The document provides an overview of topics to be covered in Chapter 16 on time series and forecasting, including using trend equations to forecast future periods and develop seasonally adjusted forecasts, determining and interpreting seasonal indexes, and deseasonalizing data using a seasonal index. It also includes examples of calculating seasonal indices and adjusting sales data to remove seasonal variation. The document is a lecture outline and review for a class on international business taught by Dr. Ning Ding at Hanze University of Applied Sciences Groningen.

1. Hanze University of
Applied Science
Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl

2. What we are going to learn?
• Review
• Chapter 16:
– Use a trend equation to forecast future time
periods
– Use a trend equation to develop seasonally
adjusted forecasts
– Determine and interpret a set of seasonal indexes
– Desearsonalize data using a seasonal index

3. Review
•Review Central Tendency? Why Dispersion?
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

4. Review
Dispersion
•Review
Range Variance Standard Deviation
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

5. Review
Dispersion
•Review
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

6. Review
Don’t compare the dispersion in data sets by using their Standard
•Review Deviations unless their means are close to each other.
•Chapter 16: Which one has more variation in the data?
–Use a trend
equation to A B
forecast future
time periods
–Use a trend
equation to
Example :
develop 20 pounds overweight
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a Mean=120 pounds Mean=170 pounds
seasonal index
CV=20/120 =16.7% CV=20/170 =12.5%
Coefficient of Variation (CV)= Standard Deviation / Mean

7. Review
Salary in hundreds of dollars
•Review
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize Companies
data using a
seasonal indexCompany
1: 350
25% of the employees earned money less than _______dollars.
Company 2: Comment on the skewness. Positive skewness
Company 3: The range of salary is ________dollars.
700
Company 4: Which one has the widest range? Company 2

8. Review
•Review Positive Correlation Negative Correlation
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

9. Review
•Review
•Chapter 16:
Secular trend
Seasonal variation
–Use a trend
Sales
equation to
forecast future
time periods
–Use a trend Q4
equation to Q2
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of Q3 Cyclical fluctuation
seasonal indexes Q1
–Desearsonalize
data using a Irregular variation
seasonal index
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Years

10. Review
•Review
Applicable when time series follows fairly linear trend
that have definite rhythmic pattern
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

11. Review
Seven-Year Moving Total Moving Average
1+2+3+4+5+4+3=22 / 7 = 3.143
•Review
•Review 2+3+4+5+4+3+2=23 / 7 = 3.286
3+4+5+4+3+2+3=24 / 7 = 3.429
Seven Year Moving Average
•Chapter 16:
•Chapter 16:
–Use a trend
–Use a trend
equation to
equation to
forecast future
time periods
forecast future
–Use a trend
time periods
equation to
–Use a trend
develop
seasonally to
equation
adjusted forecasts
develop and
–Determine
seasonally
interpret a set of
adjusted forecasts
seasonal indexes
–Desearsonalize
–Determine and
data using a
interpret a
seasonal index set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

12. Review
•Review Ŷ = a + bt xy
a Y b= 2
•Chapter 16:
x
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

13. Seasonal Variation
•Review
Understanding seasonal fluctuations help plan for
sufficient goods and materials on hand to meet varying
•Chapter 16:
–Use a trend
seasonal demand
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

14. Seasonal Variation
•Review
Seasonal variations are fluctuations that coincide with
certain seasons and are repeated year after year
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index

15. Seasonal Variation
•Review
Seasonal Index:
A number, usually expressed in percent, that expresses
•Chapter 16:
–Use a trend the relative value of a season with respect to the average
equation to
forecast future for the year (100%)
time periods
–Use a trend Sales for the Winter are 23.5% below the typical quarter.
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
Sales for the Fall are 51.9% above the typical quarter.

16. Seasonal Variation
•Review
•Chapter 16: Sales Report: in $ millions
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
2005
interpret a set of
seasonal indexes
2006
–Desearsonalize 2007
2008
data using a
seasonal index
2009
2010

17. Seasonal Variation
Step 1: Re-organize the data
•Review
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
2005
adjusted forecasts
–Determine and
2006
interpret a set of
seasonal indexes
–Desearsonalize
data using a 2007
seasonal index
2008
2009
2010

18. Seasonal Variation
Seasonal Variation
•Review 6.7+4.6+10.0+12.7=34 /4=8.50
•Review
4.6+10.0+12.7+6.5=33.8 /4=8.45
•Chapter 16:
•Chapter 16:
–Use a trend
–Use a trend
equation to
equation to
forecast future
forecast future
time periods
–Use aperiods
time trend
equation to
–Use a trend
develop
seasonally to
equation
adjusted forecasts
develop
–Determine and
seasonally of
interpret a set
adjusted forecasts
seasonal indexes
–Desearsonalize
–Determine
data using a
and interpret a
seasonal index
set of seasonal
indexes
–Desearsonalize
data using a
seasonal index
Step 2: Moving Average

19. Seasonal Variation
Seasonal Variation
•Review
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
Step 3: Centered Moving Average

20. Seasonal Variation
Seasonal Variation
•Review
•Chapter 16:
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
Step 4: Specific Seasonal Index

21. Seasonal Variation
•Review
•Review 10/8.475=1.180
12.7/8.45=1.503
•Chapter 16:
•Chapter 16: 6.5/8.425=0.772
–Use a trend
–Use a trend
equation to
equation to
forecast future
forecast future
time periods
–Use aperiods
time trend
equation to
–Use a trend
develop
seasonally to
equation
adjusted forecasts
develop
–Determine and
seasonally of
interpret a set
adjusted forecasts
seasonal indexes
–Desearsonalize
–Determine
data using a
and interpret a
seasonal index
set of seasonal
indexes
–Desearsonalize
data using a
seasonal index
Step 4: Specific Seasonal Index

22. Seasonal Variation
Seasonal Variation
2005
2006
•Review
2007
2008
•Chapter 16:
–Use a trend
2009
equation to
forecast future
2010
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
*(0.9978) +
*(0.9978) +
*(0.9978) +
*(0.9978) =
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
Step 5: Typical Quarterly Index

23. Seasonal Variation
Sales for the Winter are 23.5% below the typical quarter.
•Review
2005
•Chapter 16:
–Use a trend
2006
equation to
forecast future
2007
time periods
–Use a trend
2008
equation to
develop
2009
seasonally
adjusted forecasts
Sales for the Fall are 51.9% above the typical quarter.
2010
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
Step 6: Interpret

24. Exercise
Appliance Center sells a variety of electronic equipment and home
•Review
appliances. For the last four years the following quarterly sales (in $
•Chapter 16: millions) were reported.
–Use a trend
equation to
forecast future
time periods
–Use a trend
equation to
develop
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a Determine a typical seasonal index for each of the four quarters.
seasonal index
In Quarter 3 the sales will be ________ than average quarter.
A 12.60% higher 10.20% higher
B
C 21.00% higher D 17.60% higher
P161 No.10 Ch16

25. Exercise
A 12.60% higher 10.20% higher
B
C 21.00% higher D 17.60% higher
Step 1: Reorganize the data Step 7: Sum up the four means
Step 2: Moving Average Step 8: Divide 4 by Total of four
means to get Correction Factor
Step 3: Centered Moving Average
Step 9: Mean * Correction Factor
Step 4: Specific Seasonal Index
Step 5: Reorganize the data Hint
Step 6: Calculate the mean for each quarter

26. P161 No.10 Ch16

27. P161 No.10 Ch16

28. Deseasonalizing Data
•Review
To remove the seasonal fluctuations so that the trend and
•Chapter 16:
–Use a trend
cycle can be studied.
equation to
forecast future
time periods
–Use a trend
equation to
develop Ŷ = a + bX Ŷ = a + bt
seasonally
adjusted forecasts
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
P161 No.10 Ch16

29. 76.5
Deseasonalizing Data
57.5 114.1 151.9
•Review
•Review
/ 0.765 = 8.759
•Chapter 16:
•Chapter 16:
/ 0.575 = 8.004
–Use a trend
–Use a trend
equation to
/ 1.141 = 8.761
equation to / 1.519 = 8.361
forecast future
forecast future
time periods / 0.765 = 8.498
–Use aperiods / 0.575 = 8.004
time trend
equation to / 1.141 = 8.586
–Use a trend
develop / 1.519 = 8.953
seasonally = 9.021
equation to
adjusted forecasts
/ 0.765
/ 0.575 = 8.700
develop and
–Determine
/ 1.141 = 9.112
interpret a set of
seasonally / 1.519 = 9.283
seasonal indexes
adjusted
–Desearsonalize
forecasts
data using a
seasonal index
–Determine and
interpret a set of
seasonal indexes
–Desearsonalize
data using a
seasonal index
P161 No.10 Ch16

30. Chapter 16: Time Series & Forecasting
Ŷ = a + bt
76.5 Deseasonalizing Data
57.5 114.1 151.9
•Review
•Chapter 16: Ŷ = 9.2333 + 0.0449 t
–Use a trend
equation to
forecast future
time periods
–Use a trend Sale increased at a rate of
equation to
develop 0.0449 ($ millions) per quarter.
seasonally
adjusted forecasts
–Determine and Ŷ = 9.2333+ 0.0449 * 25
interpret a set of
seasonal indexes = 10.3558 $ millions
–Desearsonalize
data using a
seasonal index
10.3558*0.765 = 7.9222 $ millions
xy
b= 2 a Y
x

31. Home Assignment
•Review 1. Calculate the seasonal indices for each
quarter, express them as a ratio and not as a
•Chapter 16:
%. You may round to 4 dec. places.
–Use a trend
equation to
forecast future 2. Interpret the seasonal index quarter
time periods II.
–Use a trend
equation to 3. Deseasonalized the original revenue
develop
seasonally for 2008 quarter I.
adjusted forecasts
–Determine and
interpret a set of 4. For 2011 quarter II the forecasted
seasonal indexes
revenue from the trend line was 55.
–Desearsonalize
data using a Calculate the seasonalized revenue for
seasonal index 2011 quarter II.

32. What we have learnt?
•Review •Review
•Chapter 16:
–Use a trend
equation to •Chapter 16:
forecast future
time periods
–Use a trend
– Use a trend equation to forecast future time
equation to
develop
periods
seasonally
adjusted forecasts – Use a trend equation to develop seasonally
–Determine and
interpret a set of
adjusted forecasts
seasonal indexes
–Desearsonalize – Determine and interpret a set of seasonal
data using a
seasonal index indexes
– Desearsonalize data using a seasonal index