The Williams Alligator was developed by Bill Williams under the premise that financial markets trend only 15% to 30% of the time, while trading in sideways or non-trending markets for 70% - 85% of the time. The Williams %R Alligator uses the convergence-divergence of three Smoothed Moving Averages which are the 5, 8, and 13-period Simple Moving Averages.

The 5-period moving average is called the Lips.

The 8-period moving average is called the Teeth.

The 13-period moving average is a called Jaw.

The Jaw, being the longest moving average of the three, makes the slowest turns and the Lips, being the shortest, making the fastest turns.

When the Lips (5-period moving average) cross down through the other lines it signals bearish opportunity.

When the Lips (5-period moving average) cross up through the other lines it signals a bullish opportunity.

The simple moving average (SMA):

SUM1 = SUM( CLOSE, N )

SMMA1 =  SUM1  /  N
Subsequent values:

PREVSUM = SSMA( t - 1 ) * N

SMMA( t ) = PREVSUM - SMMA( t - 1 ) + CLOSE( t )  /  N
Where:

SUM1 = the sum of closing prices for N periods

PREVSUM = smoothed sum of the previous bar

SMMA1 = smoothed moving average of the first bar

SMMA( t ) = smoothed moving average of the current bar (except for the first one)

CLOSE( t ) = current closing price

N = the smoothing period