The following table shows the last six years average new weekly unemployment insurance claims.

Year Average weekly new unemployment insurance claims
2004 341,300
2005 333,600
2006 311,300
2007 321,200
2008 415,800
2009 567,600

(a) Forecast the new weekly unemployment insurance claims for all years from 2007 to 2010. Use a three-year weighted moving average with weights of 0.6, 0.3, and 0.1. Use the largest weight with the most recent data.

(b) Forecast the new weekly unemployment insurance claims using exponential smoothing with alpha = 0.6 for all years from 2005 to 2010. Use the rate for 2004 as the starting forecast for 2004.

(c) Which of the methods in parts (a) and (b) produces better forecasts for the three years from 2007 to 2009? Answer on the basis of mean square error (MSE).