There are many, many kinds of moving averages out there. All of them suffer from one kind of weakness or another, much like any sort of parameter does. The Weighted Moving Average and the Exponential Moving Average both try to address lag in the Simple Moving Average by placing emphasis in the calculation in the more recent minutes. I recommend going to Investopedia for calculations of the basic set of technical indicators. For the readers sake with regards to moving averages, an SMA is simply plotted as the average of the past 'n' periods. (usually the closing prices of said periods) General interpretations involve a faster (smaller 'n') MA crossing over a slower MA to indicate a trend. I prefer price action relative to the usual set of MA's, myself, rather than MA's relative to each other.
But, I digress. Enter the Hull Moving Average, or HMA, which attempts to address both lag as well as to smooth out what might otherwise be a choppy line moving in a choppy market. It's an obscure moving average created by Alan Hull and many chart packages won't have it available. Here is the equation based on period n:
HMA(n) = WMA(2*WMA(n/2) – WMA(n)),sqrt(n))
A bit of a mouthful I know. Let me walk you through it. An HMA of length 'n' is essentially a WMA of length 'sqrt n' of the difference between 2-times the value of a WMA of length 'n/2' and a WMA of length 'n'. Follow? Working from the bottom up, to find HMA(n), find WMA(n/2), double it, and take away the value of WMA(n) to get.... let's say 'h'. (as opposed to 'p', as in price) Now the HMA (n) = WMA (sqrt n) of 'h'. Oh and of course every parameter must end up being an integer so rounding occurs in the event of uneven, non-square numbers.... which is exactly why I prefer to use even square numbers as parameters.
Why those particular relations (n/2, sqrt n) exist in the equation is actually beyond me, (probably the result of lots of trial and error) but it doesn't matter, because as a rule the HMA does what it sets out to do: produce a smoother, less-laggy line. But, as a side effect sometimes the line is prone to overshooting. This is because the two relations can sometimes overcompensate, as any two elements that attempt to eliminate lag are bound to overtake the issue at hand; kind of like rear-ending the guy in front of you if you're following too close.
Okay, interpretation: I would say that the slope of the HMA is best used as your filter and you wait for a pullback from the direction of the HMA and then a resumption of the movement. For example, the HMA has changed from pointing down to up, and the market is doing that ahead of it. This means that you shall only take long positions in the next short while.