Question: For Alexandria Real Estate Equities between June 23, 2022 and September 28, 2022, how many times did the price break above the 10-day Exponential Moving Average line? (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,high,open
2022-04-26,190.6000061035156,194.4600067138672,190.0
2022-04-27,187.3800048828125,191.3999938964844,190.17999267578125
2022-04-28,190.44000244140625,190.9199981689453,188.4499969482422
2022-04-29,182.16000366210935,189.82000732421875,189.44000244140625
2022-05-02,178.14999389648438,182.9600067138672,182.0399932861328
2022-05-03,180.50999450683597,182.1499938964844,179.17999267578125
2022-05-04,184.30999755859372,184.67999267578125,180.69000244140625
2022-05-05,179.17999267578125,184.67999267578125,183.6100006103516
2022-05-06,176.67999267578125,178.9600067138672,178.82000732421875
2022-05-09,167.27000427246094,175.49000549316406,174.75
2022-05-10,163.16000366210938,171.30999755859375,169.27000427246094
2022-05-11,161.72000122070312,166.60000610351562,163.1300048828125
2022-05-12,161.9600067138672,163.6199951171875,161.38999938964844
2022-05-13,166.4499969482422,166.47999572753906,163.80999755859375
2022-05-16,164.9499969482422,166.92999267578125,166.77999877929688
2022-05-17,165.5399932861328,166.05999755859375,165.9499969482422
2022-05-18,158.0,165.0399932861328,164.97999572753906
2022-05-19,157.82000732421875,160.35000610351562,157.89999389648438
2022-05-20,159.7100067138672,159.88999938964844,158.0
2022-05-23,160.7100067138672,162.77999877929688,161.4199981689453
2022-05-24,160.25,160.94000244140625,160.94000244140625
2022-05-25,160.27999877929688,162.19000244140625,159.99000549316406
2022-05-26,163.3000030517578,164.38999938964844,162.07000732421875
2022-05-27,168.58999633789062,169.1199951171875,164.1300048828125
2022-05-31,165.9499969482422,167.6699981689453,167.14999389648438
2022-06-01,163.80999755859375,166.6300048828125,166.02000427246094
2022-06-02,166.64999389648438,166.77000427246094,163.10000610351562
2022-06-03,163.3699951171875,165.07000732421875,165.0
2022-06-06,162.57000732421875,165.1199951171875,164.66000366210938
2022-06-07,164.32000732421875,164.38999938964844,161.83999633789062
2022-06-08,156.0800018310547,162.8800048828125,162.8800048828125
2022-06-09,150.47000122070312,156.33999633789062,155.3000030517578
2022-06-10,146.2899932861328,148.61000061035156,148.0800018310547
2022-06-13,136.7100067138672,143.5800018310547,142.66000366210938
2022-06-14,135.3699951171875,138.5500030517578,137.27000427246094
2022-06-15,135.72999572753906,138.8000030517578,136.97999572753906
2022-06-16,130.5399932861328,133.1199951171875,132.42999267578125
2022-06-17,131.77999877929688,132.91000366210938,130.0
2022-06-21,131.6199951171875,134.22999572753906,132.88999938964844
2022-06-22,133.38999938964844,134.82000732421875,130.41000366210938
2022-06-23,137.9499969482422,138.2100067138672,133.0399932861328
2022-06-24,143.52999877929688,144.07000732421875,139.13999938964844
2022-06-27,145.66000366210938,146.7899932861328,143.36000061035156
2022-06-28,144.5,148.52999877929688,146.50999450683594
2022-06-29,144.5399932861328,145.41000366210938,142.77000427246094
2022-06-30,145.02999877929688,146.55999755859375,143.07000732421875
2022-07-01,148.1300048828125,148.89999389648438,144.8800048828125
2022-07-05,149.32000732421875,149.35000610351562,146.83999633789062
2022-07-06,150.02000427246094,151.88999938964844,150.16000366210938
2022-07-07,149.61000061035156,152.27000427246094,150.4499969482422
2022-07-08,146.35000610351562,149.07000732421875,149.07000732421875
2022-07-11,143.47000122070312,146.4499969482422,145.11000061035156
2022-07-12,143.2100067138672,144.36000061035156,142.30999755859375
2022-07-13,140.67999267578125,142.27000427246094,141.24000549316406
2022-07-14,137.41000366210938,139.89999389648438,138.47000122070312
2022-07-15,142.80999755859375,142.86000061035156,139.63999938964844
2022-07-18,141.86000061035156,144.64999389648438,143.97000122070312
2022-07-19,146.55999755859375,146.6699981689453,143.35000610351562
2022-07-20,147.8000030517578,149.35000610351562,147.38999938964844
2022-07-21,148.19000244140625,148.8000030517578,147.4499969482422
2022-07-22,150.22000122070312,151.8800048828125,149.75999450683594
2022-07-25,150.2899932861328,151.47000122070312,149.8000030517578
2022-07-26,156.49000549316406,157.2899932861328,151.3699951171875
2022-07-27,158.27000427246094,159.38999938964844,156.67999267578125
2022-07-28,163.1999969482422,163.6300048828125,159.22000122070312
2022-07-29,165.77999877929688,166.25999450683594,162.8300018310547
2022-08-01,164.32000732421875,165.55999755859375,164.19000244140625
2022-08-02,159.6699981689453,164.00999450683594,164.0
2022-08-03,159.3699951171875,162.27999877929688,160.3000030517578
2022-08-04,159.91000366210938,160.11000061035156,159.0
2022-08-05,159.77999877929688,159.97000122070312,158.69000244140625
2022-08-08,162.52000427246094,163.67999267578125,161.47999572753906
2022-08-09,162.0500030517578,163.08999633789062,163.08999633789062
2022-08-10,166.55999755859375,166.75,164.91000366210938
2022-08-11,166.97000122070312,168.1999969482422,167.69000244140625
2022-08-12,170.08999633789062,170.22000122070312,168.39999389648438
2022-08-15,170.0399932861328,170.8800048828125,169.74000549316406
2022-08-16,171.5800018310547,171.83999633789062,168.75
2022-08-17,170.72999572753906,171.41000366210938,169.7100067138672
2022-08-18,165.86000061035156,171.25999450683594,171.25999450683594
2022-08-19,163.14999389648438,165.3699951171875,164.8300018310547
2022-08-22,160.17999267578125,162.39999389648438,161.97999572753906
2022-08-23,157.67999267578125,160.7100067138672,159.99000549316406
2022-08-24,159.35000610351562,160.27000427246094,158.17999267578125
2022-08-25,161.9499969482422,162.4499969482422,160.30999755859375
2022-08-26,158.0,162.49000549316406,162.14999389648438
2022-08-29,155.7100067138672,157.41000366210938,157.16000366210938
2022-08-30,153.97999572753906,157.33999633789062,156.49000549316406
2022-08-31,153.39999389648438,156.2100067138672,155.19000244140625
2022-09-01,151.75,153.13999938964844,152.0
2022-09-02,150.38999938964844,154.27000427246094,153.72000122070312
2022-09-06,152.6699981689453,153.08999633789062,151.19000244140625
2022-09-07,154.33999633789062,154.75,152.9600067138672
2022-09-08,156.94000244140625,157.3000030517578,152.80999755859375
2022-09-09,158.83999633789062,159.36000061035156,156.77999877929688
2022-09-12,160.27999877929688,161.07000732421875,159.5800018310547
2022-09-13,153.72999572753906,158.27000427246094,156.97999572753906
2022-09-14,151.99000549316406,153.74000549316406,152.36000061035156
2022-09-15,150.88999938964844,153.1699981689453,151.7899932861328
2022-09-16,150.66000366210938,150.86000061035156,150.86000061035156
2022-09-19,149.02000427246094,149.47000122070312,149.02000427246094
2022-09-20,144.74000549316406,147.1999969482422,147.05999755859375
2022-09-21,141.24000549316406,146.5399932861328,146.0399932861328
2022-09-22,142.07000732421875,144.7100067138672,140.91000366210938
2022-09-23,143.0500030517578,143.42999267578125,140.41000366210938
2022-09-26,139.4600067138672,142.47999572753906,142.47999572753906
2022-09-27,137.92999267578125,141.10000610351562,140.8000030517578
2022-09-28,141.22000122070312,142.25999450683594,139.24000549316406

Indicator data:
date,10-day,close
2022-05-09,180.0339833083587,167.27000427246094
2022-05-10,176.96598700904065,163.16000366210938
2022-05-11,174.19398959297925,161.72000122070312
2022-05-12,171.96962906950432,161.9600067138672
2022-05-13,170.9660595929112,166.4499969482422
2022-05-16,169.87223002115317,164.9499969482422
2022-05-17,169.08455061478583,165.5399932861328
2022-05-18,167.06917777573383,158.0
2022-05-19,165.3875104209129,157.82000732421875
2022-05-20,164.35523701963183,159.7100067138672
2022-05-23,163.69246787312915,160.7100067138672
2022-05-24,163.06656462346928,160.25
2022-05-25,162.5599162881652,160.27999877929688
2022-05-26,162.69447751790932,163.3000030517578
2022-05-27,163.7663900306332,168.58999633789062
2022-05-31,164.16340947019847,165.9499969482422
2022-06-01,164.0991527589976,163.80999755859375
2022-06-02,164.56294205672245,166.64999389648438
2022-06-03,164.34604261317062,163.3699951171875
2022-06-06,164.02312710608848,162.57000732421875
2022-06-07,164.0771053275667,164.32000732421875
2022-06-08,162.62308651001905,156.0800018310547
2022-06-09,160.41343463923434,150.47000122070312
2022-06-10,157.84553621139767,146.2899932861328
2022-06-13,154.0027126663921,136.7100067138672
2022-06-14,150.61494583926398,135.3699951171875
2022-06-15,147.9085912734958,135.72999572753906
2022-06-16,144.75066436670252,130.5399932861328
2022-06-17,142.39236153262877,131.77999877929688
2022-06-21,140.433749457094,131.6199951171875
2022-06-22,139.15306762664935,133.38999938964844
2022-06-23,138.9343275033026,137.9499969482422
2022-06-24,139.76990409893793,143.52999877929688
2022-06-27,140.84083129224183,145.66000366210938
2022-06-28,141.5061346936524,144.5
2022-06-29,142.05774534683064,144.5399932861328
2022-06-30,142.59815506182449,145.02999877929688
2022-07-01,143.60394593836776,148.1300048828125
2022-07-05,144.6432298267043,149.32000732421875
2022-07-06,145.62082518047822,150.02000427246094
2022-07-07,146.34612980409156,149.61000061035156
2022-07-08,146.34683458580503,146.35000610351562
2022-07-11,145.82377397396831,143.47000122070312
2022-07-12,145.34854356304083,143.2100067138672
2022-07-13,144.49971612899364,140.67999267578125
2022-07-14,143.21067749865102,137.41000366210938
2022-07-15,143.13782660045877,142.80999755859375
2022-07-18,142.90549460225745,141.86000061035156
2022-07-19,143.56994968522767,146.55999755859375
2022-07-20,144.33905029732406,147.8000030517578
2022-07-21,145.0392234144299,148.19000244140625
2022-07-22,145.98118301557048,150.22000122070312
2022-07-25,146.7646030647636,150.2899932861328
2022-07-26,148.5328580517455,156.49000549316406
2022-07-27,150.30324827369375,158.27000427246094
2022-07-28,152.6481116690662,163.1999969482422
2022-07-29,155.03572750728995,165.77999877929688
2022-08-01,156.72377838309518,164.32000732421875
2022-08-02,157.2594547077952,159.6699981689453
2022-08-03,157.6431893276847,159.3699951171875
2022-08-04,158.0553373884892,159.91000366210938
2022-08-05,158.36891218681785,159.77999877929688
2022-08-08,159.12365620238933,162.52000427246094
2022-08-09,159.65571926591088,162.0500030517578
2022-08-10,160.9110425918532,166.55999755859375
2022-08-11,162.01267143346226,166.97000122070312
2022-08-12,163.48127596154012,170.08999633789062
2022-08-15,164.67377002055696,170.0399932861328
2022-08-16,165.92944853155655,171.5800018310547
2022-08-17,166.80227529446245,170.72999572753906
2022-08-18,166.63095262462411,165.86000061035156
2022-08-19,165.9980510376896,163.14999389648438
2022-08-22,164.94022224461534,160.17999267578125
2022-08-23,163.62018050482732,157.67999267578125
2022-08-24,162.84378515913426,159.35000610351562
2022-08-25,162.68127821169932,161.9499969482422
2022-08-26,161.83013671866306,158.0
2022-08-29,160.71738580870016,155.7100067138672
2022-08-30,159.4924057939436,153.97999572753906
2022-08-31,158.38469453986008,153.39999389648438
2022-09-01,157.17838644170368,151.75
2022-09-02,155.9441342504209,150.38999938964844
2022-09-06,155.3488367810617,152.6699981689453
2022-09-07,155.16541124593968,154.33999633789062
2022-09-08,155.48806419056996,156.94000244140625
2022-09-09,156.0975063991737,158.83999633789062
2022-09-12,156.8579595591961,160.27999877929688
2022-09-13,156.28923886253116,153.72999572753906
2022-09-14,155.50756006810076,151.99000549316406
2022-09-15,154.66800358110942,150.88999938964844
2022-09-16,153.9392763231094,150.66000366210938
2022-09-19,153.0448632229915,149.02000427246094
2022-09-20,151.5348890902956,144.74000549316406
2022-09-21,149.6630920726353,141.24000549316406
2022-09-22,148.28253120928682,142.07000732421875
2022-09-23,147.33116245337243,143.0500030517578
2022-09-26,145.90004322800783,139.4600067138672
2022-09-27,144.45094312760298,137.92999267578125
2022-09-28,143.86349914453027,141.22000122070312

Answer: 6.0