Question:

Part (a):

The quarterly earnings (in millions of dollars) of a large textile manufacturing company have been recorded for the years 2010-2013. These data are shown in the following table.

Quarter   2010   2011   2012   2013
1               52       57       60        66
2               67       75       77        82
3               85       90       94        98
4               54       61       63        67

Using a four-quarter centred moving average, measure the quarterly variation by calculating the seasonal (quarterly) indexes. Use these to obtain the seasonally adjusted earnings for each of the 16 quarters.

Part (b):

The following trend line and seasonal indexes were calculated from six years of quarterly observations:

Trend line: y^(t) = 2000 + 80t - 2(02) Seasonal indexes:

Quarter   Seasonal Index
1                     0.6
2                     0.9
3                     1.1
4                     1.4

Forecast the four quarterly values for next year.