Finding Patterns with the Lucas Time Series: Trading Is a Game of Probabilities. the Lucas Series Is Another Tool That, Combined with Traditional Technical Analysis and Fibonacci Numbers, Can Put the Probability of Winning in Your Favor

Article excerpt

Financial markets are similar to the World Series. Each game is filled with twists and turns with an uncertain outcome until the final pitch is thrown. Trends work the same in free markets as they do in sports contests. They change. Sometimes we can anticipate them. Sometimes we can take advantage of them.

Technical analysis provides us with tools to ultimately take advantage of trend changes. The most overlooked aspect of technical analysis is the time factor.

Technicians and traders have difficulty recognizing when a market will reverse. Many technicians pay a great deal of attention to price studies such as stochastics, moving average convergence-divergence (MACD), the relative strength index, moving averages, Bollinger Bands and countless others. These are good tools, but by their nature are lagging, and when their message will play out in real time isn't stable. MACD and stochastics can display divergences against the main trend for days or weeks. By the time certain moving averages cross over, a good portion of the move may already be through, leading to a whipsaw.

Random walk theorists believe it is impossible to time markets, but cycle analysts come close to identifying reversals. Static cycle theory states that markets will either crest or trough at fixed periods. For example, the four-year Presidential cycle is the most popular sequence followed by the trading community. Analysts suggest a crest will adapt to either a bull or bear market. In bull markets, a cycle will peak past the midpoint, which is known as a right translation. A bear market will peak before the midpoint, which is known as a left translation. This type of analysis is very confusing and four years later many analysts still can't agree if the true cycle bottom to the current bull market in stocks occurred in October 2002 or March 2003.

Traders need a more practical method of making financial decisions.

Fibonacci and Elliott Wave come closest to identifying the structure and shape of financial markets. R.N. Elliott argued that the Fibonacci sequence lays the groundwork for understanding the Elliott Wave Principle. Fibonacci cycle analysts identify major pivots in the market, such as the January 2000 high in the Dow or the bear market bottom in October 2002. They count the number of calendar or trading days from those pivots to determine high probability time windows where a reversal can take place.

Markets tend to turn in all degrees of trend on Fibonacci number bars away from an important pivot, plus or minus one bar. The problem for many Fibonacci analysts is markets don't always turn on Fibonacci bars (see "Lucas vs. Fibonacci," right). This doesn't mean that the Fibonacci-based methodology does not work.

There is another sequence related to Fibonacci known as the Lucas sequence. French mathematician Edouard Lucas (1842 to 1891) uncovered this series of numbers. The significance of Lucas is that as we go higher into the sequence, the relationship of the last two numbers comes closer to a perfect 0.618:1.618 ratio.

Most Fibonacci or Elliott practitioners are unaware of Lucas. So is this another one of those obsolete theories that should be buried in the back of a math textbook?

Understanding how the Lucas series reveals itself in markets can help all market participants make better decisions. These cycles or number sequences offer a superior pattern recognition methodology that works equally well for the institutional currency trader as well as the independent intraday E-mini trader trading from his kitchen table.


The last major correction in the Philadelphia Stock Exchange Gold and Silver Sector Index (XAU) from November 2004 to May 2005 completed a Lucas cycle. The anatomy of the trend included a secondary high on the 76th day of the move and a final leg of 47 daily bars that finally clustered to form a bottom on the 124th day (Lucas number 123 + 1) of the entire move. …