## Time Analysis

During the Elliott/Fibonacci seminars, held by the author in 1983 in the United States, we introduced a trading concept strictly based on Fibonacci time analysis. Today this concept is as sound as it was then. Only now it's computerized. The performance profile has not changed. It can be shown that Fibonacci ratios are a reliable and consistent tool for time analysis and should be integrated into an investment strategy.

Fibonacci ratios can be applied to any commodity or time span. Elliott introduced the Fibonacci series as;

saying, "This series is very useful in identifying and measuring every wave and the extent of each movement, and when used in conjunction with the Wave Principle is also useful in forecasting the duration of trends in various periods of time, days, weeks, months, or years. The time element as an independent device, however, continues to be baffling when attempts are made to apply any known rule of sequence to trend duration" (Elliott, p. 180).

Elliott used the Fibonacci sequence as a timing device as follows: If a trend lasted one day more than a number in the sequence, the trend must then last until the next higher number. For example, if a trend continued for 4 days, it must then last at least 5 days; if it lasted 9 days, it must then continue for at least 13 days.

Elliott had problems making this rule work, because the numbers in the sequence are too static. However, working with the ratio 1.618 in combination with peaks and valleys is very different from Elliott's time analysis. It makes the application dynamic.

Contrary to Elliott, instead of using the specific numbers in the summation series (e.g., 3, 5, 8, . . .) for time analysis, the ratio 1.618 and the reverse ratio 0.618 will be used. We will show that the ratio 1.618 can be used independently, that is, without the wave count to make time analysis possible.

### TIME COAL DAYS

Time goal days are those days in the future upon which a price event will occur. To be able to anticipate a day on which prices will achieve an objective, or reverse direction, would be a step forward in forecasting.

To calculate time goal days, we draw upon the work of the Greek mathematician Euclid, who solved the problem of relating the Golden Section to a straight line. (See Appendix A.) In Figure 1-4, the line AB of length L is divided into two segments by point C. Let the lengths of AC and CB be a and 6, respectively. If C is a point such that L \a - a :b, then C is the Golden Section AB. The ratio L :a or a :b is called the Golden ratio. In other words, point C divides the line AB into two parts in such a way that the ratios of those parts is 1.618 and 0.618.

Our time analysis is based on the findings of Euclid. If there is one way to link Nature's Law, expressed through the Fibonacci ratio 1.618, with market swings, then it should be the way it is described in Figure 7-1.

Look at the peaks, A and B, in Figure 7-1. Using the distance from A to B in days (any time unit can be used ), multiply that distance by the Fibonacci ratio 1.618 to forecast the resulting value C, which occurs on day

C is called a time goal day. This is the day on which the market trend is expected to change direction.

This geometric approach has the advantage of forecasting, rather than lagging the market; therefore, trades can be entered or exited at the time of a price change, rather than after-the-fact. In addition, this concept is dynamic, which allows it to adjust to the longer or shorter swings of the market.

When referring to the forecasting of time goals, there is no intention to indicate that the price will be high or low when the TGD is reached. It can be either one. The time goal day only forecasts a trend change (an event) at the time the goal is reached. This is shown in Figure 7-2.

Using Fibonacci ratios, timing of objectives can be measured on intraday, daily, weekly, or monthly charts.

Three parts of the time analysis must work perfectly together to get the best possible results. These factors are:

Just as with the trading signals for extensions and corrections, an investor must wait until a clear timing signal is determined before entering the market. This waiting is the toughest part of trading, for the signals always come when they are least expected. At the time of a signal, the media often recommends the opposite trade. Because this technique forecasts a change of direction, the trader must be prepared to:

The following sections will answer the questions, "What is high?" and "What is low?"

What Is a Swing?

A filter swing is a price movement of a minimum size in one direction. Each commodity has its own special minimum criteria, or filter. The filter size for a commodity varies for weekly, daily, and intraday charts. It does not change once it is identified.

It will be seen later that the number of trades generated using this technique is directly proportional to the filter size. If the filter swing is too small, there are too many signals and frequent whipsaw losses in sideways markets. If the minimum swing size is too large, there are very few signals and some important trend moves are likely to be missed.

Once the correct filter size is chosen, this method should work very well in trending markets. In sidewards markets, the whipsawing should be very limited. Examples for the minimum filter sizes for several commodities are shown below. These values were generated by hand in 1983 as part of seminar material on "The Golden Section." Current testing, as far as it was possible, shows that these mini mums have not changed. If Fibonacci ratios make sense, these figures should be consistent over time.

 Commodity Time Period Filter (in pts.) Stop Loss Swiss franc daily 100 100 weekly 400 200 Deutsche mark daily 100 100 weekly 400 200 Japanese yen daily 100 100 weekly 400 200 British pound daily 200 200 weekly 800 400 Heating oil daily 200 400 Treasury bonds daily l'Vto 1.50 weekly 3 2.00 S&P 500 daily 400 400 hourly 100 200 Soybeans daily 40 30 Wheat daily 20 25 Gold daily 15 15 Cocoa daily 80 200 Coffee daily 500 300 Pork bellies daily 200 200

Swing Highs and Lows

Step 1. Look for a move of the minimum swing size. If the Deutsche mark minimum move has been set at 100 points, then look for a move of 100 points from the lowest low to the highest high (see Figure 7-3).

Minimum swing size 100 points h

Figure 7-3 To confirm a high or a low, we need a minimum swing size.

Step 2. The minimum swing size must be confirmed. Once the minimum swing size has been reached, the close must be higher than the high of the day which exceeded the minimum swing size (for a swing up), as shown in Figure 7-4.

Close that confirms the swing size higher than the minimum swing si2e t

Minimum swing size 100 points

Figure 7-4 To confirm a swing size, the close has to be higher than the minimum swing size.

Step 3. On daily charts, look for a close which is lower than the low of the highest day to confirm the high day (vice versa for a low day), as shown in Figure 7-5. This step is not necessary on weekly charts because the swing size itself is bigger than on the daily charts and therefore the requirement of a confirmation would be too restrictive.

High day

Close to confirm swing size t t

Minimum swing size 100 points

"I

Close lower than tow of high day i

Figure 7-5 To confirm a high, the close has to be lower than the low of the highest day.

Figure 7-6 To confirm a swing high, there has to be a minimum swing size in the opposite direction from the highest high.

Step 4. Look for a minimum swing size in the opposite direction, as in Figure 7-6.

By following these four steps, the peaks and valleys are established which are needed to find the "time goal days." These four criteria may seen complicated, but they are not. The objective is to limit the number of filter swings. To do this, there must be some restrictions that reduce "noise," or there might be so many swings that we would be unable to analyze them.

Following the four-step procedure, the peaks and valleys can be marked on the daily Deutsche mark chart (Figure 7-7). Once the

Close to confirm swing size

Figure 7-6 To confirm a swing high, there has to be a minimum swing size in the opposite direction from the highest high.

Close to confirm swing size

Minimum swing size 100 points

Minimum swing size 100 points bSDD--

Peak 1

Peak 5

Peak 4

Valley 6

"■■'il.-Hi in .hi.,m .hi ..ii .hi „ii.„it .hi ..ii .mi .,ii

ZS OH II II Zb 01 II IZ Z5 Dl OS 15 Z3 3D 01 H ZI ZR 05 IZ II 2b Db 13 ZD Z

DEUTSCHE HARK 09/92.D

RATIO: ,616 DIte+1

Figure 7-7 Daily Deutsche mark chart from 02-92 to 07-92. The highs and lows are marked as peak 1 to peak 5 and valley 1 to valley 6. (Source: TradeStation, Omega Research, Inc.)

minimum swing size is determined, the four-step procedure is the same for every product and every chart, whether weekly, daily, or intraday.

Exception: No Minimum Filter Size in a Strong Trend

Looking at the daily Deutsche mark chart, both a long sideways move and a very strong uptrend can be seen in June through July, 1992. During the strong uptrend there was no move that qualified for the new "high" or "low," based on the procedure established to identify peaks or valleys.

A standard swing high and low must occur at least every 15 days. If they do not occur with this frequency, the TGDs are so far apart that the market swings can no longer be captured. In addition, a lack of time goal days significantly increases trading risk. Without a nearby objective to indicate where the market will change direction, positions are held longer, and there will be larger equity swings. Computer testing shows that the best performance occurs with TGDs indicate a high or low no more than 15 days apart.

To solve this problem, whenever the market trends for at least 15 days without a minimum filter swing, we use a smaller one. We simply select the largest swing that occurred within the past 15 days,

High 1

Norm

100 I

swini

High 1

Norm

100 I

swini

Figure 7-8 Market swing from high 1 to low 2 of 21 days without a valid swing in between.

measured from the highest high and lowest low. Figure 7-8 demonstrates this method. It is more important to maintain the frequency of TGDs than to be committed to a specific minimum swing size.

The figure shows the problem that might occur in a strongly trending market. A filter size of 100 points is assumed and shown on the left side of the chart. Low #1, high #1 and low #2 are identified.

There are 21 days between high #1 and low #2. Applying the rule for the small filter size in a trending market, look for the biggest swing between the high #1 and the low #2. That swing is located between points PI and P2 in Figure 7-9. The new time goal day can be calculated by using the distance H1-P2, in days.

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17

Returning to the daily Deutsche mark chart, the smaller swing size can be found in exactly the same way. The smaller swing high is located at peak 6 and the smaller swing low at valley 6, as seen in Figure 7-10. This is the complete procedure for establishing TGDs in strong market trends.

Smaller swing

P5 W

„ill-.ill .ill .ill ■■»' -■" nil .III ,I LI .ill „11 .. LI „III...II .III .ill

CI 02 03 DH 05 Db 01

ZB 04 II 14 Zb DH II IS ZS 01 DK 15 Z3 30 01 14 II ZR 05 IZ 11 Zb Ob 13 ZD t

DEUTSCHE KARK 09/92.D

Figure 7-10 Daily Deutsche mark from 02-92 to 07-92. Smaller swing is integrated with peak 6 and valley 6. (Source: TradeStation, Omega Research, Inc.)

Exception: Too Many Minimum Filter Swings

The previous section redefined the minimum swing size when there were no standard swings. The opposite case also exists. Too many swings may occur in only a few days. This could easily occur in a market with slightly higher than normal volatility, as shown in Figure 7-11. Swing highs, that satisfy the minimum filter, are located at points 2, 4, and 7; swing lows are at 3 and 5.

To eliminate this excessive noise, delete the swing which has a low on the third day and the high on the fifth day, based on the following rule: There must be at least three days between the highs and lows of two swings that satisfy the minimum swing filter.

This applies to both top and bottom formations. Successful time analysis depends on the correct identification of peaks and valleys. The standard filter size was chosen by historical testing, but this

MORE ON THE STRUCTURE OF TIME GOAL DAYS • 113 1 23456789

Figure 7-11 Too many minimum filter swings.

minimum filter, for example, 100 basis points in the Deutsche mark, is only the start to finding the correct peaks and valleys.

### Review of the Procedure

The four-step procedure that was developed to analyze the peaks and valleys is based on a minimum swing size. This satisfies most market situations. As we have seen, there are also exceptions. In a strong bull or bear market, there are many times when a minimum swing size does not occur. Without a swing of minimum size within 15 days, the trading analysis becomes unsatisfactory. Smaller swings are integrated to solve this problem. The case with too many swings was another problem. This can happen in periods of very erratic price movement. This situation can also be solved by establishing a procedure which eliminates some of the noise.

### MORE ON THE STRUCTURE OF TIME COAL DAYS

When we look at a chart of any time span, we look at the price swings. We see big ones and small ones. These swings rarely represent the wave structure defined in the Elliott concept, because most market patterns are "irregular." As discussed earlier, those irregular market patterns are the result of complex corrections and extensions.

Working with TGDs does not require the use of a wave count. In this analysis it is not important whether there is an uptrend, downtrend, or sideways market. The Fibonacci ratio 1.618 is applied directly to well-defined market swings.

At the time the TGDs are calculated, we never know whether the market price will be high or low at the points where the TGDs are reached. It can be either one. A TGD forecast a turning point. Our objective is to:

• Sell if the market price is high when a TGD is reached, or

• Buy if the market price is low when a TGD is reached.

By using the last two highs, the TGD can be projected, as shown in the Figure 7-12.

HigM
(a)

Figure 7-13 (a) Using two valid lows, the price can be high when the TGD is reached; (b) using two valid lows, the price can be low when the TGD is reached.

Figure 7-13 (a) Using two valid lows, the price can be high when the TGD is reached; (b) using two valid lows, the price can be low when the TGD is reached.

The same calculation performed using the two most recent highs, can be applied to the two moat recent swing lows. The results are shown in Figures 7-13.

Familiarization with these four combinations will allow an understanding of what happens to the results when the TGD calculations using highs/highs and lows/lows are combined. In the best case, TGDs calculated from highs/highs or lows/lows coincide on the same day. But that is ideal. Most likely, the TGDs are interspersed. The best realistic case is when a few TGDs appear close together, forming a time band or time barrier. When multiple TGDs coincide, there is a higher probability that the market will turn for either a short-term correction or a complete trend reversal. TGD& calculated from daily data are more reliable than intraday results; weekly data takes precedence over daily data. There is less noise using longer term data.

Figure 7-14 shows the integration of TGDs using highs/highs and lows/lows.

Figure 7-14 The same time targets are reached by calculating TCDs from high/ high or low/low.

Problems may occur in the investment decision when the only available time-goal calculations result in TGDs which do not fall near one another. This may happen when the different time signals are based on the calculations of the last two highs and the last two lows. Figure 7-15 describes this situation.

In Figure 7-15 the time interval from HI to H2 produces the time goal H3. The time span Ll to L2 gives the time goal L3. A short position must be entered when prices reach H3, because it is clearly a high price. We cannot yet know what will happen when time goal L3 is reached, but it cannot influence the trade based on H3. A short is entered at H3, and a stop-loss is placed above the high according to the entry rule. If the position is stopped out, another short may be set at L3 if the price is still at the same level as it was at H3, following the re-entry rule. If it is at a clearly low price, a new long position is entered according to the rules.

H1 High

H2 High

H3 TGD High

1.618

1.618

1.618

1.618

Low L1

Low L2

TGD Low L3

Figure 7-15 Different time targets are reached by calculating TGDs from high/ high or low/low.

Analyzing Time Goal Days Based on Highs/Highs and Lows/Lows

The basic use of time goal days should be clear. In a normal market, the distance between two highs or two lows is multiplied by the ratio 1.618 to get the TGD. To start the process of working with the time goal concept, first ask the question, "Is there a filter swing high or low?" If the answer is yes, "Are we at a time goal day?"

The application of TGDs varies based on its proximity to a peak or valley. In the normal sequence of events, the market will:

• Produce a swing satisfying the minimum filter value.

• Make a high or low for the current price move.

TGDs Occurring before or at a Peak or Valley. In the most frequent situation, a peak or valley has not yet been seen when the TGD is reached. The location of the subsequent peak or valley is not relevant to the basic trading approach (see Figure 7-16).

Figure 7-16 (a) TGD occurs before the peak; (b) TGD occurs at peak.

TGDs One Day after a Peak or Valley. There are many situations where the TGD overshoots the peaks or valleys. This may go unnoticed; however, it can have made a significant change to the trade. If the TGD is one day after the peak or valley <see Figure 7-17), and on this day the entry rule still was not in effect, wait for the entry rule (entry rules are discussed later in this chapter) to enter the market.

TGDs More Than One Day after a Peak or Valley. Whenever a TGD is more than one day after the peak or valley, the situation becomes uncertain. If no minimum swing has occurred, the TGD is ignored (see Figure 7-18).

Figure 7-17 TGD occurs one day after peak.

Figure 7-17 TGD occurs one day after peak.

Figure 7-18 TCD occurs more than one day after peak.

Trading Example. The four-step procedure establishes a method for identifying peaks and valleys. This procedure works for every product and every chart, whether intradav, daily or weekly. The daily Deutsche mark chart in Figure 7-19 shows the peaks and valleys that should be identified using this method.

bbflO--

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22 OH II II Zb DM II IS ?5 Dl 08 15 23 3D 0T It Zl 21 OS IZ II Zb Ob 13 ZD I

Mllte .618 BIfc+1

DEUTSCHE KABK 89/92.D

With the highs and lows established, the TGDs can be calculated using the distance between the highs and the distance between the lows. For easier reference, all highs are marked even numbers and all lows with odd numbers. Only the Fibonacci ratio 1.618 was used.

The high TGDs were calculated in the following sequence:

• The distance from high #1 to high #2 times 1.618 = TGD A

• The distance from high #2 to high #3 times 1.618 = TGD B

• The distance from high #3 to high #4 times 1.618 = TGD C

The low TGDs were calculated in a similar sequence:

• The distance from low #1 to low #2 times 1.618 = TGD G

• The distance from low #2 to low #3 times 1.618 = TGD H

• The distance from low #3 to low #4 times 1.618 = TGD I

Figure 7-20 shows the peaks, valleys, and the calculated TGDs, bSCD

bDOD

too*

-III..Ill -H r'l -.11 .III .11 .III .ill..Ill ..II -.11 .ill -.11 -Ii .III-n ..n -III III -.»I ■

Dl 01 03 OH OS Db 01

ZS Of II 11 Zb 04 II IS IS Dl OS IS 23 30 Dl IS 21 21 05 I? 2b 0b 13 2D 2

DEUTSCHE HfifiK 99/92.D

RATIO: .618 DIRitl

### TGDs Using Larger Filter Swings

Larger filter swings may occur many times on weekly charts. For example, whenever there is a swing of 10 full points (1,000 basis points) in the Deutsche mark, the peaks and valleys are combined in all four ways to produce TDGs based on highs/highs, lows/lows, highs/lows, and lows/highs. The method is demonstrated in Figure 7-21, the weekly Deutsche mark chart.

hj hi hj hi

..il -.il .,il ,.il ..il .nl ,.il..hi .,ii ,.il ,.il .hi -ii„H ,ill .,ii .,ii .hi .ill .nl .,il „ii ,.il ,ii;,.il.iil .,ii .nL.nl„m.„il „ii Dt Dt ID II 12 01 03 OH D5 Ob Ol 08 01 II 12 01 D2 03 DM DS 01 OS 01 10 H 12 Ol 03 OH QS 0k 01 OS DI 13 II22 ZbOZQb tl 1520 2Hlt 02 <11 11 15 22 2b 31 DS DS 13 It 22 21 3f Ob 10 IS 14 2H

Figure 7-21 Weekly Deutsche mark chart from 07-89 to 07-92. Buy and sell signals generated with the time analysis. (Source: TradeStation, Omega Research, Inc.)

..il -.il .,il ,.il ..il .nl ,.il..hi .,ii ,.il ,.il .hi -ii„H ,ill .,ii .,ii .hi .ill .nl .,il „ii ,.il ,ii;,.il.iil .,ii .nL.nl„m.„il „ii Dt Dt ID II 12 01 03 OH D5 Ob Ol 08 01 II 12 01 D2 03 DM DS 01 OS 01 10 H 12 Ol 03 OH QS 0k 01 OS DI 13 II22 ZbOZQb tl 1520 2Hlt 02 <11 11 15 22 2b 31 DS DS 13 It 22 21 3f Ob 10 IS 14 2H

DEUTSCHE KAM 55/92,H

Figure 7-21 Weekly Deutsche mark chart from 07-89 to 07-92. Buy and sell signals generated with the time analysis. (Source: TradeStation, Omega Research, Inc.)

### REVIEW

This chapter showed how important it is to produce the TGDs which integrate with the time frame of the analysis. It also showed what happens when a TGD is reached. It confirms the power that lies in this analysis, but also demonstrated how much accuracy and discipline it takes to follow the strategy.

The occurrence of the TGD in relationship to the developing peak or valley was important. Whenever a TGD fell more than one day after a peak or valley, it was ignored, provided a minimum swing has not occurred.

In strong markets, there may be intervals of 15 days in which a swing does not satisfy the minimum filter criteria needed to calculate a TGD. In this case, a combination of the previous highs/lows or lows/ highs can be used to generate the TGDs needed.

On weekly charts, there may be very large swings which produce TGDs that are months away. To solve this problem, the combination of highs/lows and lows/highs was also used. For example, a full 10-point swing (50.00-60.00) in the Deutsche mark is considered big.

Normal Entry Rule

A new short position is entered using the following steps:

• First, prices must move up by more than the minimum required swing,

• Last, we sell on the close when the closing price is below the low of the highest day.

This entry sequence is shown in Figure 7-22. The normal buy entry rule follows the same procedure.

Self signal

Close lower than low of highest day

An additional entry rule should give us the chance to enter the market when there is a very strong move. In this case we want to be invested before the market closes. For the additional entry rule, a sell signal is as follows (and shown in Figure 7-23);

• After the minimum swing up has been satisfied, and

• After a TGD has been passed, then

• Sell when the price breaks the previous 4 lows.

Minimum swing size i h tu

Low Low TGD

Sell at -4 day low breakout

• After the minimum swing down has been satisfied, and

• After a TGD has been passed, then

• Buy when prices break the 4 previous highs.

### Stop-Loss Rule

A stop loss should always be entered at the same time as the trade entry. One effective way of placing a stop loss is to work with a price square (see Chapter 3, Figure 3-14). On the daily chart, the side of the square is the distance of five business days. On a weekly chart, the side is the distance of five weeks (see Figure 7—24).

One price square stop loss

One week In time Figure 7-24 Stop loss rule.

### Re-Entry Rule

Whenever a long position is stopped out, it may be re-entered if market conditions satisfy the normal entry rule, and the market did not make an upward move satisfying the swing filter size. This can be seen in Figure 7-25.

Stop loss

Re-enter on parameter normal entry rule

Sell signal on close lower than low ot high day

Low Low TGD

### Figure 7-25 Re-entry rule.

Whenever a short position is stopped out, a re-entry occurs when market conditions satisfy the normal entry rule, and the market did not make a downward move satisfying the swing filter size.

### SUMMARY

Elliott wrote of timing, "The length of waves may vary, but not the number of waves. The numbers of this series [Fibonacci sequence] are useful in timing the waves, both advancing and declining" (p. 129).

A move that extends itself beyond three days should not reverse until five days are reached. A move that exceeds five days should last eight days. A trend of nine days should not finish before thirteen days, and so on. This basic structure of calculating trend changes is the same for hourly, daily, weekly, and monthly data. Each one of these cases is an example of the Fibonacci ratio, and the basis for time goal days.

Our approach to timing is focused only on the Fibonacci ratio 1.618. It is very mechanical and seems to work in both sideways and trending markets. While Elliott's approach is very static, our analysis is very dynamic.

The greatest difference between this and strategies introduced previously, is that in this concept we are invested most of the time.

This concept is closely related to Nature's Law, expressed through the Fibonacci ratio 1.618. This means the TGD concept has forecasting value; it anticipates price changes rather than following after them. This distinguishes it from many other trading methods. The unique combination of swing size, time goal days, and entry rules makes it possible to pinpoint tops and bottoms. In addition, this concept is dynamic, allowing it to adjust to bigger and smaller market moves.

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