The inclusion of a smooth function of time in a regression model introduces important sta- tistical generally do not know precisely the complexity of the seasonal and long-term trends in themortality time series or in the pollution time series. Therefore, a controversial issue is determining how much smoothness we should allow for the smooth function of time. This decision is critical because it determines the amount of residual temporal variation in mortality that is available to estimate the air pollution effect. Oversmoothing the series (thereby under- smoothing the residuals) can leave temporal cycles in the residuals that can produce confounding bias; undersmoothing the series (thereby oversmoothing.
