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Exponentially-Weighted Moving Average

Exponentially-Weighted Moving Average
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2019-03-13 05:59
SequenceCalculusProbability & Statistics
This example demonstrates the Exponentially-Weighted Moving Average (EMA), a statistical technique used to smooth time series data. EMA gives more weight to recent data points, reflecting the latest changes in the data. The example uses GeoGebra's sequence command and random normal distribution to generate data points and illustrate the EMA calculation process. Suitable for students studying statistics and time series analysis.

GeoGebra Commands & Parameters

  1. Sequence(i, i, 1, 100) → indx
  2. RandomNormal(10, zsigma) → B1
  3. RandomNormal(10, zsigma) → B2
  4. RandomNormal(10, zsigma) → B3
  5. RandomNormal(10, zsigma) → B4
  6. RandomNormal(10, zsigma) → B5
  7. RandomNormal(10, zsigma) → B6
  8. RandomNormal(10, zsigma) → B7
  9. RandomNormal(10, zsigma) → B8
  10. RandomNormal(10, zsigma) → B9
  11. RandomNormal(10, zsigma) → B10
  12. RandomNormal(10, zsigma) → B11
  13. RandomNormal(10, zsigma) → B12
  14. RandomNormal(10, zsigma) → B13
  15. RandomNormal(10, zsigma) → B14
  16. RandomNormal(10, zsigma) → B15
  17. RandomNormal(10, zsigma) → B16
  18. RandomNormal(10, zsigma) → B17
  19. RandomNormal(10, zsigma) → B18
  20. RandomNormal(10, zsigma) → B19
  21. RandomNormal(30, zsigma) → B20
  22. RandomNormal(30, zsigma) → B21
  23. RandomNormal(30, zsigma) → B22
  24. RandomNormal(30, zsigma) → B23
  25. RandomNormal(30, zsigma) → B24
  26. RandomNormal(30, zsigma) → B25
  27. RandomNormal(30, zsigma) → B26
  28. RandomNormal(30, zsigma) → B27
  29. RandomNormal(30, zsigma) → B28
  30. RandomNormal(30, zsigma) → B29
  31. RandomNormal(30, zsigma) → B30
  32. RandomNormal(30, zsigma) → B31
  33. RandomNormal(30, zsigma) → B32
  34. RandomNormal(30, zsigma) → B33
  35. RandomNormal(30, zsigma) → B34
  36. RandomNormal(30, zsigma) → B35
  37. RandomNormal(30, zsigma) → B36
  38. RandomNormal(30, zsigma) → B37
  39. RandomNormal(30, zsigma) → B38
  40. RandomNormal(30, zsigma) → B39
  41. RandomNormal(30, zsigma) → B40
  42. RandomNormal(30, zsigma) → B41
  43. RandomNormal(30, zsigma) → B42
  44. RandomNormal(30, zsigma) → B43
  45. RandomNormal(30, zsigma) → B44
  46. RandomNormal(30, zsigma) → B45
  47. RandomNormal(30, zsigma) → B46
  48. RandomNormal(30, zsigma) → B47
  49. RandomNormal(30, zsigma) → B48
  50. RandomNormal(30, zsigma) → B49
  51. RandomNormal(30, zsigma) → B50
  52. RandomNormal(10, zsigma) → B51
  53. RandomNormal(10, zsigma) → B52
  54. RandomNormal(10, zsigma) → B53
  55. RandomNormal(10, zsigma) → B54
  56. RandomNormal(10, zsigma) → B55
  57. RandomNormal(10, zsigma) → B56
  58. RandomNormal(10, zsigma) → B57
  59. RandomNormal(10, zsigma) → B58
  60. RandomNormal(10, zsigma) → B59
  61. RandomNormal(10, zsigma) → B60
  62. RandomNormal(10, zsigma) → B61
  63. RandomNormal(10, zsigma) → B62
  64. RandomNormal(10, zsigma) → B63
  65. RandomNormal(10, zsigma) → B64
  66. RandomNormal(10, zsigma) → B65
  67. RandomNormal(10, zsigma) → B66
  68. RandomNormal(10, zsigma) → B67
  69. RandomNormal(10, zsigma) → B68
  70. RandomNormal(10, zsigma) → B69
  71. RandomNormal(10, zsigma) → B70
  72. RandomNormal(10, zsigma) → B71
  73. RandomNormal(10, zsigma) → B72
  74. RandomNormal(10, zsigma) → B73
  75. RandomNormal(10, zsigma) → B74
  76. RandomNormal(10, zsigma) → B75
  77. RandomNormal(10, zsigma) → B76
  78. RandomNormal(10, zsigma) → B77
  79. RandomNormal(10, zsigma) → B78
  80. RandomNormal(10, zsigma) → B79
  81. RandomNormal(10, zsigma) → B80
  82. RandomNormal(10, zsigma) → B81
  83. RandomNormal(10, zsigma) → B82
  84. RandomNormal(10, zsigma) → B83
  85. RandomNormal(10, zsigma) → B84
  86. RandomNormal(10, zsigma) → B85
  87. RandomNormal(10, zsigma) → B86
  88. RandomNormal(10, zsigma) → B87
  89. RandomNormal(10, zsigma) → B88
  90. RandomNormal(10, zsigma) → B89
  91. RandomNormal(10, zsigma) → B90
  92. RandomNormal(10, zsigma) → B91
  93. RandomNormal(10, zsigma) → B92
  94. RandomNormal(10, zsigma) → B93
  95. RandomNormal(10, zsigma) → B94
  96. RandomNormal(10, zsigma) → B95
  97. RandomNormal(10, zsigma) → B96
  98. RandomNormal(10, zsigma) → B97
  99. RandomNormal(10, zsigma) → B98
  100. RandomNormal(10, zsigma) → B99
  101. RandomNormal(10, zsigma) → B100
  102. Sequence(Segment[(indx(i - 1), raw2(i - 1)), (indx(i), raw2(i))], i, 2, 100) → l1
  103. Sequence(Segment[(indx(i - 1), EWMA3(i - 1)), (indx(i), EWMA3(i))], i, 2, 100) → l2
  104. Segment((0, 10 - (2 * EWMAsig)), (100, 10 - (2 * EWMAsig))) → g
  105. Segment((0, 10 + (2 * EWMAsig)), (100, 10 + (2 * EWMAsig))) → f
  106. Segment((0, 10 + (2 * zsigma)), (100, 10 + (2 * zsigma))) → h
  107. Segment((0, 10 - (2 * zsigma)), (100, 10 - (2 * zsigma))) → i

AI Drawing Prompt Reference

Create an Exponentially-Weighted Moving Average (EMA) graph using 10 random normal distribution data points to generate three curves, each representing a different dataset. Then calculate and plot the EMA to show that recent data points have more weight. Finally, use 30 random normal distribution data points to generate one EMA curve to demonstrate changes over a longer time series.
The prompt above was compiled from the original drawing commands and is for reference only.