1. Statistics Time Series – Moving Average

2. Moving Average
Go to the Portal Open the spreadsheet

3. Time Series Analysis
Because the DJIA data is so volatile, it is hard to see the major trends

4. Time Series Analysis
One trick we use to be able to see the trends is to draw trendlines

5. Time Series Analysis
Smoothing I did by eye and by hand:

6. Time Series Analysis
But… there MUST be a more “mathy” way of doing this! It’s a MATH class… right?

7. Moving Average
Right! We use a technique called finding the “moving average” to smooth the data (sometimes this is called a “rolling average”)

8. Moving Average
What is a moving average???

9. Moving Average
What is an average??? Well… there are actually a whole bunch of “averages” (you’ll find out about a few in statistics class) The moving average “average” is the one we’re most used to

10. Moving Average
What is the average of this data set: 2 2 5

11. Moving Average
To find this average, add up the values and divide by how many values there are:
= = 3

12. Moving Average
A moving average steps along the data through time taking an average of a small subset of the data at each step
avg 1 avg 2 avg 3 avg 4 avg 5 avg 6 avg 7

13. Moving Average
Except you only move along one data observation each step:
avg 1 avg 5 avg 9 avg 13 avg 17 avg 21 avg 25
avg 2 avg 6 avg 10 avg 14 avg avg 22
avg 3 avg 7 avg 11 avg 15 avg 19 avg 23
avg 4 avg 8 avg 12 avg 16 avg 20 avg 24

14. Moving Average
Let’s try one!

15. Moving Average
Suppose we had this data set: Time Price 1 $100 2 $120 3 $110 4 $105 5 $110

16. Moving Average
The graph would look like:

17. Moving Average
Let’s take a moving average of every two observations: Time Price 1 $100 2 $120 3 $110 4 $130 5 $120
Avg = $110
Avg = $115
Avg = $120
Avg = $125

18. Moving Average
We align the moving average with the final observation used to calculate it: Time Price MovAvg 1 $100 2 $120 $110 3 $110 $115 4 $130 $120 5 $120 $125

19. Moving Average
Notice the first observation doesn’t have a moving average value: Time Price MovAvg 1 $100 2 $120 $110 3 $110 $115 4 $130 $120 5 $120 $125

20. Moving Average
Now, we make a new graph including the new column of data:

21. Moving Average
Compare the two lines… Is the moving average line less volatile? Does it show an inherent trend?

22. Moving Average
That’s why we do moving averages on volatile time series data!

23. Questions?

24. Moving Average
But there MUST be a way for Excel to do this ... (It’s an Excel class, right?)

25. Moving Average
To do moving averages in Excel, you need to install the Analysis Toolpak Add-In (This has been done on the classroom computers – you’ll have to do it yourself on your home computers)

26. Adding the Analysis ToolPak
Open Excel and click on the
'File' tab at the top left
of the screen
At the bottom of the menu,
click on the 'Options'
button
The Excel Options window
will open

27. Adding the Analysis ToolPak
In the column on the left, click on
the
'Add-Ins'
heading

28. Adding the Analysis ToolPak
On the right side of the window,
scroll down to Inactive
Application Add-Ins.
Click on 'Analysis
ToolPak' to
select it.
Then click the
'Go' Button.

29. Adding the Analysis ToolPak
An 'Add-Ins' window will open.
Click in the checkbox next to
'Analysis ToolPak'
Click the 'OK' button.

30. Adding the Analysis ToolPak
Click on the “Data” tab at the top
“Data Analysis” should be on the far
right of the ribbon

31. Moving Average
We already have a spikey graph of this VERY volatile data

32. Moving Average
For information, highlight the “VALUE” data – the number of observations is at the bottom:

33. Moving Average
It would be a HUGE PAIN to manually calculate moving averages for all 265 values!!!! Happily, Excel will do it for us (with less pain)

34. Moving Average
Step 1: At the top, click the “Data” tab At the far right, click “Data Analysis”

35. Moving Average
The Data Analysis window opens Highlight “Moving Average” Click “OK”

36. Moving Average
The Moving Average window opens – click the square at the end of “Input Range”

37. Moving Average
When Excel says “Input Range” they do not mean the input variable Usually what we want to “input” is the output variable!

38. Moving Average
On your spreadsheet data page, highlight all of the column “VALUE” Include the label at the top

39. Moving Average
Click the square at the end of the input area

40. Moving Average
Click the box next to “Labels in First Row”

41. Moving Average
Click the square at the end of “Output Range”

42. Moving Average
Again, Excel doesn’t mean the output variable, it just wants to know where we want the moving averages it calculates to go!

43. Moving Average
Highlight the area in the column I’ve labeled “Moving Average” Don’t include the label

44. Moving Average
When the entire area is highlighted, click the square at the end of the input area
Moving Average

45. Moving Average
In the “Interval” box we tell Excel how many values to include in each moving average - Let’s try 2

46. Moving Average
Click the “OK” button

47. Moving Average
AAGH! Why does Excel HATE US???

48. Moving Average
Actually, it doesn’t hate US… it just hates the #N/A’s in the data These were put in to show that no data is available

49. Moving Average
The graph handles them by just drawing a straight line between the last real value and the net real value

50. Moving Average
The moving averages function handles them by breaking and giving us an error message!

51. Moving Average
So, we’ve got to fill in those missing slots with real values

52. Moving Average
We’ll use averages!!!

53. Moving Average
We’ll take the last real value and the next real value and average them to create an estimated value to fill in the missing data

54. Moving Average
This technique is used almost universally to fill in the (inevitable) missing data values

55. Moving Average
Get out of Moving Averages (hit the red X at the top right twice)

56. Moving Average
We will modify the metadata to include our method of filling in missing values

57. Moving Average
Add a line at the bottom of the metadata

58. Moving Average
Add the title in A17: Missing data: Add the info in B17: Missing data (shown in red) have been estimated using the average of the last observed data and the next observed data

59. Moving Average

60. Moving Average
Scan the data Click on the first #N/A you see Go to the fx line

61. Moving Average
Enter the formula: =(b23+b25)/2 Hit “Enter” on your keyboard

62. Moving Average
Tah-dah! An estimated data value! But… it looks like a REAL data value…

63. Moving Average
Click on the cell, Click on the color icon or the arrow Change the color to something you can see

64. Moving Average
Now you can tell which cells are estimated!

65. Moving Average
Highlight the cell and copy to each of the #N/A cells in the data series

66. Moving Average
Oops… now what?

67. Moving Average
Paste the cell anyway, then tweak the formula to include the next
cell
containing
a value:
(B238+B241)/2

68. Moving Average
Then keep pasting! The next cell is OK!

69. Moving Average
Until all the #N/A cells are filled

70. Moving Average
When all the #N/A’s are filled, do the Moving Average again (it should remember what you entered before)

71. Moving Average
AAGH! NOW WHAT???

72. Moving Average
Oops… we added a line at the bottom of the metadata and now all the line numbers need to be adjusted…

73. Moving Average

74. Moving Average
Poof! It adds the moving average values! (Isn’t Excel wunnerful???)

75. Moving Average
Note – Excel added its own #N/A at the top of the moving averages!!

76. Moving Average
Now, create a new graph comparing the two lines – highlight all three columns of data at once

77. Moving Average
To make it pretty: Get rid of the confusing markers and add a title

78. Moving Average
Change the data axes: For the dates, min is max is major unit is 92 For the $, auto is probably OK

79. Moving Average
Drag the legend into a “safe location” where it doesn’t block any of the graph Expand the graph size You may have to tweak these a bit

80. Moving Average
Make the legend pretty! Right click the legend box Click “Format Legend” Click “Fill” Select “Solid fill” Pick a color you like

81. Moving Average
Click “Border Color” Select “Solid line” Pick a color you like

82. Moving Average

83. Moving Average
Hmm… Howcum it’s not smooth? The red line is a little smoother than the blue…

84. Moving Average
If we do bigger intervals for our averages (more than 2 data points) it will get smoother! Let’s try 5 (that is a week of DJIA data)

85. Moving Average
Better, but still not smooth! Try 22 (a full month of DJIA data)

86. Moving Average
Smooth! But now it “lags” the real data…

87. Moving Average
Comparison of my hand-drawn smoothing to the 22-period moving average

88. Moving Average
The moving average will “lag” the observed data

89. Moving Average
The bigger the interval the greater the lag

90. Moving Average
Life is cruel…

91. Questions?

92. Moving Average
You can make a “Centered” moving average that will not have the lag

93. Moving Average
The MA data are formulas:

94. Moving Average
Go to your first non#NA Moving Average value formula

95. Moving Average
It averages data in Row and puts the average in Row 40

96. Moving Average
It would “center” on Row (19+40)/2 (row 29.5) If we move it to Row 29 or 30, it would be centered

97. Moving Average
Copy the formula from the Formula Bar to cell C30

98. Moving Average
Copy cell C30 down to the bottom

99. Moving Average
Note that at the bottom the data goes into the future!

100. Moving Average
That’s OK – Excel is counting those as missing!

101. Moving Average
Now let’s fill in the early #N/A values at the beginning

102. Moving Average
Go back to cell C30 and copy it up to the top

103. Moving Average
Go to the top cell

104. Moving Average
It looks fine, but it’s hiding an evil secret…

105. Moving Average
It looks fine, but it’s hiding an evil secret… it’s adding in B8- B18 (which is not data…)

106. Moving Average
It looks fine, but it’s hiding an evil secret… Change the first cell in the formula to B$19

107. Moving Average
Make the corrected formula a different color and copy it down to cell C29

108. Moving Average
Change your column title to “Centered Moving Average”

109. Moving Average
Tah-dah! Centered MA values!

110. Questions?

111. Cyclical Moving Average
A lot of time series data spread over several years

112. Cyclical Moving Average
Time series data often have an annual cycle

113. Cyclical Moving Average
In Excel terms, an annual cycle means: However many periods are in a year, that is the interval you’ll need to use to smooth out the data and see the annual cycle

114. Cyclical Moving Average
Quarterly data will be smoothed by a 4-period moving average Monthly data will be smoothed by a 12-period moving average

115. Cyclical Moving Average
What if you had data every four months? (how many times a year would that be?)

116. Cyclical Moving Average
Open the spreadsheet in the Portal

117. Cyclical Moving Average
On the page labeled “Quarterly” make a graph of the data

118. Cyclical Moving Average
Is it volatile?

119. Cyclical Moving Average
Is it cyclical?

120. Cyclical Moving Average
Count from the max of the pattern

121. Cyclical Moving Average
Start over on the next max

122. Cyclical Moving Average
Is the cycle “4” for the most part?

123. Cyclical Moving Average
Then “4” is the interval you should use for the Moving Average

124. Cyclical Moving Average
Calculate the moving average

125. Cyclical Moving Average
Graph the data series

126. Cyclical Moving Average
Make it pretty and informative

127. Cyclical Moving Average
Do we need to center this data?

128. Cyclical Moving Average
Probably not!

129. Questions?

130. Cyclical Moving Average
Go to the “Monthly” page Add a column for the Moving Average Create a graph of the data (Be sure to include the Moving Average column)

131. Cyclical Moving Average
Yuck! What’s the problem?

132. Cyclical Moving Average
Fill in the missing data

133. Cyclical Moving Average
Much better!

134. Cyclical Moving Average
Make it more visible by adjusting the axes and getting rid of the legend (I used for the date axis: Minimum Maximum Major unit )

135. Cyclical Moving Average
Tah-dah!

136. Cyclical Moving Average
Is there a cycle?

137. Cyclical Moving Average
There is a yearly (12-month) cycle!

138. Cyclical Moving Average
Lots of things have an annual cycle (weather, schools, car license plates, etc.)

139. Cyclical Moving Average
Smooth the CO2 data using a centered 12-month Moving Average

140. Questions?