1. The data below show retail sales at hardware stores in the United States monthly between January 1992 and December 2005. The data are in millions of dollars and are not seasonally adjusted.

   Date	Sales	Date	Sales	Date	Sales
   Jan-92	846	Sep-96	1,083	May-01	1,657
   Feb-92	822	Oct-96	1,187	Jun-01	1,574
   Mar-92	962	Nov-96	1,177	Jul-01	1,460
   Apr-92	1,077	Dec-96	1,229	Aug-01	1,437
   May-92	1,235	Jan-97	1,003	Sep-01	1,328
   Jun-92	1,170	Feb-97	880	Oct-01	1,386
   Jul-92	1,147	Mar-97	1,027	Nov-01	1,399
   Aug-92	1,086	Apr-97	1,203	Dec-01	1,457
   Sep-92	1,056	May-97	1,339	Jan-02	1,158
   Oct-92	1,110	Jun-97	1,303	Feb-02	1,097
   Nov-92	1,041	Jul-97	1,277	Mar-02	1,297
   Dec-92	1,168	Aug-97	1,224	Apr-02	1,539
   Jan-93	883	Sep-97	1,172	May-02	1,691
   Feb-93	808	Oct-97	1,246	Jun-02	1,605
   Mar-93	987	Nov-97	1,140	Jul-02	1,560
   Apr-93	1,097	Dec-97	1,184	Aug-02	1,471
   May-93	1,289	Jan-98	971	Sep-02	1,325
   Jun-93	1,210	Feb-98	900	Oct-02	1,406
   Jul-93	1,186	Mar-98	1,105	Nov-02	1,400
   Aug-93	1,101	Apr-98	1,323	Dec-02	1,460
   Sep-93	1,077	May-98	1,425	Jan-03	1,186
   Oct-93	1,111	Jun-98	1,427	Feb-03	1,110
   Nov-93	1,098	Jul-98	1,357	Mar-03	1,337
   Dec-93	1,204	Aug-98	1,313	Apr-03	1,490
   Jan-94	959	Sep-98	1,297	May-03	1,743
   Feb-94	866	Oct-98	1,302	Jun-03	1,665
   Mar-94	1,053	Nov-98	1,227	Jul-03	1,616
   Apr-94	1,232	Dec-98	1,363	Aug-03	1,537
   May-94	1,296	Jan-99	1,104	Sep-03	1,485
   Jun-94	1,271	Feb-99	1,007	Oct-03	1,498
   Jul-94	1,217	Mar-99	1,210	Nov-03	1,432
   Aug-94	1,193	Apr-99	1,416	Dec-03	1,511
   Sep-94	1,138	May-99	1,495	Jan-04	1,186
   Oct-94	1,198	Jun-99	1,447	Feb-04	1,126
   Nov-94	1,165	Jul-99	1,390	Mar-04	1,406
   Dec-94	1,243	Aug-99	1,301	Apr-04	1,619
   Jan-95	875	Sep-99	1,286	May-04	1,781
   Feb-95	848	Oct-99	1,296	Jun-04	1,717
   Mar-95	1,061	Nov-99	1,295	Jul-04	1,670
   Apr-95	1,157	Dec-99	1,384	Aug-04	1,555
   May-95	1,343	Jan-00	1,073	Sep-04	1,520
   Jun-95	1,340	Feb-00	1,035	Oct-04	1,483
   Jul-95	1,230	Mar-00	1,316	Nov-04	1,478
   Aug-95	1,182	Apr-00	1,429	Dec-04	1,581
   Sep-95	1,153	May-00	1,598	Jan-05	1,241
   Oct-95	1,141	Jun-00	1,551	Feb-05	1,170
   Nov-95	1,193	Jul-00	1,445	Mar-05	1,442
   Dec-95	1,241	Aug-00	1,433	Apr-05	1,688
   Jan-96	977	Sep-00	1,328	May-05	1,803
   Feb-96	920	Oct-00	1,326	Jun-05	1,770
   Mar-96	1,028	Nov-00	1,306	Jul-05	1,607
   Apr-96	1,251	Dec-00	1,384	Aug-05	1,603
   May-96	1,369	Jan-01	1,092	Sep-05	1,562
   Jun-96	1,306	Feb-01	1,063	Oct-05	1,614
   Jul-96	1,242	Mar-01	1,290	Nov-05	1,582
   Aug-96	1,186	Apr-01	1,441	Dec-05	1,673

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

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

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

   4. Estimate an ARIMA model that you believe to be a good candidate for forecasting future retail sales at hardware stores. Test the Ljung-Box statistic and report your findings. Finally, plot the first 24 autocorrelations of the residuals to your best model.