I am forecasting a series of daily volumes in terms of units processed for a particular time period (the period around Christmas).
Historically, I have used a Holt-Winters model, with the minor modification that time period t-364, rather than t-365, is used for the seasonality component and parameter estimation, since the thing I am forecasting has a nested seasonality cycle with a week-within-year cycle and a day-within-week cycle. This has performed pretty well and generally produced unbiased estimators.
However, last year, there was a change in the intra-week seasonality pattern which was caused by a special-cause factor which has remained in place. (The change happened early enough in the year that the values from last Christmas were post-change). Accordingly, I now only have one year's values with which to perform the estimates.
If I understand correctly, this means that the only option I have (if using H-W) is to set the seasonality smoothing parameter to 1, so that the seasonality component of the projections is based exclusively on the corresponding value from one year ago, rather than on a smoothed average from the equivalent seasonal period in all years. (I should point out that, in previous years, the optimised value of the smoothing constant - derived from SSE minimisation) has been 0.9 or greater.
Obviously, this doesn't sound particularly great, but I don't know if there's any alternative forecasting approach I could use which would avoid this problem. I have been looking into possibly trying to fit an alternative ARIMA model, but I don't think that would resolve the basic problem, which is not really to do with how well the HW model fits as it is to do with the absence of data from more than one year, and I don't think an alternative ARIMA model would resolve this. Am I correct in this assumption? And if so, are there any models or approaches which might be better suited for dealing with this problem?
Finally, I assume that it will still be valid to estimate the coefficients for the level and trend parameters using SSE based on historical values - is this the case?