The Finance Book Club

A real gem from John Ehlers

According to Fourier analysis, any complex waveform can be synthesized using a combination of sine wave components.

That makes a sine wave a primitive from which all patterns can be formed.

It is best to use a primitive in trading in the interest of robustness

Cycle Analytics Chapter 17 Swing Trading Strategies

Let's analyze "Cycle Analytics" .

There is only one Chapter oriented toward Trading , the last one Chapter 17.

One Chapter among Seventeen = 6%
Which is coherent with the frequency of the vocabulary used :

in 256 pages Ehlers use

Entry = 19 occurences
Exit = 30 occurences
Stop-Loss = 10 occurences

Buy = 14 occurences
Sell = 12 occurences

It's clear that Ehlers is more interested in the engineering than in the trading. Actually this is a common feature of books written by the very clever. After all, trading is only applied knowledge, the activity of workmen, not the province of academia.

However I have for several years assumed there is no discernible pattern in cycles that can be found, and there was little value in common indicators like RSI, and now maybe I am (again) wrong. I thought I was already using the most advanced spectrometry method. Possibly also wrong. I thought that it was important to find cycles of as high degree as possible within as many bars of history as possible. Ehlers makes a compelling case why that isn't true.

If I can continue to be proven wrong eventually, maybe, I can be right. It's good that I started this project and my own journal because I am also remembering some things that I had 'forgotten' like the tendency of trends to 'wash out' and reset the cycle pattern. Probably after this I should re-read your thread.

Chapter 10 - Comb Filter Spectral Estimates

Ehlers compares these filters to a 'comb' as they let some things through the gate and some things are filtered out like a comb for hair. The technical details are as usual, highly complex and inscrutable to a novice.

Ehlers is a brilliant engineer but a lousy novel writer because this chapter, like the preceding one is an anti-climax after the periodogram chapter.

"An example of the spectral estimate computed by the array of band-pass filters using a pass-band value of 0.3 is shown in Figure 10.1. This estimate is compared with the autocorrelation periodogram and DFT methods in Figure 10.2. The three techniques provide a consistent estimate of the spectral content of the data. In my opinion, the autocorrelation periodogram is the superior approach because the measurement has less latency, has a wider range of amplitude swings, does not require historical averaging, and does not require Spectrum Dilation compensation. For these reasons I will be using the autocorrelation periodogram approach to compute the dominant cycle in the remainder of this book." (emphasis mine)

Would it not have made more sense to put these subsidiary methods before the periodogram and end nearly at the greatest achievement?

Attached Image (click to enlarge)

10.1 Comb Filter
10.2 comparison of comb filter, DFT, and periodogram. The periodogram is on the bottom.

Chapter 11 - Adaptive Filters

1. Ehlers mentions Kaufman’s adaptive moving average (KAMA) and Chande’s variable index dynamic average (VIDYA). They adapt to changes in volatility. (interesting)
2. However these are reactive indicators and “therefore they close the barn door after the horse is gone”.
3. Ehlers focuses on RSI, CCI and the band-pass filter.
4. “The key parameter in each case is the lookback period used to calculate the indicator. This lookback period is commonly a fixed value. However, since the measured cycle period is changing, as we have seen in previous chapters, it makes sense to adapt these indicators to the measured cycle period.”
5. “Tuning the indicators to the measure[d] cycle period they are optimized for current conditions and can even have predictive characteristics.” As we’ve maybe seen?
6. Ehlers then offers the code for his Adaptive RSI, Adaptive Stochastic, Adaptive CCI, and Adaptive band-pass.
7. I think I found three of them but the only way to be sure would be to convert the EasyLanguage code directly.
8. It’s important to note that Ehlers recommends three different ways of tuning these indicators, all using the periodogram.
   1. Adaptive RSI should be tuned to half the dominant cycle period
   2. CCI and Stochastic should be tuned to the full period of the dominant cycle
   3. The Band-pass filter is tuned to 90% of the dominant cycle period; this gives “~60degree phase lead-in”, whatever that is.

   
   

Ehlers also compares the indicators to each other.

“The most striking difference is that the band-pass filter has more high-frequency components. It is also apparent to me that the RSI, Stochastic, and CCI all pretty much indicate the same thing in the broad general sense. Without indicator transforms to enhance interpretation, which we cover in Chapter 15, there is no overwhelming reason to select one indicator over another.”

So I guess we are building up to something even more impressive?

Chapter 12 - the Even Better Sinewave Indicator
“The Even Better Sinewave Indicator works extraordinarily well when the market is in a trend mode. This means that the spectacular failures of most swing wave indicators are mitigated when the expected price turning point does not occur.”

“The default value of the duration input is 40 bars, so a maximum trade duration of about two months can be expected with this setting. Increasing the duration input will increase the maximum duration of a trade in a trend. This has the implication that you will be working through some additional drawdowns throughout the trade with the benefit that you will not be whipsawed out of a profitable trending trade.”



As Ehlers points out the advantage of this indicator is that the signals are easy to interpret. Hold long when the indicator is near +1 and hold short when it is near -1.

“Decreasing the duration input parameter shortens the maximum trade length when the market is in a trend, being more sensitive to the shorter wavelengths in the data.” I’m sure this is true of all the indicators with filter lengths.

 

1. The Even Better Sinewave Indicator is a variant of the roofing filter, using a single-pole high-pass filter.
2. The unambiguous signals of the Even Better Sinewave Indicator are generated by normalizing the wave amplitude to the square root of the power.
3. The only input for the Even Better Sinewave Indicator is the duration parameter.
4. The duration parameter controls the maximum length of an indicated position by setting the critical period of the high-pass filter.

This doesn’t seem to exist on the internet anymore so I re-built it with a little help from ChatGPT. As far as I can tell it works as intended. Let’s test it out, shall we?

As advertised, it performs admirably in a trend, but not so well in a range. As usual, a lot depends on the smoothing factor and the filter length. I also find it helps to reduce the cutoff to 0.9/-0.9 and you might want to reduce it even more to get more signals.

Chapter 13 - Convolution

1. Convolution is just the ticket for identifying major reversals (it’s also the ticket to padding out trading books!)
2. In mathematics, convolution is an operation on two functions that produces a third function.

These are the diagrams that Ehlers uses to explain the concept. Do you get it?

“Since high correlation exists only at the market turning point, the convolution indicator is dependent on the lookback period used in the calculation. Assuming the two price segments have an equal time duration, the peak correlation occurs at half the lookback period of the indicator. For example, if a 13-bar period is used, the market peak would appear with a 7-bar delay. The same market peak would appear with a 19-bar delay if a 39-bar lookback period were used in the convolution computation.”


Good Correlation Occurs Only When the Folding Is Done at the Market Reversal Point


Interruptions in Market Trends Have High Correlations for Only Short Periods

Usually when something causes this much confusion for me, I arrogantly assume it is the fault of the person explaining it. Let me know if you disagree, and also please explain what these diagrams are meant to show.

“When the correlation is plotted as a conventional indicator, the high-correlation point will show up at a spike that is delayed half the lookback period from the current data bar. If the lookback period is short, the correlation spikes will be relatively current, but there will be a lot of them. If the lookback period is long, convolution basically reports ancient history, and the short-term interruptions will be eliminated. Consequently, the convolution display is dependent on the lookback period used in the computation.”


When it’s all plotted out, it looks like this.

Says Ehlers, “The convolution for approximately the last year on the Dollar General (symbol DG) is shown in Figure 13.4. By taking the direction of the trend into account, market tops are displayed as red plumes (signaling a reversal to the downside), and market bottoms are displayed as green plumes (signaling a reversal to the upside). The foreshortened plumes in January 2011 signal that the uptrend from the fall of 2010 is still in play. For the remainder of 2011, the five red plumes and the six green plumes absolutely nail the major market reversals. The reversal points are located at the bottom of the convolution subgraph, and the long plumes identify each as a major turning point. Since a finite amount of data is required to make the shortest calculation, convolution is moved four bars to the left to better correlate the indicator with the actual turning point. This technique is similar to that of a centered moving average.”

1. Convolution is synonymous with “folding.” The convolution indicator finds price reversal points by identifying the highest correlation of the data by folding it in the time dimension about the lookback period.
2. The major price reversals are identified by plumes pointing backward to the time of the price reversal.
3. Tops and bottoms can be identified by color using the price slope to assign the color values.

I agree the plume points appear to foreshadow the turning points but there are also some that foreshadow nothing. And the little plumes, apparently, are meant to be ignored? That means you don’t know if the reversal is real until the plume is much bigger, and later in time.
Attached for your amusement. Let me know if you think it’s great.

Chapter 14 - The Hilbert Transformer
This is another showy chapter where Ehlers tells us why the classic Hilbert transformer is no good for trading, but his modified version might work.

1. The classic Hilbert transformer cannot be used for trading because the FIR filter introduces a large amount of lag, and shortening the FIR filter introduces large amplitude variations across the pass band.
2. A modified Hilbert transformer can be created using a one-bar difference to establish phase quadrature and AGC to provide amplitude compensation.
3. The Hilbert transformer indicator provides predictive turning points for swing trading. These predictions can be wrong if a new trend is established rather than a new swing. (as with all the indicators!)
4. Using the Hilbert transformer to compute the dominant cycle is the price data is not advised.

We are already embarrassed by Ehlers' riches, why would we waste time with an inferior offering? OR IS IT?! Test and report back, please.

It’s early to the party sometimes, but in a trend it gives a lot of conflicting signals, just like the rest.

Thank you for this huge work of sharing.

Searching for scripts.

Chapter 15 - Indicator Transforms

Ehlers finishes off his offering of unique inventions with this chapter (I’m not counting Swami charts as they’re basically just a modified way of displaying a dashboard). That tells you that there might be something special about this one? Maybe not. I do recall being somewhat enamoured of the inverse Fisher transform in my early days.

1. The purpose of a transformer is to shape the indicator to aid interpretation and use of the indicator itself.
2. Transformers do not induce lag.
3. A Fisher transform of an indicator swinging between −1 and +1 with a nominal zero mean plots that indicator in terms of standard deviations with a nearly normal probability distribution.
4. An inverse Fisher transform acts as a soft limiter to remove extraneous wiggles in indicators have a nominal zero mean.
5. A cube transform compresses the smaller values of an indicator swinging between −1 and +1.

“The Inverse Fisher Transform of the Adaptive Stochastic Indicator Gives Clear and Unambiguous Indications of the Proper Buy and Sell Points” (oh, ambiguity! An omnipresent pain in the neck)


“The Cube Transform Clarifies Swinging Signals by Compressing the Smaller Amplitude Swings” (Wouldn’t lengthening the filter do the same thing?)


Adaptive RSI with Fisher Transform Clearly Identifies Major Turning Points (not so clear to me)

I'm including a few simple examples of the Fisher and inverse Fisher transforms. I can't say how closely they hew to Ehlers original code. It seems to be difficult to find anything that isn't modified with the swell original ideas of meddlers who likely didn't read the book. Some of those ideas are likely good, and the rest...?

Chapter 16 - Swami Charts

1. Ehlers begins by explaining that “technical indicators for trading are long on precision but short on accuracy.” (indeed)
2. The precision of indicators gives traders a false sense of security and obscures the fact that indicators are basically (just) displays of a statistical process.
3. Most traders don’t have a clue about the proper lookback settings for their indis
4. A precise indicator can therefore show you whatever you want to see (Mirror of Erised!)
5. The solution, which Ehlers has been peddling, is that you make your indicator adaptive to the measured cycle period!

Then he says “I describe another completely different perspective, which is to accept that indicators are inherently inaccurate and a better approach is to look at that indicator over a range of lookback periods and view the short-term movement in the context of the longer-term indictor results. In a sense, the indicator is used as fuzzy logic.”

Sputter! Sputter! Cough! Cough! “Inherently inaccurate?” “Fuzzy Logic??” What have we been doing this whole time, J.E.?

At first I thought his solution involved ‘zooming out’ and using a longer lookback period to govern a shorter one. However he’s really just talking about looking at the indicator output over several periods.

Ehlers: “SwamiCharts retain the core functionality of the technical indicators with which you're already familiar, while packing much more information into an easy-to-interpret heat map chart. With SwamiCharts, you now visualize each indicator over a range of lookback periods to reveal a better view of the indicator's truer meaning in context.”

I liken this to a dashboard indicator that shows you what the impression of each indicator is on various time frames. Here, Ehler’s invention allows a whole dashboard to be compressed into a subgraph window, which is pretty cool. This allows you to see how a trend might be ‘bubbling up’ or a rally/dip might be fading as it returns to the trend, without having to switch views of the current chart.


“Wow! Now you can see the entire market activity at a glance. The short-term downturns are shown in the context of caution to upside trends. When the market turns down the short-term red areas expand into the longer-term down market. Then, at the right-hand edge of the chart, you can see the short-term rising area expanding into the longer-term cautionary areas.”

So, handy, but not earth-shattering? Or ARE THEY??!
I haven't tested these; please let us know what you think.

If we summarize such a book. we have to ask us the right questions ?

Is it a breakthrough ?

What is the gain for me (for a trader ) ; significant or marginal ?

in which field ? Filters, Moving Averages, Cycles, trends, Timing Sinewaves (all these subjects) being interrelated

Is it applicable - on which platform ? how ? Easily ? or does It require a lot of work ? some money ? how much ?

Can these Ehlers tools (even only one ) improve significantly my trading results ?

In short ;: is it worth it ?

Simplistic Sinewaves

The second chart is very interesting and features something that I've seen for years while studying cycles. The sinusoid is curving a downward path in the first part of the cycle (the 'belly of the beast' as I call it) but the price action is 'truncated' or sideways, or possibly even 'up' in the middle portion. Hickson (following Hurst, or even a predecessor?) explained this as the natural result of smaller degree cycles within the larger whole.

However what I see is something more like a flattening, or possibly a bit of both. That's why I like to use triangles now, more than sinusoids. They seem to me like triangles with the peaks removed. edit: I could also have traced an upward pointing triangle for the second part of the sinusoid. I just got lazy.

A local high when we expect a cycle low. A result of combined cycles?

A downward-pointing triangle; followed by an upward pointing triangle, both without peaks. Sometimes, of course, they do have peaks. My little researches have tried to find a pattern for when to expect a truncation or when to expect a peak but there is likely no pattern.

Chapter 17 - Swing Trading Strategies

This final chapter is longer than the rest and at last the maestro commits to dipping his toe into the dull pragmatism of the topic of actually using his magic tools.

Swing Trading Strategies

1. Trading systems should be simple, but writing effective ones is not easy (and how!)
2. Simplicity is needed to avoid curve-fitting
3. The fewer the parameters, the less likely the strategy is customized to a data set
4. Entry and exit rules must be predictive

“Most rule-based strategies depend on indicators, setups, or patterns. Sadly, all of these depend on historical data and are better at documenting what has happened rather than predicting what will happen. Additionally, setups and patterns are often based on just a few observations and are therefore anecdotal or heuristic. The fact that setups or patterns do not have sufficient instances to be statistically significant is usually overlooked. Therefore, finding a predictive indicator is probably the most difficult part of developing a trading strategy.”

1. Optimization is anything but optimum and can lull you into a false sense of confidence in your prospective strategy.
2. Changing a parameter should only have a gentle effect so that it is effective over a wide range of settings; otherwise the strategy is guaranteed to fail.
3. At least 30 trades needed for statistical significance of one parameter.
4. “Remember, the name of the procedure is stop loss, and half that name is loss. Therefore, stop-loss rules should be used sparingly and not be embedded so that the stop loss is an integral part of the strategy. My procedure is to develop the strategy without the use of a stop-loss rule. After the main part of the strategy is satisfactory, I then examine the maximum adverse excursions encountered, and then insert a stop-loss rule that limits only the maximum losses without interfering much with the winning trades.”
5. Test in-sample then out-of-sample

Conventional Wisdom

1. trading strategy performance is most easily characterized by percent winning trades and profit factor.
2. trading the trend means being willing to accept a relatively low percentage of winning trades to achieve a relatively high profit factor.
3. “Holding trades through adversity usually means accepting large drawdowns. In my view, trend trading works because the general market is unbounded and has an upside bias due to economic growth and inflation.”
4. Predictive indicators are more applicable to short-term processes such as swing or momentum trading because, like the weather, predicting the future is “fragile and evanescent.”
5. Waiting for confirmation of laggy indicators causes traders to enter almost exactly when they should not.

Anticipating the Turning Point

1. Here is where Ehlers explains how to trade an oscillator, which I already went over.
   1. Use the ‘anticipation rule’ - don’t wait for the indicator to get to 80 before entering; enter when it leaves the 20 zone.

2. Trading conventionally is unprofitable, trading with anticipated points is profitable (or it was)

Sine Wave Uniqueness
Wherein Ehlers claims we can use a sine wave to create a forecasting signal. The problem is sine waves are periodic, price cycles much less so.

“Buy and Sell Signals Can Be Created by Crossovers with a Cosine Wave and the Cosine Wave Delayed by a Bar or Two”

“Some whipsaw trades can be eliminated by using the zero crossings of the sine wave as an entry signal only when confirmed by the crossover of the cosine wave with itself delayed by one bar.”

Safety Valve

1. If you’re anticipating a reversal and it doesn’t come you are exactly on the wrong side of the trade.
2. “You therefore need a rule that closes out a position when losing trades like this are experienced. You basically have two options to exit the trade: base the exit on price or on time in the trade. As a practical matter, I have not found setting a stop loss to be an effective method of exiting a losing trade in these conditions because the stop value has to be set so tight that one is whipsawed out of a trade that ultimately could turn out to be profitable.”
3. A “quick out” rule that basically says that if you are not profitable in the first bar or two of a trade, exit the trade and wait for a better opportunity.
4. “I rely on technology for trading and therefore do not rely on psychology much, even though psychology certain has a place in discretionary trading.”
5. “If you even think about hoping a trade will turn around and move in your favor, then exit the trade immediately.”

Exiting a trade
Trading a trending instrument, like equities, it’s better to smooth out your filter crosses to stay in the trade rather than exiting early. This gives up some profit when prices turn down, but it’s better to avoid whipsaws.

Stop Loss

1. A stop loss is best left only as a guard against extremely large losses.
2. 2-5% for stocks.

Evaluating a Trading Strategy

1. The most common method is to look at historical track record and the equity curve
2. The problem is equity curves can have considerable variability
3. Instead you can determine the % of wins, and apply the payout probability to each trade using a random number generator. This can provide realistic expectations for equity growth of the system.
4. Ehlers describes a process for producing this kind of ‘poor-man’s Monte Carlo analysis’ (my term) using an Excel spreadsheet. As usual there are elementary errors in applying formulae to the spreadsheet. I have yet to find a trading book where the authors have not inserted basic annoying mistakes (usually forgetting that they have a header row that cannot be used to concatenate data) into their spreadsheets. I hopefully have fixed them and have added a link to the sheet rather than explaining the faulty process.
   1. Ehlers says you can press F9 to re-compute the sheet, but Google sheets as far as I can tell doesn’t have that capability, so simply go to spreadsheet settings > Calculation and press ‘save’. All the random values should change.

5. Diversification reduces deviation in portfolio returns by the square root of two for each doubling. So you need to double the number of instruments each time you want to halve the deviation.
6. Finding a sufficient number of uncorrelated instruments is tricky

Monte Carlo Analysis (MCA) Evaluation

1. The proper professional way to evaluate a trading strategy
2. Compute the profit per day for each of the trades in history (assume 1 trade every 2 weeks for 10 years)
3. Place all the profits in a proverbial hat
4. Draw a profit per day from the hat, record its value, and put it back
5. Repeat this 260 times to create a randomized year’s worth of trading
6. Note this randomized annual profit in a bin (a relative, small profit range)
7. Repeat the annualized drawing 10,000 times and place the annualized profit into the associated bin
8. The results may surprise you - some years will have nothing but wins, others nothing but losses
9. The number of counts in each bin will have a an approximate normal (Gaussian) distribution
10. Ehlers mentions his website, which is of course, long gone.
11. Since MCA results have the shape of a bell curve, you can establish the expectation (average profit) of the trading strategy (using a z-score).
12. You can also estimate the standard deviation in profitability so you won’t be surprised when your ‘actual results don’t match your expectation’ (when you lose your lunch)
13. Does anyone know of a good free or cheap monte carlo simulator?

Stockspotter dot com

1. Long gone.
2. It seems like it was pretty cool though - free indis, swami charts, stock data, screeners, data-mining, cycles analysis, signals and tracking of those signals
3. It must have been valuable because it didn’t work out, a classic example of Clemmo’s Conjecture in action.

Key points

1. The roofing filter must be used with the indicators used to generate swing-trading signals to eliminate the distortions introduced by Spectral Dilation. That is, the indicators used to create the signals must have a zero mean.
2. Effective swing-trading signals must anticipate the price turning points to mitigate the lag introduced in computing the indicators. Using conventional oscillators, this is accomplished by creating a long trading signal when the indicator crosses under a lower threshold and creating a short trading signal when the indictor crosses over an upper threshold.
3. A sine wave is a unique primitive. It can be created from price data using a relatively narrow band-pass filter described in Chapter 5.
4. A leading long entry signal can be generated when a cosine wave crosses over itself delayed by a bar or two. A leading short entry signal can be generated when a cosine wave crosses under itself delayed by a bar or two.
5. Swing trades must have a safety valve exit because the trades are entered in anticipation of a price turning point. The safety valve can be based on either time in trade or a price breakout.
6. Swing-trade entry signals indicate position reversals for always-in-the-market strategies.
7. Exit signals when trading stocks to the long side are best accomplished using a SuperSmoother filter crossing under itself delayed by a few bars. This technique minimizes whipsaws and unwarranted early trade exits.
8. Stop-loss techniques should be used only to limit major losses.
9. Monte Carlo analysis is the best and most reliable way to assess trading strategy performance.

Evaluation:

1. As I said, the book proves (to me) Ehlers was probably the smartest technical analyst since Wilder, and probably a genius.
2. Unlike JM Hurst, he seems to understand (or is willing to admit) the limitations of his discoveries.
3. Indicators, he admits reluctantly, can only do so much. They are not very predictive.
4. The greatest value in the book is probably chapter 8 (the periodogram) and chapter 17 - some good advice about how to actually trade.
5. What I wonder: if you did everything ‘by-the-book’ and used the periodogram properly, the best Ehlers spectral-dilation-removing filter (Inverse Fisher transform?? Adaptive RSI? Adaptive Stochastic? Even Better Sinewave?), converted it for use as a swami chart, anticipated the signals, and used safety valves, would this make you a profitable trader? Probably only you can answer that, but I would guess you’d be starting off on a better foundation than most.
6. I have a tough time grading this book. On the one hand Ehlers does the usual leading down the primrose path with his ever-better indicators, then dumps us with the classic ‘it’s all inaccurate’, you're-on-your-own routine. On the other hand there’s a real attempt to use science to solve an intractable problem, and he almost succeeds, and that’s damn respectable.
   
   I suppose it is like PB tells us - with every book we must ask the right questions.
   1. Is it a breakthrough? Probably the first book that proposed using digital signal processing to model market time series was a breakthrough. This one? A bit of a re-roll.
   2. What do I gain? Some marginal cyclical understanding? Maybe not even that, but at least an understanding of their limitations.
   3. Can it be applied? I think so, and no need for expensive tools.
   4. Can these Ehlers tools significantly improve my trading? Well, that depends on how you trade.
      

7. In short, is it worth it? Of course. The quest for knowledge is what makes life worth living, as Plato taught us.
8. But is it practically worth it? Ummm..

Next book: This one got a new vote since the poll opened - Tape Reading and Market Tactics by Humphrey.

In fact Sinewaves are most often an AS IF Analysis tools with predictive possibilities ( Repetitive patterns)

This Chart REPRESENTS a Way of Reading Price Action.

a) we see Real Waves in Red
b) we can draw and observe an hypothetcal Sinewave fluctuating around the TREND .

In this case the Centered Moving Average 128 Time Units in Ocre . Here 6 Months as we are in Daily.

Note that the Wawes Areas under and above the Trend are more or less equivalent.

You can also observe on the Chart 3 others phenomena :

- the Return to the Mean ( the Centered Moving Average 128 (ocre))
- the 50 % Retracement
- the Cycle "Inversion"

Hurst specificity is NOT Cycle Analysis .

It is his Trading Methodology and his exceptional Trading Tools :

Envelopes,
Focal Points ,
Valid Trend Lines (VTL)
and FLD's (Future Line of Demarcation.

ho it's a bigger waste of time to read your posts so I would not have read it in the first place lol. I love how you are mad at ehlers for doing a better work than your gurus lol.
By the way, the translated SMA and the SMA have the same mathematical content. You cant do something new with a translation.


Ehlers' idea is really jsut applying digital signal processing to the bar chart, since after all, bars are just signal, and to go as far possible with that. So the main hypothesis is that the financial data may seem super noizy signal from the outside, but there may be cycles in it, and the quest is to find those cycles and filter some of them. It turns out the signals in finance are super random compared to the repetitive signals in DSP, like they say here
https://quant.stackexchange.com/ques...ing-in-trading
so it's intellectually challenging to find cycles in those data and there is no guarantee from the outset that it works.

So under the hypothesis that the financial data is really a repetitive signal, ie sinusoidal, you have this which is true
and you get all the usual patterns


The usual theory is about the Z transform and then getting a filter which filters what the engineer wants. Mathematically, All the SMA and EMA are really just filters. This is why he talks about generalized filters. With all the filtering diagrams, Ehlers claims all those SMA are really shitty filters in the end. Ehlers claim his supersmoother is the best he could come up with, at least for the public domain.. Engineers want to filter frequencies, ie cycles. So first you need to decompose the signal in frequencies. The first thing to try to decompose a repetitive signal into smaller sinusoidal waves is really the fourrier transform. It what all students learn And Ehelrs does just that. He claims that the stock fourrier transform is not valid for this and his discrete fourier transform is the way to go. Okay so be it. So to know what you want to filter you need to find out what frequencies there are first. This where the 10 and 48 come in.

Once he finds the main frequency to focus on, he tries to denoise the signal and he wants to plot a smooth curve of prices, which really would be what the non noisy price, ie the real price, or rather the price which would be the more meaningfully real.

Afterwards, since people are infatuated with indicators, he applies his non-noisy price to those and he says he has to compensate for spectral dilation. After all this the output is really smooth indicators, and they work pretty well. For instance his RSI (with a fixed period of 14, not his main period found mathematically) is really like the usual RSi but way smoother. The price to pay for this insane smoothness is a tiny lag of a few bars.

Then his idea of swarmy chart is pretty cool, but computationally it's horrendous lol.

At the end of the day, his work is nice and its main output is really super smooth curves, with not so much lag compared to the big increase of smoothing. But finding cycles is another story. I think it is better to define two main periods like Mel dickover is doing here, the dominant and then the trend cycles. The dominant cycle is the strongest cycle you have after you have chosen a timeframe.
https://sacredtraders.com/understand...in-e-dickover/
He gets stable cycles, contrary to the periodigram for metatrader. To be fair most of the cycles are around 20--30 bars for the dominant cycles and around 130 bars for the trend period, so there is no need to compute them all the time, and the computation is too intensive anyway. So for instance, the period of 14 for the RSi is roughly good.

His idea is to swing trade the dominant cycle, and never fight the trend cycle
THen he applies the dominant cycle


to the RSI


By the way the guy at emini-watch still uses the old version of the better sine wave
https://emini-watch.com/trading-indi...ert-sine-wave/