I am using the Holt-Winters' exponential smoothing technique to forecast expenditure data 2 years into the furture. The monthly data has an increasing trend and annual seasonality.

I'm using MS Excel with the Solver add-in to calculate the optimal values of $\alpha$, $\beta$ and $\gamma$ to give the smallest MSE for the forecasts. The optimal values found for $\alpha$ and $\beta$ lie in (0,1) and $\gamma$ is found to be 1.

I am able to calculate the forecasts for the next year (season) because the seasonals from the previous year exist. However, the forecasts for the second year are calculated to be zero because the seasonals do not exist (because *m* is greater than 12). 

I have discovered that if $\gamma$ is zero, then the seasonals will be periodic, and so could be replicated after the last observed values. Is this the best way to forecast beyond one season after the last observed values? Any advice would be appreciated.

Example data is below. Forecasts are needed for every month up to December 2011. I cannot see how this is possible unless $\gamma$ is zero.

Numbers of Tourists  

Period Month No. Tourists (Yt)  

1 Jan-99 500  

2 Feb-99 543  

3 Mar-99 899  

4 Apr-99 835  

5 May-99 900  

6 Jun-99 881  

7 Jul-99 1154  

8 Aug-99 1586  

9 Sep-99 743  

10 Oct-99 1104  

11 Nov-99 799  

12 Dec-99 560  

13 Jan-00 514  

14 Feb-00 665  

15 Mar-00 949  

16 Apr-00 975  

17 May-00 924  

18 Jun-00 724  

19 Jul-00 1155  

20 Aug-00 1541  

21 Sep-00 746  

22 Oct-00 944  

23 Nov-00 786  

24 Dec-00 652  

25 Jan-01 479.4  

26 Feb-01 644.4  

27 Mar-01 815.8  

28 Apr-01 1035.4  

29 May-01 1000.9  

30 Jun-01 793.8  

31 Jul-01 1347.3  

32 Aug-01 1378  

33 Sep-01 798.1  

34 Oct-01 1070.5  

35 Nov-01 625.3  

36 Dec-01 654  

37 Jan-02 477.5  

38 Feb-02 656.2  

39 Mar-02 888.7  

40 Apr-02 926.6  

41 May-02 1000.1  

42 Jun-02 1030.8  

43 Jul-02 1123  

44 Aug-02 1473.5  

45 Sep-02 717.8  

46 Oct-02 974.7  

47 Nov-02 761.2  

48 Dec-02 641.5  

49 Jan-03 501.6  

50 Feb-03 588.3  

51 Mar-03 917.6  

52 Apr-03 990  

53 May-03 1051  

54 Jun-03 764.4  

55 Jul-03 1014.2  

56 Aug-03 1313.6  

57 Sep-03 736.3  

58 Oct-03 1042.9  

59 Nov-03 685.9  

60 Dec-03 621.5  

61 Jan-04 492.8  

62 Feb-04 722  

63 Mar-04 869.9  

64 Apr-04 927.9  

65 May-04 1028.1  

66 Jun-04 883  

67 Jul-04 1097.4  

68 Aug-04 1398.9  

69 Sep-04 834.4  

70 Oct-04 1072.3  

71 Nov-04 801.9  

72 Dec-04 711.2  

73 Jan-05 616.1  

74 Feb-05 774  

75 Mar-05 1088.5  

76 Apr-05 956.2  

77 May-05 1175.6  

78 Jun-05 949.5  

79 Jul-05 1120.8  

80 Aug-05 1426.2  

81 Sep-05 841.5  

82 Oct-05 996.6  

83 Nov-05 908  

84 Dec-05 696.7  

85 Jan-06 606.4  

86 Feb-06 771.6  

87 Mar-06 967.1  

88 Apr-06 1235  

89 May-06 1216.1  

90 Jun-06 945.1  

91 Jul-06 1194.4  

92 Aug-06 1433.4  

93 Sep-06 830.6  

94 Oct-06 984.7  

95 Nov-06 880.2  

96 Dec-06 668.3  

97 Jan-07 644.9  

98 Feb-07 808  

99 Mar-07 998.2  

100 Apr-07 1283.9  

101 May-07 1080.9  

102 Jun-07 989.9  

103 Jul-07 1167  

104 Aug-07 1568.9  

105 Sep-07 951.7  

106 Oct-07 1121.4  

107 Nov-07 859  

108 Dec-07 660.9  

109 Jan-08 647.9  

110 Feb-08 911.1  

111 Mar-08 1201.2  

112 Apr-08 1258.1  

113 May-08 1177.8  

114 Jun-08 1067.6  

115 Jul-08 1349.4  

116 Aug-08 1702.1  

117 Sep-08 982.8  

118 Oct-08 1116.5  

119 Nov-08 904.7  

120 Dec-08 655.9  

121 Jan-09 733.75  

122 Feb-09 852.67  

123 Mar-09 1049.88  

124 Apr-09 1377.11  

125 May-09 1344.05  

126 Jun-09 1030.95  

127 Jul-09 1242.56  

128 Aug-09 1542.24  

129 Sep-09 1016.42  

130 Oct-09 2301.41  

131 Nov-09 1138.9  

132 Dec-09 1032.87