The average monthly price of regular gasoline in Southern California is monitored by the Automobile Club of Southern California’s monthly Fuel Gauge Report. The prices of the time period July 2004 to June 2006 are given here.

Month Price ($) Month Price ($) Month Price ($)
7/04 2.247 5/05 2.532 3/06 2.626 8/04 2.108 6/05 2.375 4/06 2.903 9/04 2.111 7/05 2.592 5/06 3.417 10/04 2.352 8/05 2.774 6/06 3.301 11/04 2.374 9/05 3.031 12/04 2.192 10/05 2.943 1/05 1.989 11/05 2.637 2/05 2.130 12/05 2.289 3/05 2.344 1/06 2.357 4/05 2.642 2/06 2.628

a. Produce a time-series plot of the average price of regular gas in Southern California. Identify any time-series components that exist in the data.

b. Identify the recurrence period of the time series.
Determine the seasonal index for each month within the recurrence period.

c. Fit a linear trend model to the deseasonalized data.

d. Provide a seasonally adjusted forecast using the linear trend model for July 2006 and July 2010.