Not in the sense of having a regular cycle, but in the sense of high volatility begetting low volatility and vice versa. We have studied this extensively and found it to be true. The Squeeze, as an extreme tightening of the Bollinger Bands is known, is often the setup for a big move. Conversely, as soon as the Bands begin to tighten in the course of a big move, a forecast for the end of that move is in hand. Primarily because Bollinger Bands are driven by volatility and thus closely reflect the volatility cycle.
Volatility can be very informative, yet it is the least examined aspect of the price structure.
A simple plot of standard deviation or standard error along with price quickly draws the eye to important highs and lows and informs the analyst about the psychology underlying price. Higher volatility at the lows as panic and fear dominate, versus lower volatility at the highs when greed dominates illuminate the differences between those emotions as depicted in the price structure. The tools to study volatility are widely available and have been for a long time. Average true range reflects volatility nicely for those for whom statistical terms are a turn-off, and the commodity channel index highlights deviation from the trend as a function of volatility. What is surprising is that they are not used more.