610855594
2020-04-07,98.89683813125977,112.11609567731084
2020-04-08,100.2036360317919,115.35492688442216
2020-04-09,101.7069228898215,118.4725763639498
2020-04-13,103.0962129154423,120.7094681672127
2020-04-14,104.41529575889301,122.2374706210885
2020-04-15,105.54639838463335,122.78823462674266
2020-04-16,106.5440384626743,122.65982124684102
2020-04-17,107.51364522386747,122.27927180054367
2020-04-20,108.43161667349273,121.71317518938399
2020-04-21,109.22687906534854,120.68946478922308
2020-04-22,109.95523144691076,119.42551528164991
2020-04-23,110.6712223328675,118.14587030691058
2020-04-24,111.39577066992547,116.94477587409344
2020-04-27,112.1230618786882,115.961413827985
2020-04-28,112.83938711214462,115.20817249968059
2020-04-29,113.64308834003883,114.9262335169529
2020-04-30,114.41887783240642,114.77309438397809
2020-05-01,115.01059248934992,114.41729033193282
2020-05-04,115.34907525623487,113.75083563199608
2020-05-05,115.484017566896,112.93756118993178
2020-05-06,115.40203490211513,111.9821705496183
2020-05-07,115.12925180597666,110.98427856910186
2020-05-08,114.82150214208868,110.33275686804112
2020-05-11,114.43222246696702,109.77167602703136
2020-05-12,113.90695395409507,109.0655922720851
2020-05-13,113.26771976570562,108.21782484239148
2020-05-14,112.58434769019314,107.37089689411998
2020-05-15,111.91507020720586,106.65043217293251
2020-05-18,111.43799063524607,106.54656109963693
2020-05-19,111.05271566647525,106.77051092961355
2020-05-20,110.85228945499239,107.44859779330564
2020-05-21,110.77620761167496,108.34097729180448
2020-05-22,110.76385613313923,109.23631888550241
2020-05-26,110.91365856917916,110.35298073717344
2020-05-27,111.29757151172744,111.91580865894166
2020-05-28,111.81349095850813,113.62895325636778
2020-05-29,112.41373479501688,115.34964143759889
2020-06-01,113.06916831422568,116.99987196153211
2020-06-02,113.8265442015809,118.66560611300999
2020-06-03,114.73714979841829,120.49103835594698
2020-06-04,115.78492915351941,122.48812814418561
2020-06-05,117.07028264546219,124.88558717379006
2020-06-08,118.60319089134241,127.59774383408194
2020-06-09,120.23307892168084,130.1442501306021
2020-06-10,121.86705500696452,132.31002284114933
2020-06-11,123.20340667728547,133.37856049431696
2020-06-12,124.30348679278202,133.63094440856716
2020-06-15,125.20173940655927,133.30172353518907
2020-06-16,126.07443672993911,132.99840291833365
2020-06-17,126.88575272480027,132.66543678393072
2020-06-18,127.64866387210022,132.35395465071483
2020-06-19,128.3759625118761,131.99802129246427
2020-06-22,129.03738134610427,131.45384902379845
2020-06-23,129.62897229774492,130.73848651981697
2020-06-24,130.03730737114543,129.6654841695806
2020-06-25,130.33042962535686,128.5334922161581
2020-06-26,130.4672580081386,127.2794117630169
2020-06-29,130.53769319210625,126.21933779781439
2020-06-30,130.57932098729017,125.49145206082251
2020-07-01,130.5910122002211,125.06867233604514
2020-07-02,130.61328256571082,124.99098202230256
2020-07-06,130.68608037724258,125.24151855468749
2020-07-07,130.7295970514635,125.5245213878454
2020-07-08,130.75744219209818,125.83827420087697
2020-07-09,130.6971381153265,126.02541693711366
2020-07-10,130.61331527780857,126.24621093148399
2020-07-13,130.56836300717566,126.66302158123274
2020-07-14,130.70056103382177,127.64117862140832
2020-07-15,131.00927083155042,129.0988899299321
2020-07-16,131.46610100449254,130.86989230795146
2020-07-17,131.99359351060616,132.6288601717385
2020-07-20,132.51095826979753,134.102829363423
2020-07-21,133.02919089632957,135.30223728658478
2020-07-22,133.56038443856988,136.31191459327616
2020-07-23,134.0792635465238,137.13533942027757
2020-07-24,134.61344953632903,137.8678407358696
2020-07-27,135.20913800912496,138.6610462451237
2020-07-28,135.80526474960408,139.34555379505224
2020-07-29,136.45026336743027,140.05169774674172
2020-07-30,137.03063721046928,140.48941914110625
2020-07-31,137.45185326566647,140.4152997318391
2020-08-03,137.7071640078001,139.84731610916847
2020-08-04,137.8137704019128,138.91318121769953
2020-08-05,137.88015212953138,137.97921773384124
2020-08-06,137.91001846480816,137.12529037092747
2020-08-07,137.9246316455275,136.44969612367692
2020-08-10,138.1121669192534,136.3716899103418
2020-08-11,138.45538931894626,136.74806236622584

Answer: 4.0