Question: For Albemarle Corporation, how many times did the 5-day and 10-day Exponential Moving Average lines produce a golden cross between October 06, 2023 and May 24, 2024? (Smoothing factor alpha = 2 / (n + 1); Require 4n data points to warm up; Use the first data point as the initial value) 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: EMA_t = \alpha * P_t + (1 - \alpha) * EMA_{t-1}, \quad \alpha = 2 / (n + 1)
Data:
date,close
2023-08-10,191.6699981689453
2023-08-11,187.4900054931641
2023-08-14,185.5399932861328
2023-08-15,184.0399932861328
2023-08-16,181.52999877929688
2023-08-17,182.67999267578125
2023-08-18,183.38999938964844
2023-08-21,188.07000732421875
2023-08-22,188.16000366210935
2023-08-23,191.77999877929688
2023-08-24,190.7400054931641
2023-08-25,189.7400054931641
2023-08-28,189.63999938964844
2023-08-29,197.75
2023-08-30,198.58999633789065
2023-08-31,198.7100067138672
2023-09-01,200.25999450683597
2023-09-05,200.8000030517578
2023-09-06,189.8300018310547
2023-09-07,187.57000732421875
2023-09-08,184.42999267578125
2023-09-11,186.32000732421875
2023-09-12,184.3500061035156
2023-09-13,184.5800018310547
2023-09-14,184.97000122070312
2023-09-15,183.83999633789065
2023-09-18,181.6199951171875
2023-09-19,179.99000549316406
2023-09-20,174.44000244140625
2023-09-21,168.94000244140625
2023-09-22,168.2100067138672
2023-09-25,166.88999938964844
2023-09-26,163.64999389648438
2023-09-27,162.6300048828125
2023-09-28,172.39999389648438
2023-09-29,170.0399932861328
2023-10-02,162.41000366210938
2023-10-03,156.77000427246094
2023-10-04,158.39999389648438
2023-10-05,155.02999877929688
2023-10-06,159.83999633789062
2023-10-09,155.75
2023-10-10,162.0800018310547
2023-10-11,164.8000030517578
2023-10-12,170.8000030517578
2023-10-13,163.3800048828125
2023-10-16,167.72999572753906
2023-10-17,169.47999572753906
2023-10-18,152.88999938964844
2023-10-19,144.55999755859375
2023-10-20,138.67999267578125
2023-10-23,136.27999877929688
2023-10-24,139.24000549316406
2023-10-25,135.32000732421875
2023-10-26,135.2100067138672
2023-10-27,134.44000244140625
2023-10-30,127.41000366210938
2023-10-31,126.77999877929688
2023-11-01,122.95999908447266
2023-11-02,124.62000274658205
2023-11-03,127.9800033569336
2023-11-06,119.45999908447266
2023-11-07,122.11000061035156
2023-11-08,119.01000213623048
2023-11-09,114.5999984741211
2023-11-10,116.9800033569336
2023-11-13,114.19000244140624
2023-11-14,125.31999969482422
2023-11-15,127.72000122070312
2023-11-16,122.5999984741211
2023-11-17,127.38999938964844
2023-11-20,130.36000061035156
2023-11-21,126.12999725341795
2023-11-22,126.58999633789062
2023-11-24,128.8699951171875
2023-11-27,120.77999877929688
2023-11-28,123.91000366210938
2023-11-29,123.37999725341795
2023-11-30,121.2699966430664
2023-12-01,126.16000366210938
2023-12-04,119.9800033569336
2023-12-05,113.26000213623048
2023-12-06,118.3000030517578
2023-12-07,125.3499984741211
2023-12-08,127.98999786376952
2023-12-11,126.54000091552734
2023-12-12,127.94000244140624
2023-12-13,140.05999755859375
2023-12-14,145.88999938964844
2023-12-15,147.05999755859375
2023-12-18,145.91000366210938
2023-12-19,148.92999267578125
2023-12-20,142.52999877929688
2023-12-21,145.4499969482422
2023-12-22,150.08999633789062
2023-12-26,152.38999938964844
2023-12-27,149.32000732421875
2023-12-28,149.42999267578125
2023-12-29,144.47999572753906
2024-01-02,146.88999938964844
2024-01-03,140.17999267578125
2024-01-04,135.92999267578125
2024-01-05,135.8300018310547
2024-01-08,136.5800018310547
2024-01-09,133.6699981689453
2024-01-10,132.94000244140625
2024-01-11,128.64999389648438
2024-01-12,126.0500030517578
2024-01-16,125.9499969482422
2024-01-17,120.6999969482422
2024-01-18,117.98999786376952
2024-01-19,115.12999725341795
2024-01-22,120.75
2024-01-23,122.58999633789062
2024-01-24,121.69000244140624
2024-01-25,118.4499969482422
2024-01-26,119.83999633789062
2024-01-29,123.1999969482422
2024-01-30,120.30999755859376
2024-01-31,114.73999786376952
2024-02-01,116.77999877929688
2024-02-02,114.25
2024-02-05,108.7300033569336
2024-02-06,113.0199966430664
2024-02-07,115.0500030517578
2024-02-08,114.33000183105467
2024-02-09,115.77999877929688
2024-02-12,120.08999633789062
2024-02-13,112.1999969482422
2024-02-14,114.38999938964844
2024-02-15,117.5
2024-02-16,122.58999633789062
2024-02-20,114.81999969482422
2024-02-21,118.5500030517578
2024-02-22,118.18000030517578
2024-02-23,120.6500015258789
2024-02-26,121.5199966430664
2024-02-27,128.58999633789062
2024-02-28,132.05999755859375
2024-02-29,137.85000610351562
2024-03-01,142.8000030517578
2024-03-04,133.1999969482422
2024-03-05,109.4000015258789
2024-03-06,119.58999633789062
2024-03-07,122.66000366210938
2024-03-08,118.33000183105467
2024-03-11,124.75
2024-03-12,123.93000030517578
2024-03-13,125.79000091552734
2024-03-14,119.88999938964844
2024-03-15,122.13999938964844
2024-03-18,124.58000183105467
2024-03-19,120.54000091552734
2024-03-20,124.4499969482422
2024-03-21,124.86000061035156
2024-03-22,120.86000061035156
2024-03-25,118.3499984741211
2024-03-26,119.01000213623048
2024-03-27,128.8000030517578
2024-03-28,131.74000549316406
2024-04-01,129.17999267578125
2024-04-02,126.4800033569336
2024-04-03,128.8699951171875
2024-04-04,121.12000274658205
2024-04-05,123.4499969482422
2024-04-08,131.69000244140625
2024-04-09,129.16000366210938
2024-04-10,127.6500015258789
2024-04-11,130.30999755859375
2024-04-12,122.58000183105467
2024-04-15,120.5
2024-04-16,114.11000061035156
2024-04-17,114.38999938964844
2024-04-18,111.8000030517578
2024-04-19,112.1500015258789
2024-04-22,112.29000091552734
2024-04-23,114.20999908447266
2024-04-24,115.2699966430664
2024-04-25,114.9800033569336
2024-04-26,116.87999725341795
2024-04-29,125.7300033569336
2024-04-30,120.30999755859376
2024-05-01,119.0
2024-05-02,125.3000030517578
2024-05-03,128.10000610351562
2024-05-06,130.77999877929688
2024-05-07,131.5500030517578
2024-05-08,130.4600067138672
2024-05-09,133.5500030517578
2024-05-10,129.6199951171875
2024-05-13,131.50999450683594
2024-05-14,135.4600067138672
2024-05-15,127.56999969482422
2024-05-16,129.19000244140625
2024-05-17,131.1199951171875
2024-05-20,130.14999389648438
2024-05-21,126.63999938964844
2024-05-22,126.4800033569336
2024-05-23,122.9499969482422
2024-05-24,127.58999633789062

Indicator data:
date,5-day,10-day
2023-08-23,188.14127885263906,187.65435085981778
2023-08-24,189.0075210661474,188.21537897497166
2023-08-25,189.25168254181966,188.4925837964612
2023-08-28,189.38112149109594,188.70120481340433
2023-08-29,192.17074766073063,190.34644030187627
2023-08-30,194.310497219784,191.84526867206068
2023-08-31,195.7770003844784,193.09340286148003
2023-09-01,197.27133175859763,194.396419524272
2023-09-05,198.44755552298437,195.5607074383603
2023-09-06,195.5750376256745,194.51876096430473
2023-09-07,192.90669419185593,193.25535121156182
2023-09-08,190.08112701983106,191.65074056869264
2023-09-11,188.82742045462697,190.68151634242466
2023-09-12,187.33494900425652,189.530332662623
2023-09-13,186.41663327985592,188.63027251142876
2023-09-14,185.93442259347165,187.96476864038775
2023-09-15,185.23628050827799,187.2148100399337
2023-09-18,184.03085204458117,186.19757096307075
2023-09-19,182.6839031941088,185.068922695815
2023-09-20,179.9359362765413,183.13639174046793
2023-09-21,176.27062499816296,180.55523004972943
2023-09-22,173.58375223673104,178.31064398866357
2023-09-25,171.35250128770352,176.23416315247897
2023-09-26,168.7849988239638,173.94613237866176
2023-09-27,166.7333341769134,171.8886546521437
2023-09-28,168.62222075010374,171.98162542384202
2023-09-29,169.09481159544677,171.62860139880397
2023-10-02,166.86654228433432,169.95249271940494
2023-10-03,163.50102961370987,167.5556766381424
2023-10-04,161.80068437463473,165.89100704875
2023-10-05,159.5437891761888,163.91627827248578
2023-10-06,159.64252489675607,163.17513610255938
2023-10-09,158.3450165978374,161.82511135663947
2023-10-10,159.5900116755765,161.87145507926041
2023-10-11,161.32667546763696,162.4039183469872
2023-10-12,164.4844513290106,163.93047920240002
2023-10-13,164.11630251361123,163.830392962475
2023-10-16,165.32086691825384,164.5394116470321
2023-10-17,166.70724318801558,165.4376996616697
2023-10-18,162.10149525522655,163.15629961221128
2023-10-19,156.25432935634896,159.7751537842808
2023-10-20,150.39621712949307,155.93966994637177
2023-10-23,145.690811012761,152.36518427963085
2023-10-24,143.5405425062287,149.9787881366369
2023-10-25,140.8003641122254,147.31355526165177
2023-10-26,138.936911646106,145.11291007114548
2023-10-27,137.4379419112061,143.17238141119287
2023-10-30,134.09529582817387,140.30649454772313
2023-10-31,131.65686347854822,137.84713168073654
2023-11-01,128.75790868052303,135.14038029959764
2023-11-02,127.37860670254271,133.2275843808675
2023-11-03,127.57907225400635,132.27347874015226
2023-11-06,124.87271453082846,129.94375516639232
2023-11-07,123.9518098906695,128.51943615620308
2023-11-08,122.30454063918984,126.7904481525717
2023-11-09,119.73635991750027,124.57400275648976
2023-11-10,118.81757439731138,123.19327559293409
2023-11-13,117.27505041200966,121.55631683811083
2023-11-14,119.95670017294785,122.24062281205872
2023-11-15,122.54446718886628,123.23687343181224
2023-11-16,122.56297761728456,123.1210779849593
2023-11-17,124.1719848747392,123.89724551308458
2023-11-20,126.23465678661,125.07229189440585
2023-11-21,126.199770275546,125.26460195968077
2023-11-22,126.3298456296609,125.50558275571893
2023-11-24,127.17656212550311,126.11729409416776
2023-11-27,125.04437434343437,125.14687676419123
2023-11-28,124.6662507829927,124.9219907456309
2023-11-29,124.2374996064678,124.64162829250127
2023-11-30,123.24833195200067,124.02860435624038
2023-12-01,124.21888918870357,124.41613150276201
2023-12-04,122.80592724478026,123.60956274897502
2023-12-05,119.623952208597,121.72782445574873
2023-12-06,119.18263582298394,121.10458420047765
2023-12-07,121.238423373363,121.87647770477645
2023-12-08,123.48894820349851,122.98802682459336
2023-12-11,124.5059657741748,123.63384029567227
2023-12-12,125.65064466325194,124.41677886762389
2023-12-13,130.45376229503256,127.26100044780021
2023-12-14,135.59917465990452,130.64809116449987
2023-12-15,139.41944895946762,133.63207414524422
2023-12-18,141.58296719368155,135.8644249664924
2023-12-19,144.0319756877148,138.23998273181763
2023-12-20,143.53131671824218,139.01998564954113
2023-12-21,144.17087679490885,140.1890786129413
2023-12-22,146.14391664256945,141.989245472023
2023-12-26,148.22594422492912,143.88029163886395
2023-12-27,148.59063192469233,144.869330854383
2023-12-28,148.87041884172197,145.69854209463722
2023-12-29,147.4069444703277,145.47698820971027
2024-01-02,147.2346294434346,145.7338993333354
2024-01-03,144.88308385421684,144.724098122871
2024-01-04,141.89872012807166,143.12516985976376
2024-01-05,139.87581402906602,141.79877567272575
2024-01-08,138.77720996306226,140.84990770151282
2024-01-09,137.07480603168995,139.54446960468235
2024-01-10,135.69653816826207,138.34365739317758
2024-01-11,133.3476900776695,136.58117312105153
2024-01-12,130.91512773569895,134.66641492663447
2024-01-16,129.26008413988004,133.08161165783588
2024-01-17,126.40672174266743,130.8304089833643
2024-01-18,123.60114711636814,128.4957887798016
2024-01-19,120.77743049538475,126.06564486591364
2024-01-22,120.76828699692318,125.09916398120205
2024-01-23,121.37552344391233,124.64295168241816
2024-01-24,121.4803497764103,124.10605182041598
2024-01-25,120.47023216702095,123.07767820729347
2024-01-26,120.26015355731084,122.48900877649295
2024-01-29,121.24010135428797,122.61827935317461
2024-01-30,120.93006675572325,122.1985917541599
2024-01-31,118.86671045840535,120.84248377408892
2024-02-01,118.17113989870253,120.10385013867217
2024-02-02,116.8640932658017,119.03951374982267
2024-02-05,114.15272996284568,117.16505731475192
2024-02-06,113.77515218958594,116.4114099199
2024-02-07,114.20010247697657,116.16388139841959
2024-02-08,114.24340226166927,115.83044874980777
2024-02-09,114.7556011008785,115.82127602789669
2024-02-12,116.53373284654921,116.59740699335013
2024-02-13,115.0891542137802,115.7978778942396
2024-02-14,114.85610260573628,115.54189998431394
2024-02-15,115.73740173715754,115.89791816898412
2024-02-16,118.0215999374019,117.11465965423984
2024-02-20,116.9543998565427,116.69744875252792
2024-02-21,117.48626758828107,117.03427680693335
2024-02-22,117.71751182724599,117.24259017025015
2024-02-23,118.69500839345697,117.8621195076372
2024-02-26,119.6366711433268,118.52718807771524
2024-02-27,122.62111287484808,120.3567895795653
2024-02-28,125.76740776942998,122.48464557575228
2024-02-29,129.79494054745854,125.27834748989108
2024-03-01,134.12996138222496,128.46410304659412
2024-03-04,133.81997323756406,129.32517466507556
2024-03-05,125.67998266700235,125.70241591249435
2024-03-06,123.64998722396511,124.59106689893002
2024-03-07,123.31999270334654,124.23996449223536
2024-03-08,121.65666241258259,123.16542582656614
2024-03-11,122.68777494172173,123.45353022173593
2024-03-12,123.1018500628731,123.54016114599771
2024-03-13,123.99790034709119,123.94922292227582
2024-03-14,122.62860002794362,123.21118227997994
2024-03-15,122.4657331485119,123.01642175446511
2024-03-18,123.17048937602617,123.30070904111776
2024-03-19,122.29365988919324,122.79876210919223
2024-03-20,123.01243890887623,123.09898662538312
2024-03-21,123.62829280936802,123.41917098628647
2024-03-22,122.7055287430292,122.95386728157104
2024-03-25,121.25368532005984,122.11680022567103
2024-03-26,120.50579092545007,121.55192784577274
2024-03-27,123.270528300886,122.86975970140638
2024-03-28,126.09368736497869,124.48253166354414
2024-04-01,127.12245580191289,125.33661548395088
2024-04-02,126.9083049869198,125.54450418812955
2024-04-03,127.56220169700904,126.14913890250372
2024-04-04,125.41480204686673,125.23475051051796
2024-04-05,124.75986701399188,124.91024986283145
2024-04-08,127.06991215646335,126.14293214984504
2024-04-09,127.76660932501203,126.69149060662036
2024-04-10,127.72774005863432,126.86576531921281
2024-04-11,128.5884925586208,127.4919893627366
2024-04-12,126.58566231609876,126.59890072061262
2024-04-15,124.55710821073251,125.49000968050122
2024-04-16,121.07473901060554,123.42091712229218
2024-04-17,118.8464924702865,121.77893207999331
2024-04-18,116.49766266411028,119.96458134758684
2024-04-19,115.04844228469983,118.54374865273086
2024-04-22,114.12896182830902,117.40670360960294
2024-04-23,114.15597424703024,116.8254846050338
2024-04-24,114.52731504570897,116.54266861194881
2024-04-25,114.67821114945052,116.2585476564915
2024-04-26,115.412139850773,116.37153849229631
2024-04-29,118.85142768615987,118.073077558594
2024-04-30,119.33761764363784,118.47979028586667
2024-05-01,119.2250784290919,118.57437387025455
2024-05-02,121.25005330331388,119.79721553961876
2024-05-03,123.53337090338113,121.30681382396364
2024-05-06,125.94891352868638,123.02921108856967
2024-05-07,127.8159433697102,124.57844599096751
2024-05-08,128.69729781776255,125.64782066785835
2024-05-09,130.31486622909432,127.0845811012946
2024-05-10,130.0832425251254,127.54556546782058
2024-05-13,130.5588265190289,128.26637074764156
2024-05-14,132.19255325064168,129.5743045596826
2024-05-15,130.6517020653692,129.2098854933447
2024-05-16,130.16446885738156,129.20627039299225
2024-05-17,130.4829776106502,129.55422034284592
2024-05-20,130.3719830392616,129.66254280714384
2024-05-21,129.12798848939056,129.1129894585083
2024-05-22,128.24532677857158,128.63426471276745
2024-05-23,126.48021683512846,127.60076148285377
2024-05-24,126.85014333604919,127.59880418376956

Answer: 9.0