Question:Is there a way to find what moving average ( ex. 12 day vs. 15 day) tracks an asset's price best through least squares?Thanks

You can find which average has, in the past, tracked best with the price. If you search for one, you have a 100% chance of finding one that tracked pretty well.Obviously the 1-period moving average tracks best. But suppose you adjust for that, by assuming an n-period moving average will deviate from the price by some square pyramidal function of the 1-period standard deviation. What you will presumably be looking for is what is known as an "oscillator," or the timeframe in which a price is more likely to reverse than to trend.What you probably want to find, is under what circumstances the moving average which it pulled back across over the last five days, will be the one it crosses back over during the next five days.You might want to experiment with what is known as an "adaptive moving average." Just remember, of all the things that worked well in the past, there is only a tiny subset which you could have predicted would have worked well.Generally, the one which you could have predicted would fit in advance, will still not end up fitting as well as something you can discover to have fit afterwards. In other words, suppose you predict in advance that the 10-period will fit best. And the 10-period ends up fitting okay, but the 12-period ends up fitting better. The 10-period still fits better, as the 12-period is a random filtration out of dozens of possible numbers. As such, the 12-period is still the N-period, where N is still unknown.

Thanks for the info farmer!