THE LUCAS SERIES: PART ONE

The Lucas Series: Part One

Jeff Greenblatt unlocks the key to market cycles with the Lucas Series.

T
his article discusses what may be the most important half sessions due to holidays). It was this kind of ‘completion’ and
breakthrough in cycle analysis in financial markets ‘precision’ that gave me definitive evidence that an important high was
in 25 years. Technical analysis using price and in place that would last for 11 months.
volume became very popular in the twentieth century. Here was the degree of completion that dynamic cycle analysis failed to
Japanese candlesticks were introduced to the west deliver. I found this level of completion on smaller cycles as well.
in the past quarter century, enabling traders to However, my search hit a roadblock when I discovered that patterns
understand market behaviour more thoroughly than would not always turn on Fibonacci numbers. I found turns occurring
they could by using simple bars. While these methods were important on 11, 18, 29 and 47 number bars. It happened with such regularity
in advancing our understanding of financial markets they did not that I concluded this Fibonacci stuff just didn’t work. Then one day
determine when a market would reverse. My research has uncovered while I was surfing the Internet, I discovered the Lucas series. French
a simple yet powerful timing method so that I have never again looked mathematician Edouard Lucas (1842-1891) uncovered a series of
at charts in the same way. numbers: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, and so on,
Cycle analysts track consistent intervals of time between highs which is similar to the Fibonacci sequence beginning 1, 1, 2, 3, 5, 8,
and lows in the market to decide the most opportune time for entry. 13, 21, 34, 55, 89, 144, 233, 377. The importance of the Lucas series
From historical data they calculate, on average, when a market may is that as we get higher in the sequence the ratio of the two numbers
change direction. Overlapping cycles present a challenge. Analysts comes closer to a perfect 1.618/0.618. It was actually Lucas who gave
cannot agree about when a cycle has completed until weeks, if not the Fibonacci series its name.
months, have elapsed, because cycles tend to contract or expand When I discovered Lucas the light bulb really went on. I found that
from the mean. financial markets were turning according to Fibonacci numbered bars,
What happens if we end up in a complex sideways period like 1966- and Lucas numbered bars as well. Uncovering these number patterns
82? As an example, take the last four-year cycle in the Dow. Most has enabled me to anticipate turns in the market ahead of time. It
analysts agree the cycle peak was January 2000. What about the enabled me to anticipate the important August 2004 low to the day
bottom? In hindsight we recognise October 2002 as the technical low, over a month in advance. I was also able to anticipate the high at
but in the months that followed, leading up to the Iraq war, sentiment the start of 2005, as well as many other smaller turns. We can scale
was that the October low would be taken out decisively. Buyers took down from weekly to daily to hourly and even to a five- or one-minute
every low as a buying opportunity during the bear, without any certainty chart to anticipate turns. Using the time principle enables the trader
it was the bottom of a cycle. Even though we came close to creating a to greatly increase his entry precision and confidence. This method is
double bottom in March 2003, there is still disagreement about when meant not to replace traditional technical analysis but to take it to a
the bottom of the cycle completed. Until recently, analysts thought the much higher level. I am going to take you through a series of examples
March 2005 high was the top of this Dow cycle. that demonstrate how it works.
Many cycle analysts have never been able to figure out precisely The first example can be found on the Nasdaq weekly chart. The
when is the proper time to enter a trade. While I believe cycle analysts first phase of the rally topped in January 2004 at 68 weeks off the low.
do a great job quantifying historical cycles and come close to solving 68 is significant for two reasons. First, it is a double 34 (Fibonacci)
a trader’s dilemma, it is still too complicated. I’ve looked for a way to but also derived from the Fibonacci ratio of 6.84. From that high we
simplify time analysis that anybody can use. My method, based upon dropped for 29 (Lucas) weeks into the August 2004 low. Next we rallied
recognisable and repeatable patterns, allows the trader to enter and and topped on the 21st week of the move which was also the 118th
exit trades more precisely in all degrees of trend. (Lucas derivative) week off the low. Check out the chart (see Figure
Elliott first wrote about the Fibonacci sequence in Nature’s Law. He 1) and you will see a big black candle announcing the reversal. Had
explained that it was the mathematical basis for the Wave Principle. you waited for the completion of that candle to enter a short position
Elliotticians as well as Fibonacci analysts use basic wave calculations you would already have been taking on a higher risk. Knowing the
and retracements to measure price movement, but they have been turn comes on an important cycle point gives one confidence to enter
missing an important piece of the puzzle. What they have not realised positions where the risk/reward ratio is more favourable. Recall we
is the degree to which waves are moving in Fibonacci time sequences topped on the first trading day of the year. You could have entered
as well. this trade much sooner knowing the cycles confirmed momentum
I became fascinated with Fibonacci when I discovered markets indicators which were overbought at the time. The next leg dropped
turned on Fibonacci dates (either calendar or trading days). I found 17 weeks to week 134 of the trend. All turn windows are plus or minus
that markets routinely turned on 34, 55, 89, 144, 233 or 377 days from one unit. The next leg up is 14 weeks in duration and tops in the 148th
an important pivot. My research discovered that markets would also week of the trend, which, in both cases, misses a Fibonacci (13) or
turn on these numbers on intra-day times as well. In fact, the first leg Lucas derivative (147) by one bar.
of the rally off the bottom in the Dow (October 9-December 2, 2002)
completed in 235 trading hours and the rally from March 2003-February
2004 completed in 234 trading days (market precision allowing for

30 YOURTRADINGEDGE MAR/APR 2006

THE LUCAS SERIES: PART ONE

The next leg down was 11 weeks in duration. All of the pieces of the per cent price retracement. Traders armed with knowledge of the time
puzzle are coming together. This pattern has three down legs, which function gain a huge edge over the competition. At that point not only
are 29, 17 (18-1) and 11 weeks in duration. They are all Lucas series. would you cover shorts, but you could also consider going long with
When we total the whole pattern from the January 2004 high to the greater confidence.
October 2005 low we get an 89 + 1 (Fibonacci) week triangle. If you Two bars off the low we had two consecutive big white candles.
follow the pattern very closely you will see that the combination of Without understanding the time factor many traders might have gone
the three legs which have Lucas symmetry cluster with the larger long after the second white candle, but others would have gained the
degree 89-week pattern. The confidence to go long after the
stronger the numerical cluster, first white candle. One big white
the better chance there is of a Figure 1: NASDAQ WEEKLY candle makes the difference
change of direction. It is this between a mediocre risk/reward
powerful cluster that kicked ratio where you may elect to
off the current rally leg from pass or pull the trigger on a
October. good trade. Observe how these
The significance of patterns line up with commonly
the 89-week triangle is used momentum indicators.
a key to understanding The next leg is 18 days up
corrective waves. Perhaps and also creates a 47-day high
the trader’s most difficult to high cycle. It is now high time
task is determining when a to liquidate longs as we failed at
correction leg will end. This resistance on a double Lucas
example shows an 89-week cluster. A couple of days later
pattern coming to completion. there is a series of black candles.
Complex corrective legs are Once again, armed with time
commonplace – an excellent cycles the trader can get into
way to recognise the end of a the trade with a more favourable
pattern is when a white candle risk/reward ratio, ahead of the
buy signal occurs within one competition. Finally, the big leg
bar of the correct Fibonacci or ends on a 62-day (Fibonacci
Lucas number bar. Source: Prophet Financial Systems www.prophet.net) 61.8 derivative) low to low cycle
The next example concerns with the first major pivot low.
the US Treasury Bond futures Figure 2: U.S. Treasury bond combined (dec 2005) This method is a leading
contract. There was an initial indicator as distinct from other
high in early June, with a common market indicators,
retest of resistance at the end which lag. You will get stopped
of the month. Figure 2 shows out more often with very small
that the retest failed on the losses, but you will generally
17th daily bar in a high to high find yourself in high probability
cycle off the initial top. The risk/reward situations of 4/1, 5/1
secondary high was formed or even better, because most
when the 18th (Lucas) bar entries are so close to major
began to fade the top. As the pivot points. If you want to be
down leg progressed it formed more conservative and wait for
a cluster low on a combination confirmation by a stochastic,
of the 47th (Lucas) bar off MACD or candle signal your
the top and 38th (Fibonacci risk reward ratios will generally
derivative 38.6) bar in a low to be 2 or 3/1.
low cycle off the first low. This This method will enable
cluster also coincides with the the trader to gain greater
50 per cent price retracement understanding of the market
(a common retracement) of and to have confidence to
the prior spring rally leg. One pull the trigger at the precise
might suggest that this pattern time when the move starts.
Source: Prophet Financial Systems (www.prophet.net)
would quit going down on a 50 In my opinion, once you start
per cent retracement level but following these sequences you’ll never look at a chart the same
as all traders know, in the heat of the action this conclusion is far from way again.
certain. However, when we get a cluster of three relationships lining up
Jeff Greenblatt is the editor of The Fibonacci Forecaster, an email
in the same place (two time and one price), the probabilities increase
forecasting service that covers the major indices as well as gold, bonds,
that a bounce might stick and we need to cover our short positions.
currencies and crude. He can be reached at Fibonacciman@aol.com
Once again, if you are not tuned into these time relationships, you
may conclude that the only event worth noting at this level is the 50

Article originally published in the Mar/Apr 07 issue of YourTradingEdge magazine (www.yte.com.au).

All rights reserved. © Copyright 2006, MarketSource International Pty Ltd.
31 YOURTRADINGEDGE MAR/APR 2006