1. Statistics Cyclical Time Series

2. Cyclical Forecasting
Time series data often are annual summaries

3. Cyclical Forecasting
Time series data for months or quarters often exhibit a cycle

4. Cyclical Forecasting
Time series data for months or quarters often exhibit a cycle: candy sales are highest at what times during the year?

5. Cyclical Moving Average
Suppose our data looks like:

6. Cyclical Moving Average
Is it cyclical?

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

8. Cyclical Moving Average
Start over on the next max

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

10. Cyclical Forecasting
Open the spreadsheet

11. Time Series
Make a graph

12. Time Series
Make it “purty”

13. Time Series
Why does it start in July 1998??

14. Time Series
Right click on the x-axis dates to adjust the start and end dates

15. Time Series
Click: “Format Axis”

16. Time Series
What are and ??

17. Time Series
Excel uses a “Julian Date” calendar (weird and hard to understand)

18. Time Series
In Excel: January 1, 1900 is day 1 July 1, 1998 is day (because it is 35,975 days after January 1, 1900)

19. http://forums. penny-arcade

20. Time Series The formula to convert a date to an Excel date is:
=ROUNDDOWN(((YEAR(A1)-
1900)*365.24),0)+A1-
DATE(YEAR(A1),1,0)

21. Time Series 3/31/2000 (our first date) is day 36615.0

22. Time Series 12/31/2014 (our last date) is day 42002.0
tscng.files.wordpress.com/2012/06/crying-man2.jpg

23. Time Series Time Series
So we know our data starts at 35615, but we also want to get the right Mo-Yr shown on the graph, and not have the first datapoint chopped off of our graph…

24. Time Series Time Series
…and maybe start with Jan rather than March? I just mess around with (iterate) the values until I get what I want…

25. Time Series
Change the minimum to and the maximum to with major unit 732

26. Time Series
Better!

27. Time Series
Note: for our class, I’ll give you the numbers…

28. Cyclical Forecasting
We need a way to include the cycle in our equation

29. Cyclical Forecasting
Add another column Label it “Cycle”

30. Cyclical Forecasting
Using the data values for the first year, see which has the highest value

31. Cyclical Forecasting
In the “Cycle” column, mark it with a number (use 4, since this is quarterly data)

32. Cyclical Forecasting
Now check the data values to find the lowest value during the first year

33. Cyclical Forecasting
Mark it with a different number (use 1 since it’s low)

34. Cyclical Forecasting
Check to see if the max quarter for the following year is the same

35. Cyclical Forecasting
Check to see if the min quarter for the following year is the same

36. Cyclical Forecasting
If they are (or at least are close) you have a pattern!

37. Cyclical Forecasting
A cycle is often symmetrical Our “1” has 1 space before the “4” followed by 1 space before the low value for the following year

38. Cyclical Forecasting
Fill in the blank spaces with a value between 1 and 4 (2, 2.5, or 3)

39. Cyclical Forecasting
If your data are not symmetrical, that’s OK!

40. Cyclical Forecasting
Asymmetrical patterns are very common in business data

41. Cyclical Forecasting
Monthly data often have a couple of spikes Fill these in with numbers approximating how high the spikes go, how low the depressions go, and fill in the spaces with “smoothed” values

42. Cyclical Forecasting
Now copy this pattern for the year down for the entire series!

43. Cyclical Forecasting
Now we can create a regression equation that includes the linear increase over time (based on year), the curvilinear increase in trend over time (if you have one – we don’t) and the cyclical annual pattern for the months (using the cycle data)

44. Questions?

45. Cyclical Forecasting
Note: the Excel regression app will not handle dates in the form: 5/14/2017 Add a "Year" column using: =YEAR(A11)+(MONTH(A11)-1)/12

46. Cyclical Forecasting
Forecast electricity consumption in Portugal

47. Questions?

48. Cyclical Forecasting
What if our time series data has a cyclical pattern as well as a trend?

49. Cyclical Forecasting
If you include the cycle in the forecast, you will have a better forecast!

50. Questions?