The following table lists a portion of the University of Michigan's Consumer Sentiment Index. This index is normalized to have a value of 100 in 1965 and is used to record changes in consumer morale.

Year................... Month............... Consumer Sentiment

2005....................... Jan ....................................95.5

2005....................... Feb................................... 91.2

⋮............................ ⋮.......................................... ⋮

2010.......................... Oct.................................. 67.7

a. Plot and interpret the series.

b. Construct and interpret seasonal indices for the series.

c. Estimate linear, quadratic and cubic trend models to the seasonally adjusted data. Select the best fitting model.

d. Use decomposition analysis to make a forecast for November and December of 2010.