Question 1 (14 marks) Sales for the Forever Young Cosmetics Company (in $ millions) are as follows:

Year

Sales ($ millions)

Year

Sales ($ Millions)

Year

Sales ($ Milions

1996

2.4

2003

4.4

2010

4.5

1997

2.7

2004

4.8

2011

4.8

1998

3.3

2005

5.1

2012

5.1

1999

4.6

2006

5.3

2013

5.5

2000

3.2

2007

5.2

2014

5.7

2001

3.9

2008

4.6

2002

4

2009

4.5

(a) Develop a three-year moving average.

(b) Develop a four-year moving average.

(c) Develop a five-year moving average.

(d) Develop a seven-year rmoving average.

Question 2 (16 marks) Sales for the Mont SkyHigh Ski Resorts (in $ millions) are as follows:

Year

Winter

Spring

Summer

Fall

2012

13.7

10.7

8.6

5.1

2013

14.9

10.9

8.9

4.8

2014

15.3

11.2

9.1

5.3

Determine a typical seasonal index for each of the four quarters and comment on the indexes.

Question 3 (5 marks) Which type of variation are the following:

a)What time series component was exemplified during the 1980's when the World economy enjoyed a period of prosperity?

b)What is variation within a year, such as high sales at Christmas and Easter and low sales in January, called?

c)The merchants in Morris, Manitoba suffered flood damage in May 1997. Stores were closed for remodeling nearly two months. What is this type of variation in sales called?

d)Since a ski resort does most of its business in the winter, what is the major source of variation in income due to?

e)What is the long-term behavior of a variable over an extended period of time called?

Question 4 (5 marks) Answer the following questions regarding time series:

a)If the exports ($ millions) for the period 1997 through 2001 were $878, $892, $864, $870, and $912 respectively, what are these values called?

b)A time series is a collection of data that:

c)For an annual time series extending from 1993 through 2001, how many years would be lost in a five-year moving average?

d)For a three-year moving average, how many values will be lost at the beginning and end of the time series?

e)How can you describe the moving average method?