In the last post we looked at smoothing time series by focusing mainly, or exclusively, on local data, i.e., data which are nearby (in time) to the moment at which we’re trying to estimate the smooth. This is usually accomplished by having an observation window or weighting function which is centered at the moment of estimation, and we let this window “slide” through time to generate smoothed estimates at all times. We even showed that fitting a polynomial or a Fourier series globally (i.e. to all the data at once) gives results which are, for times not near the edges of the observation window, nearly the same.
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