Smoother EWMA that mean-reverts

EWMA (exponential weighted moving average) is one way to estimate variance of time series data, and is pretty well known. The issue I have with EWMA is the maximums aren't smooth, especially when recovering from a time-series large spike, and it can take a little while to recover to pre-spike levels. I'm wondering if you know of (or are creative enough to come up with it yourself) a smoother EWMA that reverts to previous-spike levels quicker.

Let me know if I'm not clear, and thanks again for your advice!

You might consider a fixed-time moving average. The data of Covid-19 deaths is a good example. That data is often presented with 3-day and 7-day moving average options. The 7-day MA has an advantage of always including one weekend, when reporting is always low, and a Monday/Tuesday, when the reports catch up for the weekend (either this weekend or the prior weekend). The advantage is that it greatly smooths out the daily average numbers and suppresses the weekly cycles. The disadvantage is that any spike or variation is watered down by the surrounding 6 days.

Alternatively, you could use your own weights.

Covid was an interesting example @FactChecker mentioned. It shows the questions I had (and didn't post as they missed rigor until I saw the Covid example).

What is a spike, a potential data error (random), or a system immanent error (repeated) as in the Covid case? Is there a specific point above which you call data a spike? The word spike has a connotation of something you see in the data, not of something you measure. You first have to make it measurable in order to deal with it.

fresh_42 said:

Covid was an interesting example @FactChecker mentioned. It shows the questions I had (and didn't post as they missed rigor until I saw the Covid example).

What is a spike, a potential data error (random), or a system immanent error (repeated) as in the Covid case? Is there a specific point above which you call data a spike? The word spike has a connotation of something you see in the data, not of something you measure. You first have to make it measurable in order to deal with it.

Those are the big questions: What do you measure, how do you measure it? Maybe too many only deal with technical aspects but don't dwell on such important questions.