We're talking about modifications to the usual moving average(s) of Prices by considering moving averages of Returns.
We're calling these moving averages return Moving Averages, or rMAs.

>Why are we doing this? We'd like to generate Buy and Sell signals so that ... >What's wrong with Bollinger Bands which use moving averages of Prices? Okay, let's see what we'd like in a moving average. Look at the chart here The upper chart shows stock prices in blue and a couple of other graphs, in red and green. >Bollinger bands, right? That's not relevant. I just want to point out the characteristics we want in a moving average. Notice that when the Price is decreasing (as in region A), it's followed by a lower green graph. When the Price dips below, that should be a Buy signal ... as noted in the lower chart. When the Price is increasing (as in region B), it's followed by an upper red graph. When the Price rises above, that should be a Sell signal ... as noted in the lower chart. >I'd buy a little earlier and sell a little later! Nobuddy's perfect. Pay attention.

What I'd like are red and green graphs which are something like the Price graph, but shifted UP or DOWN ... and to the right ! >Huh? Look at this chart We've shifted the Price graph UP and to the right ... and coloured it green. When they cross, that's a Buy. >We Buy when Price crosses green from below, right?

Figure 1

Right, and if we do the same for our red graph, we'd want to have a situation like this Notice that we've shifted the Price graph DOWN and to the right ... and coloured it red. >When Price crosses red from above we Sell, right? Sounds good to me

Figure 2

>And just how do you intend to move the price graph up and down and especially to the right?
I'm not sure, but I hope that using moving averages of returns might do that.
We'll see.

>But what makes you think that averaging returns, instead of prices, will do that?
Okay, here's my thinking:

• Suppose the stock prices are in a downtrend ... recent returns have been mostly negative.
• The average of those recent returns will then be negative, so the rMA will be decreasing just like the stock prices.
      (See Figure 1, above.)
• Then the returns start to be positive. It may be the start of an uptrend and the price graph starts to rise.
• However, the average of recent return will still be negative for a while so the rMA continues to fall.
      (A few positive returns won't change the average immediately.)
• If the uptrend continues (with associated positive returns), eventually that average will become positive and our rMA will start to rise.
• If the price graph continues to rise (so the uptrend is confirmed), then it should intersect the rMA and ...