Weekly forecasting is quite inadequate due to the deterministic effect of holidays and other events. Weekly data can be severely skewed by when the holiday occurs and activity before and after the holiday. Daily data analysis can provide not only good daily forecasts but good weekly forecasts. In my opinion most software errs by exclusively using autoprojective schemes when combining deterministic and autoprojective schemes should be used. Care must be taken not to assume the form of the deterministic structure and to allow the data to speak to the identification. The problem with using Fourier procedures is that it enforces a presumed structure which leads to forecasts looking like the fit but not necessarily like the data. This is easily observable by performing diagnostic checks of model residuals from these kinds of assumed procedures. If the error aren't random, the model/parameters should be questioned. If the software you are using doesn't verify the assumption of random errors to ensure that this requirement is in place by both ACF (stochastic effects) and Intervention Detection (deterministic effects) then you might be wary. We have used Fourier approaches and have been stunned by the non-independence of the error terms (residuals)
On the other hand we have found that incorporating day-of-the-week effects , changes in day-of-the-week effects, month-of-the-year effects, long-weekend effects, lead and lag structures around holidays, specific- week-of-the-month effects, specific day-of-the-month effects, changes in either levels or trends over time CAN be very useful in predicting daily, weekly and monthly aggregates.
Seldom are there any repetitious effects for a particular week in the year although we have seen some! If you are insistent on building a weekly model identify which weeks of the year, if any, have a repetitive pattern. When encountering a year with 53 weeks some clients have eliminated one week where the response is low.