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The algorithm mentioned on Wikipedia has a line $$s_t = \alpha \frac{x_t}{c_{t-L}} + (1-\alpha) (s_{t-1} + b_{t-1})$$.

For $1 < t < L$ how should we interpret $c_{t-L}$? On that interval, should we replace it with $c_t$?

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For triple exponential smoothing it says that at least one seasonal cycle of length L must be completed. So t is actually greater than L. The notation is 1 < t < L but the t is given modulo L.

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Thanks, seems like we initialize $c_1 ... c_L$ in a certain way. Suppose there are 10 whole periods with $L = 10$ so 100 data points. After we initialize $c_1 ... c_{10}$, how do we compute $s_1$, which is a function of $c_{-9}$? – JCWong Aug 28 '12 at 3:32
@JCWong My answer was partially hidden. Read it now and see if it makes more sense. – Michael Chernick Aug 28 '12 at 10:53
The index $t$ is not understood modulo $L$. Use initial estimates as explained on the NIST site. – whuber♦ Aug 28 '12 at 15:37
@whuber That is how it is describe in the Wikipedia article provided by the OP. Did you look at that? That is what I was going by. – Michael Chernick Aug 28 '12 at 15:43
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@Michael, not only did I look at it, I implemented the algorithm to make sure it made sense. Of course I could be mistaken: if you have a different interpretation, then please share your code with us to demonstrate how it really works. – whuber♦ Aug 28 '12 at 15:45
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