The usual asymptotic arguments for many of these estimators do not apply in the case of air pollution time series, where the time points get more numerous without getting closer together.
On the other hand, it has been suggested that much of the mortality and morbidity attributed to air pollution may merely involve short-term mortality displacement: advancing the deaths of extremely frail individuals by a few days. This can be examined by considering associations excluding the shortest time scales. Kelsall, Zeger & Samet (Applied Statistics in press) gave an estimator of this kind based on Fourier series.
I am investigating the ability of various estimators to remove seasonal confounding in simulations based on real data from King County, Washington. The two main goals are to discover if seasonal confounding alone can explain associations that we see in King County data, and to find conceptually simple estimators that are resistant to confounding and mortality displacement effects.