a. Plot the series. What can you learn from examining this plot? 

b. Calculate and display the first 24 autocorrelations for the series. What do the ACF and PACF suggest about the series? 

c. Suggest a possible set of differencing to use with the series. 

d. Estimate an ARIMA model that you believe to be a good candidate for forecasting future retail sales at hardware stores. Test the Lunge-Box statistic and report your findings.

2,000.00 1,800.00 1,600.00 1,400.00 1,200.00 1,000.00 800.00 600.00 400.00 200.00 0.00 Mar-2006 Jun-2006 Sep-2006 Dec-2006 Date Mar-2007 Jun-2007 M Sep-2007 Dec-2007 Mar-2008 Mar-1964 Apr-1965 May-1966 Jun-1967- Jun-2008 Sep-2008 Dec-2008 Forecast -- Box Jenkins Selected -896T-inr Total Avg Max Min - Aug-1969- Sep-1970- Oct-1971- Nov-1972- Dec-1973- Jan-1975- - Quarterly 1,316.63 1,248.67 1,520.90 1,749.40 1,882.02 1,832.59 1,717.59 1,662.33 1,621.36 1,631.89 1,609.28 1,703.18 Feb-1976 Mar-1977- Apr-1978- May-1979- Jun-1980- Jul-1981- Statistical Forecast 19,495.84 1,624.65 1,882.02 1,248.67 - Annual 5,835.60 7,094.52 -Actual - Statistical Forecast 6,565.72 6,498.61 7,094.52 5,835.60 - Summary Comments The forecast has an average error of The data has a standard deviation of The forecast exceeds the accuracy of a simple average by Sales MM -7861-6nv Sep-1983- Oct-1984 Nov-1985- Dec-1986- Jan-1988 Feb-1989- Mar-1990- Apr-1991- May-1992 Jun-1993 -Fitted Values 2.42% 221.00 96 69% Jul-1994 Aug-1995- Sep-1996- Oct-1997- Nov-1998 Dec-1999 Jan-2001- Feb-2002- - Series4 Mar-2003- Apr-2004 May-2005- Jun-2006 Jul-2007- Aug-2008-