I see that you were a little uncertain what people mean by “robustness” in this context. Let me help.

Folks in signal processing like to use median filters. Consider for instance processing an image from a digital camera. We can take the data and use an MA filter, but this will just smooth out the image, making it blurry. Since the camera is digital the errors are pretty all or nothing. Dead pixels, as an example, can give black or white spots in the image. The image looks a lot better if you apply a median filter because this “salt and pepper” noise is replaced with median values from nearby pixels. This empirically looks good.

Robustness must always be in reference to some disturbance or uncertainty. One should not generalize to think of this as good for return or variance. Median is considered a robust estimator because it downplays the role of any specific data point, so a small set of erroneous or non-representative data won’t skew results. Since you are using daily settle prices, these are already typically the average of the last few trades of the day. These “outliers” are thus very real and discarding them is essentially throwing away data.

as a second note a multi time frame macd/mmdi may be useful to create a long/cash/short strategy whereby you enter in the direction of the long term using the short term indicator and you exit to cash with the short term indicator etc

keep up the good work…..the trend side of things is certainly under-researched
best
dv