After your detailed message, I noticed that I made 2 big mistakes. They can be seen from the excel file I uploaded in my previous message.  1) The order of the seasonal index values was wrong. 2) The formula for Model Constant was wrong.   Now, I have the same results with you. Thanks a lot.    Could you please suggest me a source about this subject? Do you figure out the formulas just by looking at the SAS results? Do you follow a source to solve the problem?   Thanks again. I am sorry that I have taken lots of your time. ... View more

Thanks again, but why is that your backcasting results are different than mine? Were there any mistakes in my excel file? You say the following, but how did you get those values?   From My EXECL calculations: S1 = -27.13818 S2 = -21.86446 S3 = 103.519 S4 = -51.49149   Even if I use the weights you mention, I cannot get those results. My trend value after backcasting is also different than yours (Mine is 173.248441693523, yours is 173.081). Am I missing some point? Could you explain it by looking at backcasting results?     ... View more

Thanks again. Now I have my backcasting results (attached as an excel file) and need the initial values for Level, Trend, and Seasonal Index Values in the forecasting step. I know that I will use the original order of my time series. What should the initial values be regarding to the backcasting results? ... View more

Thank you for the quick response. I tried what you said, but  the sum of the adjusted seasonal index values is not zero. Here is my time series:   z t s1 s2 s3 17754 1 1 0 0 18220 2 0 1 0 18223 3 0 0 1 18047 4 0 0 0 19030 5 1 0 0 19122 6 0 1 0 18921 7 0 0 1 19023 8 0 0 0 19147 9 1 0 0 19397 10 0 1 0 19405 11 0 0 1 19605 12 0 0 0 20181 13 1 0 0 20067 14 0 1 0 20708 15 0 0 1 20476 16 0 0 0 20247 17 1 0 0 20351 18 0 1 0 21393 19 0 0 1 21590 20 0 0 0 21236 21 1 0 0   The regression results are:     Coeffients b0 17669,01053 b1 173,2657895 s1 24,23245614 s2 29,73157895 s3 155,0657895   Adjusted seasonal index values: unadjusted adjusted   24,23245614 93,90906433 s1 29,73157895 99,40818713 s2 155,0657895 224,7423977 s3   -69,67660819 s4 mean     69,67660819       Am I doing something wrong? ... View more

Could you please write down the steps for backcasting with Holt-Winters Additive model? I could not figure out how to update seasonal index values. ... View more