# Exponential moving average before computing std

In which cases it would make sense to use exponentially weighted moving average (EWMA) before, for example, computing sample variance or other statistical analysis? Could you give an example when one needs to remove high frequencies before performing some analysis?

My idea: A random walk + noise state-space model is equivalent to a EWMA, see, for example, discussion here:What is the difference between Kalman filter and moving average?

Therefore, if one first performs EWMA and then computing std, then it is an estimate of the transition std.

• Note clear what transition std is. Not to be sarscastic but if you calculate the ewma and the compute the std, then it's the std of the ewma. – mlofton Nov 19 '19 at 13:04
• I have a feeling that you are trying to do quadratic volatility estimation using EWMA. Basically EWMA can be used as a poor-man's GARCH. breakingdownfinance.com/finance-topics/risk-management/ewma, investopedia.com/articles/07/ewma.asp – Cagdas Ozgenc Nov 19 '19 at 13:13
• @ABK: I'm still not clear on your question but I hope it was answered by Cazdas Ozgenc. Cazdas, thanks for link. – mlofton Nov 19 '19 at 17:49
• @ABK: I read your question again. . A lot of people use the EWMA as one would a moving average and, for \$\lambda = 2/(n+1), they are pretty similar. But there's a much broader usage-perspective of the EWMA that shows up in econometrics when doing expectations modelling. See Sargent's text , "macro-economic theory", 1979 for all the gory details of what I mean by this. – mlofton Nov 19 '19 at 17:56
• Another book I highly recommend for the EWMA is Brown's text: amazon.com/Smoothing-Forecasting-Prediction-Descrete-Time/dp/… – mlofton Nov 19 '19 at 17:59