# Do EWMA weights remove autocorrelation in asset returns?

I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their serial correlation functions (ACF) during the estimation of volatility,

but if I instead only apply the same weighting scheme to a univariate asset return series, without going the step further of estimating volatility, does this new weighted return series have less or no autocorrelation compared to the unweighted returns?

• Have you considered accepting the answer? Let me know if something is still unclear. Commented Dec 13, 2020 at 18:12

• @develarist: ewma is just an estimation procedure that trades off how much one weights the distant past with the closer past. So, depending on the value of $\lambda$, one is giving either more or less weight to the distant past of the thing one is trying to estimate. One may not want to give the same weight to a data point that was a year ago as you do to a point that was a week ago. The value of $\lambda$ determines the weighting scheme. Also, note that the first paragraph you quoted is not correct. The EWMA is not a function of the serial correlation of the series it being used on. Commented Sep 2, 2020 at 12:36
• @develarist: I just want to add that EWMA must alter the statistical properties of the original series because it's a non-linear transformation of the original series. But I also don't think the statistical properties of the resulting EWMA sequence are terribly important. The EWMA is used as an estimator so it's the most recent value of the EWMA that matters. Note though, if you're interested in the process, the resulting EWMA can be viewed as an ARIMA(0,1,1) applied to the original series where the MA coefficient is a function of $\lambda$. If I remember correctly, $\theta = 1 - \lambda$. Commented Sep 3, 2020 at 3:45