2.2Estimating seasonality and making seasonal forecasts(13 marks)

(F)Indicate the patterns in the above-fitted errors {et} (by plotting the data and observing the graph).(1 mark)

(G)Define and write down the four quarterly dummy variables D1t, D2t, D3t and D4t.(2 marks)

(H)Regress {et} on the quarterly dummy variables: et = 1D1t + 2D2t + 3D3t + 4D4t + t. Write down this new fitted-model, and briefly explain the meanings of the results.(3 marks)

(I)Is this model a good one? Comment using R2 and t-test.(2 marks)

(J) Based on this fitted model, forecast the et values from Q1-2007 to Q4-2007. Also find the confidence interval for the forecast for Q4-2012. (3 marks)

(K)Adding up the above two forecasts [one for trend and one for errors] results in the final forecasts for yt. Write down these forecasts from Q1-2007 to Q4-2007.(2 marks)

9:42 PM Fri Oct 11 EBF2014Asgn1-Data G Beverage Shipments (yt) 11.654 Quarter Q1-1992 Q2-1992 1 2 13.723 13.242 12.002 11.502 13.627 13.662 12.155 12.024 14.378 14.070 13.049 Q3-1992 3 4 04-1992 6 Q1-1993 Q2-1993 Q3-1993 5 6 7 Q4-1993 Q1-1994 Q2-1994 Q3-1994 Q4-1994 Q1-1995 Q2-1995 8 9 10 10 11 12 11 13 12 14 13 12.491 14.861 15.115 13.610 15 14 16 Q3-1995 Q4-1995 Q1-1996 Q2-1996 Q3-1996 15 16 17 18 17 13.318 15.962 15.832 14.554 13.609 15.995 16.136 19 18 20 19 20 25 Q4-1996 Q1-1997 21 Q2-1997 22 23 22 24 Q3-1997 23 25 26 Q4-1997 24 15.156 14.393 16.740 Q1-1998 25 Q2-1998 26 27 28 20 Q3-1998 Q4-1998 28 27 16.504 14.745 14.152 16.470 16.091 14.910 14.536 16.901 16.468 30 Q1-1999 Q2-1999 30 Q3-1999 31 29 31 32 30 34 Q4-1999 Q1-2000 33 Q2-2000 Q3-2000 35 04-2000 Q1-2001 37 Q2-2001 32 34 35 36 37 36 15.278 14,929 17.103 17.255 15.952 14.849 17.161 16.979 38 39 38 401 Q3-2001 Q4-2001 Q1-2002 Q2-2002 39 41 40 42 41 42 430 44 Q3-2002 Q4-2002 Q1-2003 Q2-2003 Q3-2003 43 4% 44 45 46 15.870 15.294 17.857 17.735 16.910 16.743 19.495 46 47 48 47 49 Q4-2003 Q1-2004 Q2-2004 48 49 50 50 51 2 Q3-2004 04-2004 Q1-2005 Q2-2005 54 51 19.424 17.795 16.337 19.761 53 57 53 Q3-2005 55 19.920 18.894 17.680 20.634 57 58 Q4-2005 56 Q1-2006 57 Q2-2006 58 Q3-2006 59 Q4-2006 60 60 19.984 61 19.483 62 Style Common Viewing Font Insert + 9:42 PM Fri Oct 11 EBF2014Asgn1-Data G Beverage Shipments (yt) 11.654 Quarter Q1-1992 Q2-1992 1 2 13.723 13.242 12.002 11.502 13.627 13.662 12.155 12.024 14.378 14.070 13.049 Q3-1992 3 4 04-1992 6 Q1-1993 Q2-1993 Q3-1993 5 6 7 Q4-1993 Q1-1994 Q2-1994 Q3-1994 Q4-1994 Q1-1995 Q2-1995 8 9 10 10 11 12 11 13 12 14 13 12.491 14.861 15.115 13.610 15 14 16 Q3-1995 Q4-1995 Q1-1996 Q2-1996 Q3-1996 15 16 17 18 17 13.318 15.962 15.832 14.554 13.609 15.995 16.136 19 18 20 19 20 25 Q4-1996 Q1-1997 21 Q2-1997 22 23 22 24 Q3-1997 23 25 26 Q4-1997 24 15.156 14.393 16.740 Q1-1998 25 Q2-1998 26 27 28 20 Q3-1998 Q4-1998 28 27 16.504 14.745 14.152 16.470 16.091 14.910 14.536 16.901 16.468 30 Q1-1999 Q2-1999 30 Q3-1999 31 29 31 32 30 34 Q4-1999 Q1-2000 33 Q2-2000 Q3-2000 35 04-2000 Q1-2001 37 Q2-2001 32 34 35 36 37 36 15.278 14,929 17.103 17.255 15.952 14.849 17.161 16.979 38 39 38 401 Q3-2001 Q4-2001 Q1-2002 Q2-2002 39 41 40 42 41 42 430 44 Q3-2002 Q4-2002 Q1-2003 Q2-2003 Q3-2003 43 4% 44 45 46 15.870 15.294 17.857 17.735 16.910 16.743 19.495 46 47 48 47 49 Q4-2003 Q1-2004 Q2-2004 48 49 50 50 51 2 Q3-2004 04-2004 Q1-2005 Q2-2005 54 51 19.424 17.795 16.337 19.761 53 57 53 Q3-2005 55 19.920 18.894 17.680 20.634 57 58 Q4-2005 56 Q1-2006 57 Q2-2006 58 Q3-2006 59 Q4-2006 60 60 19.984 61 19.483 62 Style Common Viewing Font Insert +