Elliott Wave Timing Beyond ordinary Fibonacci methods

ELLIOTT WAVE TIMINGBEYOND ORDINARY

FIBONACCI METHODS

By

Mark A. Lytle

Copyright 2009

Preface

In this short book I will outline a new and original procedure for showing the underlying math relationships that exist between adjacent waves in the markets.

Up to the present, Market Technicians have relied almost exclusively on Fibonacci time series to make estimates as to when trend changes in charts might appear. The biggest problem with this method is that Fibonacci time relationships happen infrequently, and produce relatively few signals. Redundancy across more than one time scale is often required to produce the desired level of probability to make a trade worth attempting.

The reality is, there are far more Fibonacci relationships present in most charts than what is commonly perceived. The reason for their invisibility comes down to the unappreciated fact that much of the activity in the markets is distorted in the direction of the flow of time by logarithmic effects of previously existing events, which are generally major tops and bottoms. It can be shown that prior market tops and bottoms can have an influence over considerable periods of time, and when the normally 'time linear' charts in customary use are corrected for this effect, trend change points relating to Fibonacci can be observed to emerge.

It is common in most charting programs for price to be plotted logarithmically in order to show trendlines not visible on price linear charts, so on the face of it, it shouldn't be totally surprising that the time dimension might also manifest similar properties.

I will in the following pages outline the major concepts behind Exponential Time in the markets, and show how this effect can be calculated. It took months of intensive statistics to find these relationships. The math is freshman algebra throughout, no calculus needed. This math can be performed on a programmable calculator, but best results are obtained by the use of spreadsheets, because in addition to the hidden Fibonacci time points, there are also hidden trendlines revealed by charts plotted with an Exponential Time element, and these are best seen on a spreadsheet XY plot. All of the formulas presented in this work are based solely on the two core measurable parameters of a chart, price and time. Enjoy this information, and good luck to all!

Mark Lytle, Houston, Texas July, 2009

Dedicated to my mother, Elizabeth A. Lytle

I wish to thank my wife Barbara for her support. In addition, I wish to thank Trevor Nichols and Dan Havlik for proofreading this manuscript.

All charts courtesy of bigcharts.marketwatch.com

Created on a computer running Ubuntu Linux version 8.1 and composed on Openoffice 2.4

The greatest shortcoming of the human race is our inability to understand the exponential function.

Albert Bartlett

Contents

Chapter 1 Definitions and Core Concepts (Exponential Time Nodes) Chapter 2 – Converting to Spreadsheets Chapter 3 – Exponential Trendlines and Crossovers Chapter 4 – Final Thoughts Index of Charts Index of Topics

Chapter 1

Definitions and Core ConceptsExponential Time Nodes

This chapter will explain how to begin the process of analysis, what to look for, and how to select the appropriate input information to do an analysis with.

For starters we are looking for Elliott Wave patterns. I prefer simple ones, standard ABC patterns (3's), and sometimes 12345 patterns (5's). This book will not be an Elliott Wave primer, I will assume some familiarity with these concepts.

Being that the simplest pattern is the ABC pattern, this is where we will start.

Here is an example of this pattern:

It would be nice to know where this pattern would bottom, wouldn't it? To help determine this, we need some standard concepts to apply to all charts, and this will help to determine what price and time information is to be copied from this, or any other price chart, to make calculations possible.

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All price and time measurements will be taken from a 'start' point that represents where the pattern started. You can see that this clearly is the point where the two red lines cross in the picture below. This is the 'start' point, which is the most important price and time point.

So what are the important parameters and how do we measure them? We need the price and time covered by wave A, and the price and time covered by wave C. The parameters of wave B are unimportant, and won't be needed. So what we are looking for is the following quantities as in this diagram:

We are seeking the price spans and time spans of waves A and C, as they relate to the price and time levels of the 'start' point.

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So these calculations are fairly straightforward. We subtract the height of waves A and C from the 'base price' of the 'start' point to get the price spans of waves A and C. Then, we subtract the date of the 'start' date, from the dates of the tops of waves A and C to get the time spans of waves A and C. No higher math here.

So when we have these quantities measured, we have one final calculation yet to do to produce a very simple but important measurement. It is as follows:

(price span of C) * (time span of C) = PriceTimeProduct (PTP) (price span of A) (time span of A)

The PTP is the basic math concept, the building block of all of the math to follow. It is clearly a simple concept. Now, what do we use this for?

The PTP is the 'atom' of this analysis. In a sense, we are going to use it to build a slightly more complex formula, sort of an analogue to a 'molecule'. This new formula is expressed as follows:

EPTP = e^((LN(PTP) *time span of A) / time span of C)

For 'timespan of A', and 'timespan of C', let's call them Ta and Tc, respectively, and for 'price span of A' and price span of C', let's call them Pa and Pc. Finally, 'e' is the base of the natural logarithms with a value of 2.71828.

Then we have: PTP = (Pc/Pa) * (Tc/Ta) and EPTP = e^((LN(PTP)*Ta)/Tc)

That looks a little cleaner. EPTP stands for Exponential Price Time Product. Not imaginative, but accurate and useful. This is again, sort of a math 'molecule' composed of building on the PTP 'atom'.

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Now what is this new formula (EPTP) for?

What this formula does for us, is that it compares the relative power of the two waves A and C, and using the time span of the first wave 'A', as a yardstick, permits extensions into the future by a set of measured amounts of time. This is the basis of projecting future trend changes from past price and time patterns, which is actually what markets do. Stated another way, they take past patterns and perform computations on them, and project them forward as mood swings (and therefore, market action) to be performed later. Is this process totally deterministic? No, it is not. There are several possible trend change points indicated, only some are taken. Remember, functionally, we are doing familiar Fibonacci projections, but by the method of taking out or decoding out the exponential and logarithmic components, in order to let a subtle Fibonacci influence be revealed.

Now the final, and most important formulas, the magic ones.

O.K., how many days out will we have a trend change?

Well, counting days out from the 'start' point, shown on our initial graphic, these equations are what computes this:

You should see PTP and EPTP, as constituting the foundation of this method.

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The reason why you compute these first, is to simplify the computations later. Imagine how complicated these would be if we substituted all of the math for PTP and EPTP back into the above equations. They would be unmanageable.

Now, do you see the Fibonacci in the above? The Fib. ratios 1.382 and 1.272 when inverted, gives you .723 and .786. So there, deep in the math formulas, there is Fibonacci. Further, for those of you who are a little rusty, 1.382 = 2.0 .618 and 1.272 = (1+.618) ^2 ( that's squared, of course).

The .759 is an oddball, but it is related to Fibonacci too, just take my word for it.

Now, for an additional wrinkle, it turns out that intensive analysis showed a second series of calculations that also produced trend changes. The math is exactly the same as the first, but in place of .786, .759 and .723, you use .886 .871 and .851, respectively. The characteristics of these points in time, were that they often terminated the counter trend move, as in the first set of calculations above, or sometimes, produced an earlier, intermediate trend change of significant magnitude.

Now if all of this has you somewhat confused, at the time, so was I. Over time I realized that all of the equations above, and their variants, were permutations of a more basic equation. I will give it to you here, the final time formula:

That's it, that's the core! W(n) is the number of trading days beyond the 'start' point for the expected trend change.

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Now, before we go on to some worked examples, some general discussion is in order. The formula just given is designed to provide the number of days out from the 'start' date as to when a major trend change might occur. The most powerful exponents to use, as I have mentioned, are the .500 and 1.000. When a trend change occurs on or near one of the dates corresponding to that many days out, that moment is referred to as a 'node'. Also, the values of 1.272, 1.317, and 1.382 are referred to as 'bases' as in 'time bases'. So for each analysis, there will be results for each 'time base' (obviously, 3 in all), and each time base has a potential .500 and 1.000 node. With two powerful nodes, and 3 time bases, you should have 6 results. It will be necessary to watch the behavior of the price chart in question, and also conventional indicators as the price pattern approaches these time points. Positive or negative divergence of indicators should be observed near one of these 6 points, helping to define the right one. Also, Fibonacci ratios in price, and in conventional linear time, should be observable near the correct node.

What are the characteristics of the nodes that end a counter trend rally? Using backtesting, most counter trend rallies don't end until they have reached the time periods in the future representing at least the .500 node on either the 1.272, 1.317, or 1.382 time bases. They may end at one of the three .500 nodes, or three .750 nodes or three 1.000 nodes. Keep in mind that a counter trend move that hasn't reached at least a .500 node is still 'young', and has a ways to go. (Very important!) Also, it seems that the probability of a node that is being currently crossed over in time, being the 'right one', has success ratios of 2.0, 1.0, and 1.6 for the sets of three (for three time bases) at .500 , .750, and 1.000 nodes, respectively. That is, a typical analysis should resolve to one of the three potential .500 nodes twice as often as one of three .750 nodes.

At the deeper level, what is the distribution across, say, the three potential 1.000 nodes? My research suggests probabilities of 2.0, 1.6 and 1.0, for the 1.272, 1.317, and 1.382 1.000 nodes, respectively. Notice the Fibonacci tendency here, in the ratios of probability.

Another question comes up, ”How accurate are nodes?” When a node hits, it's within 3%, usually. That is, expect a 1.000 node to actually hit between .970 and 1.030, although the date that the trend change occurs, will often be right at the theoretical 1.000 node point, if the overall pattern is of relatively short duration.

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It's useful to keep in mind, that of the three .500 time nodes (dates) that are possible (remember, using the 1.272, 1.317, and 1.382 time bases) , one will be useful, more rarely two, very seldom, all three. This is also true, for the 1.000 nodes as well. Do you remember your high school algebra, where a trinomial equation might have three solutions, but often one or more of the solutions was not relevant, and thrown out? This is similar. One more interesting topic, is that there are some novel characteristics to the EPTP index. Normally this computes to a number somewhere between .5 and .65, but can go beyond this range in either direction. Numbers higher than .7, imply a very quick counter trend move. Sometimes I consider these waves 'old' and unstable. If one gets this result for a stock on the impulsive side, the counter trend side (in this case, downside) will resemble a crash. In those cases where the value of EPTP is as low as .45 (or even lower) that wave is considered 'young', and after a mild correction, the initial direction may resume. An analysis of just the first Elliott waves of many stocks often gives low values, and the same analysis run on just the fifth waves (using the bottom of wave 4 as the 'start' point) will sometimes show numbers higher than .7, indicating the likelihood of a strong failure.

It is possible to run the analysis on all 5 waves, impulsive and corrective, in an overall 5 wave Elliott sequence, to get, not just their individual EPTP characteristics, but a complete analysis that can provide timing possibilities at the smaller time frames.

One question that will come up is, “If the math only works for 3's (ABC patterns), how can you analyze and get nodes for, say, a 5 wave structure”? The answer, is that in a 5 wave structure, one correction, either 2 or 4, is usually the deepest and most severe. Use that information to convert the '5' into the most likely '3' (for analysis purposes).

Don't neglect the other possibility, however, just give the choice of your breakpoint that is the most severe, the stronger possibility of correctness in outcomes. It really makes sense to run a '5' as two different '3's', by neglecting the importance of either waves 2 and 4, as the two limiting cases. Sometimes, helpfully, the two analyses will give a pair of the same dates, and that makes it easy.

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This is what this looks like, in practice. The original Elliott count in gray has been replaced by a pattern that looks like a three wave pattern (in black). An alternate three wave pattern can be created by labeling the old wave 3 in this diagram as wave 1. Though not as dominant in the power of its results, that analysis should be run also, as this alternate pattern will have some influence. Note that the proper time to attempt any analysis and computation relative to the next (projected) swing is when the price action falls below the gray trendline in the diagram below. Until that happens, one can't be sure that maybe more bullish action is perhaps forthcoming, and that this overall pattern may not yet be complete.

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Interestingly, if the price action doesn't fail at the trendline, and in the example above, makes another high (a potential 5th wave based on the dark black lettering, or perhaps a 'B' wave), then the top of the final impulse will often be accurately predicted by one of the .250 or .500 nodes. In a real steep accent, occasionally the rare .125 (1/8) node, may determine the top.

Keep in mind that if the above diagram were inverted, the same principles would apply. The math works equally well in either the bullish or bearish case.

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Chapter 1(continued)

Examples of Calculations

In the following examples, we will show how to calculate the dates on which trend changes have the highest probability of occurring. Examine this drawing:

We will now provide dates and prices for the points labeled “Start”, A and C, and show how to calculate the .500 and 1.00 nodes.

Here's the data:

Start: 2/7/07, $12.00/share Top of Wave A: 2/28/07, $19.50/share Top of Wave C: 4/2/07, $28.00/share

This is all of the data that's needed for node calculations.

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All time periods are expressed in trading days, not calendar days. Excel and Openoffice spreadsheets have the NETWORKDAYS function to calculate the difference between dates as work days, which is of course the same as trading days in most situations.

Using this capability in our spreadsheets, we find that Wave A took 16 trading days, and had a price span of $7.50 dollars ($19.50 – $12.00). Wave C terminated 39 days from the “Start” point, and had a price span of $16.00 dollars ($28.00 $12.00). Note that wave durations and wave price spans are all taken from the “start” date and price.

Now, the first real calculation we need to do is the PTP. It is:

PTP = ($16.00/$7.50) * (39 days/16 days) = 5.200 (Step 1)

Next, calculate the EPTP. This is slightly more work.

First, take the natural log of the PTP times the span of wave A:

LN(5.200) = 1.6487, and then 1.6487 * 16 days = 26.3785 days

Second, divide this by the timespan of wave C from “Start”:

26.3785 days/ 39 days = .67637.

Third, give it a minus sign and use it as an exponent for the scientific constant 'e':

EPTP = e^(.67637) = .508457 (End of Step 2)

Now we must calculate the number of trading days, starting from the “Start” date, out to which the 1.000 nodes (all three of them) might be found. Each of these three dates represent the center of a very small bell curve of probabilities for each 1.000 node.

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For the 1.272 (1.000) node the calculations are:

Take the natural log of .786 over the EPTP. Remember, .786 is 1.272 taken to the minus 1.000 power:

LN(.786/.508457) = .43557

Divide the natural log of the PTP by this value:

LN(5.200)/.43557 = 3.7850

Final Step!

Now, multiply this number by the number of trading days that Wave A took to complete:

3.7850 * 16 days = 60.56 trading days. Bingo! That's how many days out from “start” that the first trend change might happen.

What is the calendar date for that? Use the spreadsheet WORKDAY function to add 60.56 trading days to the start date, 2/7/07, to get the 1.272 (1.000 node) date of 5/2/07.

For the 1.382 (1.000) node the calculations are:

Take the natural log of .7236 over the EPTP. Remember, .7236 is 1.382 taken to the minus 1.000 power:

LN(.7236/.508457) = .35286


LN(5.200)/.35286 = 4.67227

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Now again, multiply this number by the number of trading days that Wave A took to complete:

4.67227 * 16 days = 74.75 trading days into the future from “start”.

What date is that? Using again, the WORKDAY function, you get 5/22/07, when you add 74.75 days to the start date of 2/7/07. This is the 1.382 (1.000 node).

Results for the 1.317 node:

Do this as an exercise, confirm that trading days out from start equals 65.88, and the Exponential node (1.317 (1.000 node) happens around 5/9/07. This date always falls between the 1.272 and 1.382 results for a given node exponent. (Here, obviously 1.000) If this didn't happen, you did something wrong.

Now those are the 1.000 nodes by each of the three bases, next we will proceed to calculate a .500 node for the 1.272 base.

First, take 1.272, the base to the .500 power and put it over the EPTP, and take the natural log of that:

LN(.88666/.508457) = .556079


LN(5.200)/.556079 = 2.9647

Again, multiply this number by the number of trading days that Wave A took to complete:

2.9647 * 16 trading days = 47.44 trading days

This, added to the start date, gives a node date of 4/13/07 for the 1.272 (.5000 node). You should also now be able to calculate the .5000 nodes for the 1.317 and 1.382 bases. The dates you should come up with are 4/16/07 and 4/19/07, respectively.

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It's worth mentioning that nodes work on hourly charts also (intraday).

Charted Examples

Here is a charted example. Macy's had a run up from 3/6/03 to 3/23/07. 3/6/03 becomes the 'start' date, at a price of $11.98 a share. The top on 3/23/07 was at a price of $46.70 a share. Near the midpoint of these two dates was an intermediate peak on 8/1/05 at $39.025 a share. I have labeled these points as Start, A, and C on the chart below. You can see the 1.317 .5000 node did a good job of approximating the bottom. The previous 1.272 .5000 node delineated the top of a small rally before the actual bottom. Again, as an exercise, try to compute the 1.382 .5000 node, which is off of the chart on the right. It comes in on 6/10/09. The PTP is 2.161 and the EPTP is .632700.

Here is another example, on the next page, this time it's Goodyear Tire (GT) and it's formed a perfect Elliott '5' wave pattern down. I've relabeled it as two overlapping ABC patterns, one in blue lettering and the other in red. I have included the long range chart and the expanded, zoomed view, to show the top of the bounce from the bottom of the '5' wave completion.

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Zoomed View:

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The input dates are: 'start' (blue and red) at 3/31/98 @ $76.75, wave 'A' (blue), happens at 9/4/98 @ $45.875, wave 'A' (red) occurs at 10/11/00 @ $15.60, and wave 'C' (blue and red) are spotted at 2/6/03 @ 3.35.

The output node dates for the .5000 nodes, blue series, are 6/19/06, 5/23/07, and 1/9/09, for the three bases 1.272, 1.317, and 1.382, respectively. The red series gives 7/21/06, 7/10/07, and 3/31/09, in the same way. The reader should be able to verify these output dates. When nodes overlap in time, especially when both nodes are either .500 or 1.00 in some combination, strong warnings of trend change are indicated.

So, the Exponential Time Node mathematics gave a good clue as to where the top of the bounce might occur. Note that the pairs of time nodes aligned well with the inflection points seen in the chart above. With standard indicators to help, one could use these techniques to help determine, in this case, when to exit a long position in this stock in the summer of 2007.

Our last example is GM. This chart shows the 1.000 nodes for the three bases as they are projected into the future. Clearly, GM wasted no time heading for the 1.000 node using the 1.272 base for the target of it's collapse.

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**********************************************

........................Just some advice to help you.....................

Please, at this point, consult your documentation on Excel or Openoffice on how to create Scatter Plots. If you are unfamiliar with this process, it would be good to get some practice at this point.

Create some simple columnar tables of values, and make sure the leftmost column is in ascending order (although they don't have to be spaced at even values apart, numerically). Make the first (top) value in this column equal to zero. That column will be your Xaxis, and the columns to the right of that one, will be 'Y' values. You should have at least two columns of 'Y' values. They need not be in perfect ascending or descending order, but make them just random enough to create an attractive graph. This skill will help you follow what is to come in Chapter 2, and beyond.

************************************************

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Chapter 2

Converting to Spreadsheets

In the previous chapter we covered the core concepts and calculations that gave us points in time, where trend changes had a high probability of occurring. These points in time we call Exponential Nodes. It became possible then to create a conventional chart, stretch out the time scale, and sketch in the times in the future where these dates were found, with well placed vertical lines.

It turns out that a better and more useful representation of price action is obtained by plotting major highs and lows on a chart that reflects the exponential nature of time demonstrated by the equations we have already described. Computer spreadsheets are ideal for this purpose. Let's now describe how to set them up, and how they should look.

First, it's necessary to rewrite the core equations in a different format, as we will want to plot the dates of various intermediate trend changes on a graph that will show their placement in exponential time rather than linear time. The needed components, PTP and EPTP, are computed as before, so the spreadsheet author must provide input fields on the spreadsheet for the dates and prices of the three essential points on the daily chart that allow computation of these. As a convention, one might usually shade these fields light green so they can be spotted quickly. These spreadsheets tend to get quite busy, so this is helpful in keeping things clear. Note: If the following instructions seem onerous, the complete spreadsheet can be obtained from the author.

On the next page you will see an example of how the upper part of the spreadsheet should be laid out. The area highlighted in black can be ignored for now, as that math hasn't been covered yet. The most important thing at this point is to create the 'foundation' for the spreadsheet set up. In the example shown, there are sample values placed in the input cells, which are light green.

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Spreadsheet example 1

It's not a bad idea to duplicate this example, and use a calculator to understand how all of the numeric fields in light blue were arrived at before proceeding. Remember to use the NETWORKDAYS function to get the difference in trading days between input dates. This will save a lot of headaches down the road. Just for review, the phrase 'EARLIER WAVE' refers to the extremes of wave 'A' and 'FINAL WAVE' refers to the extreme value of wave 'C'. The lettering here is in red, just above the input values in the light green cells.

Once the 'foundation' as above is created, we come to the next part which will allow short term tops and bottoms to be entered in a columnar fashion. This will produce the effect of getting a 'visual' on how the pattern of the security in question is unfolding with respect to nodes and trendlines (which will be described shortly). It will be important to pick off by eye, all of the significant tops and bottoms after the major high or low, following the extremes of the 'C' wave.

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Here is the next look at how the spreadsheet is constructed:


It can be seen that another light green field, a column, is visible on the left. This really contains two fields, a date and then a price (In columns 'B and 'C'). This is where the intermediate tops and bottoms are recorded for display on the spreadsheet graph we are creating. Referring to the first spreadsheet example, cells C36 and D36 are just a copies of the value in I7, E36 is a copy of the contents of G7.

The column labeled 'Days from start:' in column 'F' is just the NETWORKDAYS function applied to the difference between the 'start' date and the series of dates in the light green column starting at cell B37. The columns to the right of this one just represent the 'Days' column manipulated to give the number of days weeks and month past the final wave. This sometimes lets the user see important changes occurring at Fibonacci numbers of days, weeks, or months past the wave 'C' trend change point (here denoted as 'Final Wave'). These columns are really optional, but sometimes they are useful.

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The column that's really needed and useful is the one labeled 'Core Index'. The spreadsheet math in the top cell of that one (J36) is as follows:

Core Index = EXP((LN($G$26)/(F36/$G$24))+LN($G$28))

The more familiar form of this equation looks like this: Core Index = e^((LN(PTP)/((Days from Start)/(First wave duration))) +LN(EPTP))

This equation allows for the rapid calculation of where the dates entered into the vertical light green column (on the left of the spreadsheet) fit onto the graphs based on the three bases (1.272, 1.317 and 1.382). If the setup is done correctly, the first value in the first cell will always be 1.0000 and will decline down the column. Since most of the cell references have double dollar signs, as they are copied down the column, the only cell reference that will change is the reference to 'Days from start'.

Now the magic part. On spreadsheet example 2, note cell L34, labeled 1.317 basis. All of the numbers below that represent the node value of the date referenced in the green input field in column 'B'. The math contained in cell L36 is as follows:

Node value (base 1.317) = LN(1/J36)/LN(1.317803365)

In plain English, it's this:

Node value (base 1.317) = LN(1/Core Index)/LN(1.317803365)

The execution of this cell gives the 'node' value of the date across from it in the vertical green date column (in column 'B'), in this case 9/12/06, which being the start of the next swing, has a node value of '0.0000'. The next date down, 9/15/06 has a 1.317 base node value of 0.00654, and so on.

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It's then rather easy to pair the node values with the price, and produce a spreadsheet scatterplot. For completeness, one also produces a 1.272 and 1.382 scatter plot by substituting those numbers in for the 1.317 base already shown. You then should see three scatter plots representing the three time bases, and the impact of the nodes should be clear as they evolve forward in time. Each day you can put in the current day's date and it's high or low to see if something extreme is forming as you approach the .500 or 1.000 nodes on one of the three base charts. The dates in column 'B' and the prices in column 'C' , as shown in the spreadsheet snapshot examples above, represents just this kind of activity.

Here in the example shown, you can see the plunge into the .5000 node for the 1.272 base. The rise out of it was anemic, some .5000 bounces are much stronger. You also can see some red and blue trendlines on this chart. We will cover these in the next chapter.

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It would be good practice to use the above formulas to compute the node values for the example given in this chapter. So, some of the raw data is here given on the left, below, as dates in the light green column, and the task is to come up with the node values for all three bases, 1.272, 1.317, and 1.382.

The input values are:

Start: 10/22/02 $1.80 Earlier wave: 1/20/04 $13.20 Final wave: 9/12/06 $26.49

From these, produce the following:

PTP: 6.74982 EPTP: .541886

From the PTP and EPTP, and the dates in the green column below, produce the values for the 1.272, 1.317 and 1.382 bases as in the columns to the right of the date column.

Let's work through one sample calculation...

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For the second listing, the date 9/22/06, use this equation from above:

Core Index = e^((LN(PTP)/((Days from Start)/(First wave duration))) +LN(EPTP))

'Days from start' is arrived at using the NETWORKDAYS function comparing 9/22/06 with 10/22/02.

Substituting, to get the Core Index value:

Core Index = e^((LN(6.74982)/(1024/326))+LN(.541886)) = .995224

Now to get the node value, say, for base 1.382, we use:

Node value (base 1.38197) = LN(1/Core Index)/LN(1.38197)

Substituting, we get:

Node value (base 1.38197) = LN(1/.995224)/LN(1.38197) = .01480

Use 1.27202 and 1.31780 instead of 1.38197 to get those respective node values for this date, 9/22/06.

This wraps up the conversion of dates to their respective node values, which is the goal of chapter 2. Chapter 1 demonstrated how to go the other way, from a node value to a predicted date.

Chapter 3 will show that exponential trendlines exist, and are only visible, when mapped with time as an exponential function. When exponential trendlines cross, those moments in time, are also often trend change points. When all is said and done, trend changes, under this system, can be instigated by one or more of the following:

(1) Passing through dates representing Exponential Time Nodes, (2) reacting to resistance or support at an exponentially generated trendline, or by (3) passing through dates representing crossovers of exponentially generated trendlines.

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Chapter 3

Exponential Trendlines and Crossovers

This chapter is where we introduce the final math, and concepts, that constitute the basis of exponential math as it applies to the markets.

The idea of drawing trendlines on charts to predict future price action has obviously been around a while. It has been, and remains, one of the most basic practices within technical analysis. The discovery that an exponential decay of the influence of previous major events, exists on the charts, in a somewhat hidden manner, forms the basis for the logical development of trendlines derived from that principle. Once a market swing has completed, either as a rally or a decline, the wave structure of that completed swing has a huge influence on the swing in the opposite direction that follows. Exponential Nodes were the first signpost along the way, where the rate of time decay was found to produce clear statistical groupings, as it were, of minor or major trend changes in the new direction. These effects are effects in time. It turns out that there are also effects in price, and that is what needs to be tackled next, in this chapter.

Originally, all of the concepts in this book came about because of an insight dating back to the 19992000 time period. Quite a number of the stocks of that time had no fundamentals whatsoever, and had the advantage from an analytical standpoint, that they were pure 'greed and fear'. Every so often, nature and history perform experiments for us that we could not perform for ourselves. One just needs to be attentive.

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Patiently collecting examples of about 50 'dotbombs' that rose and collapsed, it was found to be possible to correlate wave structures on the way up, with the rate of decline (change of price with time) on the way down, as well as determine the clusters of time points where the declines had a tendency to end. The former correlations led to the math for exponential trendlines while the latter math relationships led to the discovery of the exponential nodes.

One thing stood out in this research, which should surprise no one, really. The markets are not deterministic, but they are probabilistic. Just as electrons around an atom can occupy any one of several levels (but not randomly inbetween), in zones called orbitals, the market has similar constraints. When declining from a top or rising from a bottom, it will follow one of a very few lines down or up, of calculated steepness. The first person to notice this was probably William Gann.

Gann's technique was to handdraw a chart of a tradeable commodity or stock, such that the candles on the chart always rose at a 45 degree angle across the page. He recognized that the price action would sometimes rise or fall faster than this, or more slowly, by certain fractional multiples of the original slope, and he would often redraw his charts as needed to get them in compliance with the market's behavior. Gann was also aware of waves, and knew that a move would often complete after 4 or 5 had passed. However without the labor savings of modern computers and software, he had no practical way to isolate the relationship between the waves and the trendlines that resulted. Ralph Elliott, similarly, was very successful at documenting the taxonomy of the wave forms encountered in markets, but lacked the technology to isolate any other internal relationships.

The strength of Gann's ideas, in particular, was that he could anticipate the slopes of the trendlines followed by the markets, sometimes well in advance, as a mathematical transformation of an already existing trendline. This is a rather different approach from Elliott's work, where trendlines are only drawn as seen or belatedly recognized, and these therefore were purely empirical in nature.

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Now, fast forwarding to the present day, we can run statistics on large number of charts, and using the insights of power law mathematics (and it's offshoots), discover the relationships this book is presenting.

In Chapter 2, we used the principles of Exponential Time to build a simple spreadsheet that showed the decline from a top in a stock (that was randomly chosen). If you look at a lot of original charts of stocks and commodities, and their exponential plots, side by side, it becomes clear what the math is doing. Close to the left side, where the new swing up or down is starting, the spacing of price events (minor tops and bottoms) is nearly the same as it's exponentially charted counterpart. At further distances to the right, as time progresses, the exponential chart appears compressed compared to it's normal time plotted brother. This is why the high volatility seen at market tops and bottoms often seems to flatten out and lose both magnitude and frequency as time moves forward. The underlying time field is compressing, and the price field is deflating or inflating along one of a few possible predetermined routes. Now remember, I'm not making some outrageous claim that real, calendar time is being compressed. This is not a metaphysical tract. It's just that subjective time, as experienced by the participants in the market, appears to compress in such a way that it takes more calendar time to produce price action far from a major top or bottom then when nearer that event.

Once price action is plotted exponentially, some price patterns that look like a slanted or leaning bowl or dome, transform magically into a straight line. Thus, an exponential trendline is born.

Note also throughout this book, in constant references to this math, it is characterized as predominately, exponential. This is just a convention, really, as an examination of the equations presented so far shows them to be a mix of logarithmic and exponential functions, but this concept is very cumbersome to talk about. It's important to differentiate these methods from less sophisticated plots of price on logarithmic scales, so this is what determines my use of the nomenclature included here to distinguish this methodology. This is an apology to math purists.

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Here is a graphic showing how the exponential trendlines tend to work. The trendlines (shown in blue and magenta) act as ordinary trendlines do, offering support and resistance, and are occasionally breached. This image shows how trendlines look when plotted on normal time scales. The curves morph into a straight line when plotted on a log scale. The part of the diagram that gets plotted on exponential charts, starts at the vertical red line and grows to the right with the passing of time.

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If the diagram above were to be extended further to the right, the trendlines eventually crossover each other, (the lines never become parallel as the diagram might infer) and the points in time where they crossover are also points of potential trend changes.

Shown next is a general representation of the above diagrams as to how the data might look when plotted using exponential time as the Xaxis , rather than normal calendar time. You can see the similarities, but also the profound differences.

30

Notice that the exponential charts always have, as their origin, a vertical line that bisects the 'C' wave of the previous swing.

Once data is plotted on an exponential time scale, the trendlines are straight lines that follow the normal format of all linear relationships (Y=MX +B).

In this case 'X' is an exponential time value, 'Y' is price and the slope ('S') needs to be determined.

The way this is done is what we describe next.

The Slope index

The first step is to calculate the last of our three indexes, the Slope Index.

The formula is as follows:

Slope Index = e^((LN(PTP)*Pa/Pc)))

In this formula, Pa and Pc are the price spans of waves 'A' and 'C' respectively, as compared to the price at the 'start' point.

This Index is somewhat similar to the EPTP Index talked about in chapter 1, though it's important not to confuse them.

Next we derive two slope constants for the 1.272 and 1.382 time bases. (The 1.317 base is (strangely) included in these, it's a little more complicated)

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Here are the formulas:

Notice the two formulas are almost identical, except for the constant on the bottom of the last term, where one is 2.6180339 and the other one is 1.309017. The variable 'SI' in the above is the Slope Index that we covered on the previous page and 'TS' is the Time Span Ratio of waves C and A, (ratio of the time elapsed from 'start' to waves 'C' and 'A' respectively). In other words:

TS = Tc/Ta (see page 3)

Pa is the price difference between the extremes of wave 'A' and the price of the 'start' date.

The units of the answer are in $Dollars per 1.0 node (or, per unit node if you prefer).

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These base slope formulas essentially provide the 'm' in the standard equation “Y=m*X+b”. For the spreadsheet example given in Chapter 2, we had the following parameters:

PTP: 6.74982 EPTP: .541886

Pa = Extreme price value of wave 'A' minus price value of 'start' Pc = Extreme price value of wave 'C' minus price value of 'start'

So Pa = $13.20 $1.80 = $11.40 and Pc = $26.49 $1.80 = $24.69

The Slope Index then is:

Slope index or (SI)= e^((LN(PTP)*(Pa/Pc)))

Substituting:

SI = e^((LN(6.74982)*($11.40/$24.69)))

SI = e^((1.90952)*(.461725)) = e^((.881674)) = .41409

So, now to compute the 1.272 and 1.382 Base slope formulas, the time span (TS) must be computed. This is the length of time from 'start' to the extreme price of wave 'C' divided by the length of time from 'start' to the extreme price of wave 'A'. Referring to the important dates of that example in Chapter 2, and using the NETWORKDAYS spreadsheet function, we get:

TS = (1016 trading days duration for wave 'C') / (326 Trading days duration for wave 'A') = 3.11656

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Continuing, we now can compute the 1.272 Slope function as follows:

1.272 Base Slope = LN(PTP)/SI * (Pa/(LN(TS*1.27202)*2.6180339))

Substituting:

1.272 Base Slope = LN(6.74982)/(.41409) * ($11.40/(LN(3.11656*1.27202)*2.6180339))

= 4.61136 * ($11.40/(LN(3.96432)*2.6180339))

= 4.61136 * ($11.40/(1.37733*2.6180339))

= 4.61136 * ($11.40)/(3.6059)

= 4.61136 * $3.16149

= $14.5788 / per unit node

Doing the same calculation, as above, for the 1.382 Base slope will give you a value of $29.1573 / per unit node.

These again, are the slope values for a linear equation that describes trendlines that radiate from the most recent highs and lows as shown in the diagrams at the beginning of this chapter.

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The final step is to calculate what the value of the slope of the trendlines will be as time moves forward from time = 0, which is also clearly, node value = 0.

For an up sloping trendline, we take the 'start' price value at $1.80, and add the newly determined slope value multiplied by the current 'node value' of the date we have in mind. If the date 10/15/07, for instance, maps with the equations of Chapter 2 to a 1.272 node value of .55631, then the price value of the ascending trendline at that point will be ($14.5778*.55631) + $1.80. That works out to a level of $9.91. For the down sloping 1.272 trendline, since the top of the previous swing was at $26.49, the value of the descending trendline on 10/15/07 would be $26.49 ($14.5778*.55631) or $18.38.

The real point here, is to subtract the product of the base slope times the current node value from the previous high, for the down sloping trendlines, and add the product of the base slope times the current node value to the previous low for the up sloping trendlines. That is how the values for exponential trendlines are computed.

Now we have the information and understanding necessary to complete the spreadsheet started in Chapter 2.

35

You might remember in Spreadsheet example 1, we had blacked out a small area on the screenshot, we'll repeat it here:

Now we can replicate it, and show what goes in those cells:

36

Cell J24, as pictured below, contains the calculation for the Slope Index and it's internal math is this:

=1/EXP(LN(G26)*F12/F15)

Cell J27 contains the calculations for the 1.272 Base Slope and it's internals are:

=LN(G26)/J24*F12/(LN(I12*1.27202)*2.6180339)

Cell J29 contains this, which is the 1.382 Base Slope formula:

=LN(G26)/J24*F12/(LN(I12*1.27202)*1.309017)

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This takes care of all of the 'core math' needed to complete the Trendline Spreadsheet. A few finishing touches are in order.

Look at the next example.


You should be able to spot where this screenshot is in relation to the previous ones. Cell S54 displays the value of 18.38 which was the down sloping trendline price value we computed manually earlier in this chapter. Also, a while back I said that the trendline situation for the 1.317 base was slightly different. It is, for it uses both the 1.272 slope base and the 1.382 slope base, as you can see. All of the columns here are showing the computed data for declining trendlines.

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The final screenshot is shown next. This is further to the right than the one on the previous page. These particular columns contain all of the calculations for the up sloping trendlines, and here on cell AJ53, can be found the value of 9.91, which we calculated as an example of a price point at the node value of .55631, which in turn corresponded to a date of 10/15/07.


It's important, once you can generate all of these many columns of data, to be able to perform the mechanical task of creating the nice scatter plots seen in these screenshots. You must gather all of the up and down sloping calculated price points, as well as the actual price of the stock or security, and plot it with the node values as the Xaxis for each of the three time bases. Though a bit tedious to set up, once the basic templates of these spreadsheets are created, they can be used endlessly over and over again to produce powerful insights into how markets really work.

39

One final hint. This becomes a very wide spreadsheet, but the length going down the spreadsheet is up to the end user. The author has found it convenient to produce about 200 rows going down the page, in case I wish to plot 200 intermediate tops and bottoms in the current market swing. As you go, it seems to work best, to fill the green input data columns on the far left of the spreadsheet with the last known entered data points for date and price, each day, all the way down to that last set of active rows. Uncommitted cells in these areas seem to cause problems on some scatter plots.

40

Chapter 3 (continued)

The Mechanics and Relationships of Nodes, Trendlines and Crossovers

Now that you have a spreadsheet that plots nice scatter plots showing carefully chosen data from a market swing with trendlines and nodes as the Xaxis, what does it mean? What does it tell you?

Let's look at the example we've been following.

This is the raw chart:

41

I have decided to work with the labeled ABC pattern shown (up swing), and chart the following downswing. I could have picked the downswing from 2000 to 2003 and matched it to predicted features in the upswing to late 2006, but that's for another time. The scatter plots that this chosen ABC pattern has produced, start temporally at the thick red vertical line in the above 'normal' chart, and proceed with time left to right. Here is how it appears for all three time bases (three charts):

42

43

What can be seen in the charts on the previous two pages, is that the downtrend was arrested for a while in the top 1.272 time base chart, where the Xaxis reached the .500 node. It can be seen in the following chart (1.317 time base) that this same feature aligned with a crossover of both a red and a blue dotted trendline, and finally the last chart, of the 1.382 time base, shows that this point also coincided with the price bounce off of a blue up sloping trendline. Now, all of these charts are demonstrating the three possible warnings of trend termination, if not trend reversal: a .500 node, a crossover of trendlines, and a bounce from yet a different trendline. The presence of all three of these conditions made the bear trend in this stock almost sure to stop and reverse (at least temporarily). What could not be produced was a playable bounce. There was little conventional indicator divergence associated with this point in time, so a large bounce would not have made any sense. The reason for persisting with this rather nonenergetic example is to make the important point that having several coincident trend change signals on an exponential chart, does make a change quite certain, it does not, however, indicate the strength of the change or reaction. Normal indicator divergences should be used with this methodology to estimate the power of any anticipated bounce.

Commonly, the most reliable reversal warnings occur when two major time nodes coincide in time, those nodes being generated by earlier overlapping ABC patterns in a normal 5 wave setup (covered in Chapter 1) or by nodes created by different ABC patterns from different time scales. The next most reliable signal is a reversal of price at a trendline which also happens to be at a major time node. The nodes that matter most in these combinations are, of course, .500 or 1.00 in value, although occasionally the .250 node is important, especially when the associated EPTP index is higher than .68 or so. Crossovers, work slightly more rarely, and tend to be weaker reactions, but have the highest time precision, meaning the bell curve of probability around the date of a crossover is very small. They also work best in combination with a reversal at a trendline on a different chart (different time base) then the chart showing the crossover. Being that there are always three time bases, keep in mind to look for these clues on all three charts.

44

It should be noted that trendline bounces at support or failures at resistance usually entail a slight penetration of the trendline in question, followed by reversal. It's rare for trendlines to work without being breached slightly.

Also, remember that time nodes can forecast trend changes in advance even when they occur singly, but you need conventional indicators like RSI to help with oversold and or overbought conditions to give a more confident evaluation.

45

Chapter 3 (continued)

Some Charted Examples

What can be seen here is that trendlines actually created from price points as far back as 1974, largely contained the post 2002 advance of the S&P 500, and proximity to a 1.00 node signaled the beginning of the decline that started in October 2007. The value on 10/11/07 was close to .97. The much anticipated early 2009 rally found support at one of the exponential trendlines.

46

The data points used to set up the trendlines and nodes in the above diagram are:

Start : 10/4/1974 @ 60.96 Wave 'A': 1/31/1994 @482.85 Wave 'C' : 3/24/00 @ 1552.87

One may ask, why, in this $SPX example, the 1.00 node was a top rather then a bottom. This was a highly manipulated market, and the 20022007 market rally was in fact a 'B' wave, and therefore corrective. Left alone, it could have indeed been a bottom rather than an artificially lifted top. Elliott Wave theory runs true here. Corrective waves after an impulse generally go down, but they can run up as well. In the examples below we have concentrated on the Nasdaq 100.

First, look at the ABC patterns we have selected, in order to do the analysis:

47

As is customary, the scatter plots below start at the point in time defined by the thick red vertical line in the chart on $NDX above. The reader should be able to identify the values for these points and duplicate the charts being presented.

First, the chart resulting from the 'Red' ABC pattern:

Here you can see the 'top' of the 2002 to 2007 rally corresponded very closely with the .500 node, relative to the 1.382 time base. The actual value was .478.

48

In a complimentary way, the descending blue trendline above capped the top of the $NDX advance as the .500 node was reached in time.

The next group of charts is based on the 'Blue' ABC pattern.

With this set of calculations, the top comes in very close to the 1.00 node. The value here was .984. Mathematically, 1.00/.984 gives an error of 1.58%. See also, the top was near the region of the trendline crossover, above.

49

In the last chart shown, a downward blue trendline, at a different slope then from the previous set of calculations, helps to limit the maximum of the 20022007 $NDX rally. Summary: The pairing of an important time node on one chart, being reached with a trendline bounce or failure either on the same or different chart, (of perhaps a different time base) provides a powerful confirmation of major changes in trend.

This concludes Chapter 3, and covers all of the concepts behind trendlines, and their relationship to nodes.

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Chapter 4

Final Thoughts

Now we wish to wrap up a few loose ends, and discuss areas open for additional research.

Treating a Five as a Five.

In a previous discussion, (Chapter 1) we showed that the equations presented were designed to work from three points, a 'start' point, and a two consecutive waves in the same direction, usually labeled 'A' and 'C'. In a five wave pattern this was commonly applied in such a way as to have two overlapping ABC patterns. Applying the equations to this pair of patterns was usually the best methodology for predicting the end of the next move in time. In strict Elliott terms, this would be “StartWave 1Wave 5” as one set and “StartWave 3 Wave 5” for the other set. The calculations performed on “StartWave 1Wave 3” will more generally find the end of Wave 5 at the .25 or .50 nodes, and possibly the time node of the end of the counter trend move, but usually not as often as the overlapping ABC method already described.

Five waves and trendlines.

There are occasions when a 5 wave pattern is seen as a normal Wave 1 with a much larger and higher Wave 3 and Wave 5 of nearly equal magnitude, forming almost a double top. The decline from these formations is very steep, and the rise from a double bottom derived from a similar inverted structure are very fast as well. The trendlines these moves follow, run quickly beyond the calculated trendlines presented so far.

The fix for this is in the slope index.

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The normal slope index is:

Slope index = e^((LN(PTP)*(Pa/Pc)))

Where PTP in this above equation is a computation relative to a Wave 'A' and Wave 'C', based on a three wave ABC system. The fix for the double top or bottom is to compute the PTP for Waves 3 and Wave 5, both relative to a Wave 1, and substitute this way:

Slope index (steep))= e^((LN(PTP(3)*PTP(5))*(Pa/Pc)))

calculate the 1.272 and 1.382 Base slopes in the normal way, and apply these slopes to the node timing occurring between Wave 5 and Wave 1. This will normally produce the correct slope.

Hidden Fibonacci Relationships

The number of time bases = 3

The number of trendline crossovers across the three time bases = 5

The number of trendlines across the three time bases = 8

This wasn't forced, it just works out this way. Fibonacci numbers are everywhere.

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Overlapping trendline analysis from different time scales

Here, at the .25 node, you can see a top formed in $Gold, but the wispier set of trendlines are created by running an analysis on the smaller wave patterns in this diagram (labeled StartABC) and then overlapping the smaller results with the major ones. A separate set of time nodes are also created on this smaller time scale, and this same top is a 1.00 node on the smaller time scale, which helps confirm the .25 major node. Some of these charts become rather aesthetically pleasing as well.

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Verifying the proper initial 'StartWave AWave C' points for analysis.

It is occasionally difficult to pick the correct points to start the analysis where the wave pattern is 'noisy'. Double bottoms or tops can create ambiguity in many cases, where they exist near the appropriate place to pick one or several of the initial setup points in price and time. After making an initial guess, and assuming the counter trend move has already started, watch for compliance with the generated trendlines, early on. If the trendlines are doing their job, then the nodes generated from those initial choices will most likely be valid. It is a good idea to test all scenarios for the best possible 'fit'. In some cases there is more then one 'right' answer, so build spreadsheets for every worthwhile combination, and use them all in parallel. It will generates more time nodes when this is done, but watch for nodes from different initial setup points that overlap. These can be very profitable. The same holds for price contacts with major trendlines across several setups. Keep in mind, however, that a pattern with many more than the normal '5' Elliott waves is not normally going to produce reliable trend changes, or, they may occur when expected, but be weak in effect.

Exponential Math and Elliott Wave Theory

In almost all cases, exponential math backs up and supports Elliott Wave Theory. Some complex structures, like triangles, are challenging because they are influenced in their formation from prior patterns of more than one time scale. This becomes clear as the components of their immediate environment on the chart are labeled and used as the basis for computation. There are plenty of opportunities here for original research.

I know that Ralph Elliott felt his discovery had applications beyond the Stock Market. I feel also that these equations, or variations of them, probably are found in other places. Perhaps they exist in nature in other growth fractals containing Fibonacci relationships. Perhaps someone reading this book may know of them or be the first to discover them.

There is still much in the world to discover! This concludes the description and demonstration of Exponential Math!

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Index of Charts

55

Equity Chart Type Pages

General Motors normal time 17General Tire normal time 15,16$GOLD exponential time 53Macy's normal time 14Telefonica de Argentina normal time 41Telefonica de Argentina exponential time 23,42,43Nasdaq 100 normal time 47Nasdaq 100 exponential time 48,49Standard & Poor's 500 exponential time 46

Index of Topics

56

Subjects Pages

Base Slope (1.272 and 1.382) 3235,37,525 waves 7ABC pattern 7,14,42,44,51,52Core Index 22,25Crossovers 25,30,44,49,52Elliott Wave 1,7,47,54Elliott, Ralph 27,54EPTP 35,1114,19,22,24,25,31,33,44Exponential time 17,19,25,28,30,31Exponential trendline 2529,46Fibonacci 46,21,52Final Time formula 5Gann, William 27intraday 14NETWORKDAYS function 11,20,21,25,33Nodes 1,6,1013,19,26,27Pa 2,3,3134,52Pc 2,3,3133,52PTP 35,1114,19,22,24,25,33,34,52Slope Index 3133,37,51,52Ta 24,32Tc 2,3,32TS 3234WORKDAY function 12,13

DISCLAIMER

Remember! Be careful out there!

Always consult a Licensed Financial Advisor before trading securities. This book is for educational and informational purposes only. Trading involves considerable financial risk, so decide in advance to practice sound money management before you enter the market, and seek the help of local professionals in your area if you are new to trading. No warranty is either expressed or implied on the information provided here, or your performance in taking advantage of this information.

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Elliott Wave Timing Beyond ordinary Fibonacci methods

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