1. Statistics Time Series

2. Time Series
In business, a lot of things happen over time

3. Time Series
Another variable we are interested in happens over time… changes over time… DEPENDS on what time is is…

4. Time Series
This variable that depends on time we call the “dependent” variable

5. Time Series
Time is called the “independent” variable – we can’t control it!

6. Time Series
Data that change over time are called a “time series”

7. Time Series
Time is the “input” variable that we put on the horizontal ↔ x-axis The other “output” variable goes on the vertical ↕ y-axis

8. Time Series
Time series or not? Federal debt

9. Time Series
Time series or not? Taxes paid by income level

10. Time Series
Time series or not? Global atmospheric temperature

11. Time Series
Time series or not? Average salary by education level

12. Time Series
Time series or not? Average annual salary of US workers

13. Questions?

14. Time Series Forecasting
Go to the Portal Open the spreadsheet

15. Time Series Forecasting
Go to the Portal Open the spreadsheet

16. Time Series Forecasting
Is it a time series?

17. Time Series Forecasting
Suppose the Australian Tourist Bureau (your boss) wants to forecast the number of tourists in 2020…

18. Time Series Forecasting
If the data are too volatile, (especially at the end of the series) we won’t be able to make a good forecast…

19. Time Series Forecasting
Assume it will work! Add labels for two more columns: Trend and Forecast

20. Time Series Forecasting
Add years up to 2020 at the bottom of the data

21. Time Series Forecasting
Graph the data! Include the variable labels (and the two new columns)

22. Time Series Forecasting
Include the forecast years

23. Time Series Forecasting
Poof! A graph!

24. Time Series Forecasting
Make it “purty”

25. Time Series Forecasting
Redo the x-axis limits if necessary

26. Time Series Forecasting
Poof! T-O-B!

27. Time Series Forecasting
Does it look too volatile to make a forecast?

28. Time Series Forecasting
Does it look too volatile to make a forecast? I’m willing to take the risk…

29. Time Series Forecasting
Since it kinda looks like an increasing line will fit the data…

30. Time Series Forecasting
To make a forecast, we need to come up with a line of best fit

31. Time Series Forecasting
To make a forecast, we need to come up with a formula for a line of best fit

32. Time Series Forecasting
To make a forecast, we need to come up with a formula for a line of best fit – a regression line

33. Time Series Forecasting
Excel will do that for you! (yay)

34. Time Series Forecasting
Click the “Data” tab Click “Data Analysis” Scroll to “Regression” Click “OK”

35. Time Series Forecasting
Excel does this backward The “input” (x) should go first then the “output” (y)

36. Time Series Forecasting
They didn’t consult me first…

37. Time Series Forecasting
Go to “Input X” Enter your “Year” data Include the label Only go down to the end of your observed data

38. Time Series Forecasting
Now you can “Input Y” Enter your “Arrivals” Include the label Mark “Labels” Click “OK”

39. Time Series Forecasting
Eek!
dreamstime.com

40. Time Series Forecasting
I’s OK, we’re not using most of it…

41. Time Series Forecasting
The R Square will tell you in % how well the line is fitting the data – highlight it and click “%”

42. Time Series Forecasting
Over 98% Is it a good fit?

43. Time Series Forecasting
98% is a SUPER fit (Usually it lurks around 25-35%)

44. Time Series Forecasting
So, if it’s a good fit, lets make a forecast!

45. Time Series Forecasting
Copy the “Coefficients” for “Intercept” and “Year” (include the labels)

46. Time Series Forecasting
Paste them on your Tourism page (I put them in F3-G5)

47. Time Series Forecasting
Believe it or not, this is the formula for our line of best fit!

48. Time Series Forecasting
Arrivals = InterceptCoefficient + YearCoefficient × Year

49. Time Series Forecasting
Arrivals = × Year

50. Time Series Forecasting
Use that for our trend formula!

51. Time Series Forecasting
Don’t forget the “$”s!

52. Time Series Forecasting
Copy it down ALL the way to the bottom…

53. Time Series Forecasting
Poof! Now you have a trend line! (And you didn’t have to draw it!)

54. Time Series Forecasting
But, where is our forecast?

55. Time Series Forecasting
It’s actually here

56. Time Series Forecasting
The trend line after our observed data ends is the forecast

57. Time Series Forecasting
Extending a regression line beyond the observed data produces forecast values

58. Time Series Forecasting
To make it look obvious, go to the bottom of your data and highlight the forecast values

59. Time Series Forecasting
Drag and drop them to the forecast column “D”

60. Time Series Forecasting
Poof! You have a forecast!

61. Time Series Forecasting
But… it’s detached from the trendline…

62. Time Series Forecasting
Go back to the bottom of your data and type the last trend value in the forecast column

63. Time Series Forecasting
Poof! It’s attached!

64. Time Series Forecasting
Make it “purty”

65. Time Series Forecasting
But, now your boss wants a forecast for 2025

66. Time Series Forecasting
Don’t panic…

67. Time Series Forecasting
Don’t panic… use your formula!

68. Time Series Forecasting
Don’t panic… use your formula: Arrivals = × Year

69. Time Series Forecasting
Arrivals = × 2025

70. Time Series Forecasting
Add the new years at the bottom of your spreadsheet and copy your forecast formula

71. Time Series Forecasting
There’s your forecast for 2025

72. Time Series Forecasting
Adjust your x-axis limits

73. Time Series Forecasting
Right click on any data line in your graph and click “Select Data”

74. Time Series Forecasting
Click Forecast under “Legend Entries” then the “Edit” button

75. Time Series Forecasting
Adjust the ending values for the series X and series Y data

76. Time Series Forecasting
Click “OK” then Click “OK” Poof! A graph of your new forecast!

77. Time Series Forecasting
The boss can’t beat you!

78. Questions?

79. Time Series Forecasting
Go to the Annual CO2 sheet Create a graph of the time series data

80. Time Series Forecasting
Because the data are now annual averages, the cyclical volatility is gone!

81. Time Series Forecasting
Scientists use annual averages to smooth out the cyclical nature of the data

82. Time Series Forecasting
Why would using moving averages be better than calculating annual averages?

83. Time Series Forecasting
Annual averages have only one value per year Moving averages of monthly data will have 12 per year (after the initial “start-up period”)

84. Time Series Forecasting
Statistical rule: More Data Is Better Than Less Data

85. Time Series Forecasting
So, if you have monthly data, a moving average will preserve more data after smoothing than annual averages Moving averages are better!

86. Time Series Forecasting
Why don’t scientists use them?

87. Time Series Forecasting
Good question! They just don’t!

88. Time Series Forecasting
Business people use Moving Averages!

89. Time Series Forecasting
Back to our annual data… Looks like there is an upward trend!

90. Time Series Forecasting
Click “Data” “Data Analysis” “Regression” “OK”

91. Time Series Forecasting
The “Y Range” is the ppm CO2 data in column B The “X Range” is the Year data in column A Include the labels!

92. Time Series Forecasting
Click “Labels” Click “OK”

93. Time Series Forecasting
Highlight the “Coefficients” for “Intercept” and “Year” and copy them to the clipboard

94. Time Series Forecasting
Paste them on your “Annual” sheet

95. Time Series Forecasting
In the column labeled “Trend” fill in the formula for the line Copy it down

96. Time Series Forecasting
Poof! Forecasts of ppm CO2 values!

97. Time Series Forecasting
Drag the forecasts to the adjacent column labeled “forecasts”

98. Time Series Forecasting
You can see the original data, the trend line and the forecast

99. Time Series Forecasting
Does it look like a GOOD forecast?

100. Time Series Forecasting
It would be considered a CONSERVATIVE forecast

101. Time Series Forecasting
A better forecast would begin where the observed data left off

102. Time Series Forecasting
Scroll down to where the forecast numbers begin

103. Time Series Forecasting
Copy up to the last observed data line

104. Time Series Forecasting
What would the forecast have to be to line up with the last observed data value?

105. Time Series Forecasting
= 5.48 The forecast would need to be 5.48 higher to start where the observed data ended

106. Time Series Forecasting
Start a new forecast column: =d

107. Time Series Forecasting
Copy it down

108. Time Series Forecasting
Adjusted forecast values

109. Time Series Forecasting
A better forecast!

110. Questions?