Solved – Difference between smoothed and moving average

There's no official definition, but in univariate time series analysis, a "smoother" uses data to the left (t-1,2..) and to the right (t+1,2,..) of the current observation to calculate its current (t) value. In other words: it is "not causal","acausal", or "time symmetric". A Moving average is a filter that uses only past (and current) values to calculate the current value of the filter: no future data is used.

If you use a smoother on an online system, e.g. a live stock chart (so the graph is moving all the time), you will see that the past calculated values of the smoother can change as new data arrives (not so with the moving average: past mov avg values stay the same as new stock prices are created). A good way to detect a non-causal smoother is to look at sudden jumps: if your input data is in a decreasing segment, after which there is a sudden jump, and your smoothed line is already increasing in the declining segment (or vice versa), you intuitively know the used method is not causal: a causal filter can not "know" so many observations ahead of time it has to jump, only a non-causal smoother can. Causal methods can't "see into the future", while a smoother will sometimes appear to be able to do so.

And no, trying to make a smoother "one-sided" does not solve this problem.