The Alligator Indicator uses the previously mentioned 5, 8, and 13 smoothed moving averages. These are all Fibonacci numbers, so it makes sense that there will be a certain amount of mystique around the indicator as a lot of traders like the idea of using Fibonacci.
The Jaw is the 13 smoothed moving average, which is smoothed by eight bars on previous values. The Teeth is the 8 smoothed moving average, which is smoothed by five bars on previous values. The Lips features the five bar smoothed moving average, which is smoothed even further by three bars on previous values. This will plot a green (5) moving average, a red (8) moving average, and a blue (13) moving average.
The indicator looks for convergence/divergence in order to build signals. The Jaw (blue) makes slower turns than the others, while the Lips (green) will be the fastest moving average in the indicator. Because of this, the triple indicators are used very similar to a three moving average server system. For example, if the green indicator slices through the other two to the downside, it's a sell signal. On other hand, if the green indicator slices through the other two to the upside, that’s a bullish sign and a potential buy signal.
Bill Williams suggested that when the downward cross occurred, it was when the alligator was sleeping, while an upward cross is the alligator awakening. It’s probably not that important as to whether or not he calls it one thing or the other, because this will follow a lot of the same rules that a triple moving average crossover system will. After all, that’s all this is but there are some tweaks to the calculations because they are smoothed.
If the three moving averages are stretched apart, that is generally a sign that you are in a trend and should maintain whatever the position is. In the example below, you can see that the moving averages go from being twisted to spread out relatively far at the first red arrow, they compress, and then spread out even further at the second red arrow.
At both of those arrows, the Alligator Indicator is letting you know that the market is extremely bearish, and you should be hanging on to short positions. In fact, you can even make an argument for the compression between the two red arrows as not quite enough to get you out of the original position.
The indicator showing a couple of strong downtrend is the first thing he would notice, but the question then becomes whether or not you are extraordinarily cautious or if you are a little bit more aggressive. In other words, the Lips rising above the Teeth of the indicator, or the green moving average digging into the red moving average between the two arrows could be a sign to start taking profits if you are already short of the currency pair. At this point, it truly comes down to your personal preference, and traders will use both methodologies when it comes to using the Bill Williams Alligator Indicator.
According to the description Bill Williams himself uses, there are a couple of ways to describe what’s going on. When the moving averages are short and choppy, then quite often he will describe it as either the market sleeping, or the alligator “being sated.” When the three moving averages start to spread and move in the same direction, then the mouth is opening and the “alligator is starting to eat.” In the chart just below, you can see that there are blue, red, and orange boxes.
In the blue boxes, the moving averages start to spread and rise, which is a very bullish sign, while the orange boxes show choppy trading conditions with the moving averages, meaning that you are either flat of the market or trying to take profits from your position previously. The red rectangle is the mouth opening for the alligator to eat again, this time driving to the downside.