ΣL Cycle Summary

This robust ‘B’ class cycle in TSLA persists, delivering consistent performance across 14 iterations since May 2020, with an average wavelength of approximately 158 days at the current sample. The signal has yielded an impressive 716.31% over the sample period, a testament to it’s stability. Currently, the cycle is troughing, showing mild frequency modulation of +/-14 days, in line with a very stationary periodic feature. Following the recent fairly sideways down leg, the next bullish phase of this cycle is upon us with the upcoming peak anticipated toward the middle of April 2026.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Sell - TSLA October 21st, 2025
Entry: 21st October, 2025 @ 442.60
Exit: 30th January, 2025 @ 429.34
Gain: 3.00%

Time Frequency Analysis

Read more

ΣL Cycle Summary

This tremendous cycle in TSLA continues to bring in impressive gains on each subsequent leg that we feature on site, most notably to the upside this time. This particular up leg was a typical bullish continuation with early clues to the surge up when the previous down leg was relatively flat, a sure sign of power at underlying trend. Now we reach the next peak of this component and, at the time of writing, slightly early. There is some mild degree of modulation at a higher frequency creeping into the spectrogram (see below) so it would be wise to lock in the result of an excellent long here. The modulation in this case is reflected in the average wavelength moving from around 166 days, from the last report, to 156 days. The next low is due early in 2026, let’s keep tracking this superb feature and see how the down leg unfolds.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Early Buy - Tesla Inc 19th August 2025
Entry: 19th August 2025 @ 329.31
Exit: 21st October 2025 @ 445.41
Gain: 35.26%

Time Frequency Analysis

Read more

ΣL Cycle Summary

After we noted the peaking process of the nominal 40 week wave in the wider market a few weeks ago, it is now time to revisit our S&P 500 analysis, via the popular ETF, SPY. The S&P 500 exhibits this cycle exceptionally well and is the standout long term wave for many years in this index. Indeed this feature has been stable for well over 10 years but we need not take that many sample iterations to conclude this is a significant periodic feature.

The most recent trough, back in April of this year, kicked off a very sharp bullish retrace that eventually broke new highs. Due to the fact there is very little evidence in the frequency domain of powerful cycles at larger magnitudes (aside from the 3.5 year wave, which is hard down), it is tricky to say whether that low was also a low of larger magnitude. The amplitude of the move up suggests it but we must remember that is only one half of the cycle! Let’s see how the down leg progresses now and how much power the bears have to fight back into the next trough, due late 2025/early 2026.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Buy - S&P 500 (SPY) 1st April 2025
Entry: 1st April 2025 @ 560.97
Exit: 21st August 2025 @ 635.55
Gain: 13.29%

Time Frequency Analysis

Read more

ΣL Cycle Summary

After the fairly serene up leg from the trough earlier this year we have seen a period of consolidation for the most recent down leg of Elon’s secret signal. On the face of it this implies a larger feature is pushing up and we can expect further acceleration from the imminent trough. At the time of writing the phase of the component around 160 days is troughing but the frequency modulation is fairly wide (hence ‘B’ rating). Therefore we should be on the lookout for breaks to the upside over the next few weeks. I thought it wise to update subscribers of this possibility relatively early and the inherent margin of error (via FM), shown in detail below.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Early Sell - TSLA 28th May 2025
Entry: 28th May 2025 @ 356.89
Exit: 18th August 2025 @ 334.88
Gain: 6.17%

Time Frequency Analysis

Read more

Cycle Scanner Results

Markets scanned in this run (qualifying threshold at > 800 Sigma-L rank):

MMM | AXP | AMGN | AAPL | BA | CAT | CVX | CSCO | KO | DIS | DOW | GS | HD | HON | IBM | INTC | JNJ | JPM | MCD | MRK | MSFT | NKE | PG | CRM | TRV | UNH | VZ | V | WMT | NVDA

Time Frequency & Cycle Return

Here we show the full time frequency spectra for some of our top picks from the scanner results. We also display the return over time for each cycle via the gain per frequency metric.

Read more

ΣL Cycle Summary

It is that time again where we return to one of our favourite cycles in US stock markets (and indeed to some extent global stock markets), the 40 week nominal wave - in Hurst nomenclature. Although not the most coherent cycle when considered against all other types of financial market, this wave is still one of the more stationary cycles in stock markets of the last 20 years. Gaining dominance around 2016 (see SPY chart below) this cycle has retained power since then to a decent degree, yielding exceptional results between 2016-2020.

The most recent up leg has been remarkably linear in nature, yielding over 20% in both IWM (Russell 2000) and QQQ (Nasdaq) whilst SPY gained 14.57% over the period. Phase is now hard-up/peaking so we are a touch early here, however, with the larger 3.5 year wave now pushing hard down subscribers should be aware.

Amplitude has increased massively for the last two legs of this cycle, shown in the high pass filtered SPY chart below. Whether it is retained for the upcoming down leg into late this year remains to be seen.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Early Buy - ΣL US Stock Market Composite 13th March 2025
Entry: 13th March 2025
Exit: 22nd July 2025

For a composite analysis, each constituent’s respective gain over the period is displayed, in descending order. The average of the constituent gain is also shown.

Constituent Gain:
IWM (20.99%)
QQQ (20.97%)
SPY (14.57%)

Composite Average Gain:
18.84%

Time Frequency Analysis

Read more

ΣL Cycle Summary

An interesting feature of US Stock Markets over the last year or so has been the emergence of power around 180 days, suggesting a periodic feature at that bandwidth is becoming dominant in price action. Gaining amplitude in early 2023, this wave has been on our radar for some time, after making the requisite number of iterations to avoid being fooled by randomness.

The current peak that is forming at the time of writing may well be crucial if the larger behemoth wave around 3.5 years is now pushing hard down. The trough of that wave is due late 2026 and this latest move up from April 2025, powered by the 40 week nominal wave, may well be the last hurrah prior to the path down. Keen readers will also note the exemplary 40 week nominal wave is still phased as hard up at the time of writing. If we see an early price peak here that is a good sign the long and more powerful behemoth wave is indeed exerting more influence on price action.

Time Frequency Analysis

Read more

ΣL Cycle Summary

A serene up leg overall here in TSLA from this excellent signal around 160 days, largely stationary in our sample over the last 5 years or so and measured via 13 iterations. A period of consolidation marked the early stages of the move, such is the case in many price structures at cycle inflection points - it is rare to get a ‘V’ shaped reversal. Time did the rest, resulting in a ~ 50% retrace of the last down leg. At the time of writing we are near the next peak, perhaps slightly early, see the trade details below for more.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Buy - TSLA (Tesla Inc.) 10th March 2025
Entry: 10th March 2025 @ 222.15
Exit: 28th May 2025 @ 362.89
Gain: 63.35%

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white.

Before and After

Signal comparison between our last report and the current time, in chart format.

High-Pass Filtered Price

Our high-pass filter isolates the component of interest from underlying trend and presents buy and sell threshold envelopes (green and red). The envelopes are based upon the amplitude envelope of the bandpass filter +- 2 standard deviations. Breaches of either by high-passed price is a strong reversal action signal.

Current Signal Detail & Targets

Here we give more detail on the signal relative to speculative price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample (learn more).

Detected Signal Class: B - learn more
Average Wavelength: 162.1 Days
Completed Iterations: 13
Component Yield Over Sample: 667.79% - learn more

Phase: Peaking
FM: +- 13 Days
AM: 15.81658

Next Trough Range: 25th August - 8th September, 2025
Sigma-L Recommendation: Early Sell
Time Target: ~ 1st September, 2025

Current Signal Phase

This is ‘how far along’ the cycle is in it’s period at now time and is related to the predicted price action direction.

Current Signal Frequency Modulation (FM)

This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency usually modulates relatively slowly and over several iterations.

Current Signal Amplitude Modulation (AM)

This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.

ΣL Cycle Summary

We return to this remarkably stationary periodic feature in JPM as an analogy for the wider feature on US indices and many similar stocks around 80 days (notionally the Hurst 80 day nominal wave). Downgrading it slightly to a ‘B’ category due to a touch of recent modulation, this may well prove to be transient as we approach the next trough in late June. Amplitude has picked up quite a bit over the last few iterations, seen most clearly in the high-pass filtered price below. All in all an excellent cycle, highly stationary over 15+ samples since December 2021 and one to keep a very close eye on as a barometer. Watch for this feature in other stocks (AAPL, GS, V come to mind) and, of course, in the wider averages.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Buy - JP Morgan and Chase (JPM) 20th March 2025
Entry: 20th March 2025 @ 239.00
Exit: 14th May 2025 @ 265.64
Gain: 11.15%

Time Frequency Analysis

Read more

ΣL Cycle Summary

The move down from the peak of the 40 week nominal wave in stock markets has been quite apparent this time around, helping to retain it’s status as one of the few stationary features of global equity measures at the longer term scale. In SPY, we are moving into the latest trough imminently, with a small margin of error, measured at around one 30 day cycle wavelength, to contend with. This was covered in more depth in the recent post on US stock market indices and the same 40 week nominal wave.

This wave is common across most global indices and should always be on your radar as a cycle trader. It’s historical performance well worth the ‘A’ rating on Sigma-L.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Sell - S&P 500 (SPY) 14th November 2024
Entry: 14th November 2024 @ 593.35
Exit: 1st April 2025 @ 561.2
Gain: 5.42%

Time Frequency Analysis

Read more

ΣL Cycle Summary

This excellent signal, an example of the Hurst 80 day nominal wave, really increased in amplitude over the last couple of iterations. This is seen most clearly in the high pass filtered price below where a smooth rise in the amplitude envelope is clearly evident. Fortunately as the frequency modulation is minimal and therefore the signal relatively stationary, we can take advantage of good timing. The most recent peak a profitable example. This signal is also perhaps a good barometer for the wider market and the 80 day nominal wave; for it is almost entirely without power in the wider US stock market indices over the last year or two.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Sell - JP Morgan & Chase 14th February 2025
Entry: 14th February 2025 @ 276.59
Exit: 19th March 2025 @ 239.11
Gain: 13.55%

Time Frequency Analysis

Read more

ΣL Cycle Summary

It’s time once again to turn our attention to the one cycle in stock markets that has been relatively stationary for years (under ~ 500 days), the 40 week nominal wave. As mentioned in the last report, this wave was identified by JM Hurst some decades ago and it is fantastic to see it represented clearly in the spectra to this day. While other components of his nominal model have proved to be somewhat spurious, this cycle is evidently stable over time, at wavelengths under 500 days.

That said, we have still seen some attenuation of this wave over the last few years. The most stationary period in the sample since 2014 was an excellent series of peaks and troughs between 2016-2020. Subsequent to that power has diminished somewhat as the larger component (around 3.5 years wavelength) pushed price around, reducing the ability to detect periodicity, even with our sensitive tools. That longer cycle may well have peaked, see the report linked here.

We now approach the troughing zone for this cycle. I have included a phasing of the 40 day nominal wave, one of the clearer shorter terms components in US stock markets. It is likely that the 40 week nominal wave trough will co-incide with a trough of this shorter wave, either imminently or mid April. Both are well within the margin of error for the 40 week wave’s frequency modulation from the sample.

Within our composite IWM (Russell 2000) performed the best, yielding 10.5% over the trade period.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Early Sell - ΣL US Stock Market Composite 14th October 2024
Entry: 14th October 2024
Exit: 13th March 2025

For a composite analysis, each constituent’s respective gain over the period is displayed, in descending order. The average of the constituent gain is also shown.

Constituent Gain:
IWM (10.50%)
QQQ (5.75%)
SPY (5.27%)
DIA (4.30%)

Composite Average Gain:
6.45%

Time Frequency Analysis

Read more

ΣL Cycle Summary

Here we have an excellent and recently high amplitude cycle in one of the world’s most famous companies, Tesla. Beautifully stationary in this sample since May 2020 over 11 iterations and due to trough imminently. Bulls will hope the volatility (amplitude) that helped drive the move up from the most recent trough in October 2024 is retained for this iteration too.

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white.

High-Pass Filtered Price

Our high-pass filter isolates the component of interest from underlying trend and presents buy and sell threshold envelopes (green and red). The envelopes are based upon the amplitude envelope of the bandpass filter +- 2 standard deviations. Breaches of either by high-passed price is a strong reversal action signal.

Current Signal Detail & Targets

Here we give more detail on the signal relative to speculative price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample (learn more).

Detected Signal Class: B - learn more
Average Wavelength: 162.12 Days
Completed Iterations: 11
Component Yield Over Sample: 499.78% - learn more

Phase: Troughing
FM: +- 24 Days
AM: 10.63332

Next Peak Range: 29th May - 21st June, 2024
Sigma-L Recommendation: Buy
Time Target: ~ 9th June, 2025

Current Signal Phase

This is ‘how far along’ the cycle is in it’s period at now time and is related to the predicted price action direction.

Current Signal Frequency Modulation (FM)

This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency usually modulates relatively slowly and over several iterations.

Current Signal Amplitude Modulation (AM)

This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.

ΣL Cycle Summary

A sublime signal here in JP Morgan & Chase (JPM), punctuating the uptrend since 2021 and now peaking according to the current phasing. There is little more to add aside from saying this is a cycle one should keep an eye on as a measure for the wider financial sector, given it’s quality. It is also reflected in more broad measures, such as the XLF ETF. A test of the lows around mid December 2024 would be bearish for underlying trend.

Time Frequency Analysis

Read more

ΣL Cycle Summary

This is the 40 week nominal wave as described recently in the S&P 500 (SPY) but features a good deal more modulation in the tech based index. For that reason the signal is rated a C category here, moderated with the knowledge that, regardless of the lower rating, this component is correlated across indices worldwide. The reason for the increased modulation is a larger influence from higher frequency components over the last few years. In simple terms it has been more volatile over shorter periods. This can be seen below with a powerful periodic feature around 115 days shining through and competing with the much longer (theoretically more powerful due to 1/f) lower frequency components.

The 40 week nominal wave is now peaking, the next trough estimates are described in more detail in the signal target & detail section below.

Time Frequency Analysis

Read more

ΣL Cycle Summary

This excellent longer term wave, familiar to regular readers and subscribers, is notionally the Hurst 40 week nominal wave. Whilst the approach we now take is one of objective evidence for periodicity in markets, via a time frequency analysis, one of the original pioneers of numerical/spectral analysis was JM Hurst. The fact this component is so very apparent long after he established his nominal model in the 1960’s and 1970’s is a wonderful tribute. We recently published a report for this wave in our US Stock Market composite but I thought it was worth also sharing this specific analysis for SPY as it is particularly clear.

Superbly stationary in the period 2016-2020, this wave has lost some power and price influence since then but is still front and center at a bandwidth below 400 days, in most stock markets. The S&P 500 (via SPY here) is a good example of this component, being very well spectrally separated. Indeed in the area below this wave (300-500 days) there is almost a complete vacuum of power, a telling sign of consistency over time for the prominent wavelength.

Subscribers should also be aware of the possibility that this incoming peak is also the peak of the much longer cycle around 3.5 years, published on Sigma-L back in September this year.

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white.

High-Pass Filtered Price

Our high-pass filter isolates the component of interest from underlying trend and presents buy and sell threshold envelopes (green and red). The envelopes are based upon the amplitude envelope of the bandpass filter +- 2 standard deviations. Breaches of either by high-passed price is a strong reversal action signal.

Current Signal Detail & Targets

Here we give more detail on the signal relative to speculative price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample (learn more).

Detected Signal Class: A - learn more
Average Wavelength: 254.05 Days (36.29 weeks)
Completed Iterations: 14
Component Yield Over Sample: 130.73% (SPY) - learn more

Phase: Peaking / Peaked
FM: +- 25 Days
AM: 4.61053 (SPY)
Next Trough Range: 19th March - 13th April, 2025
Next Peak Range: 23rd July - 23rd August, 2025

Sigma-L Recommendation: Sell
Time Target: ~ 1st April, 2025

Current Signal Phase

This is ‘how far along’ the cycle is in it’s period at now time and is related to the predicted price action direction.

Current Signal Frequency Modulation (FM)

This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency usually modulates relatively slowly and over several iterations.

Current Signal Amplitude Modulation (AM)

This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.

ΣL Cycle Summary

This longer term cycle, sampled here since 2014, is notionally the Hurst 40 week nominal wave, discovered by Hurst via early spectral analysis (FFT) in the 1960’s. Here we take a sample via popular US stock market ETFs, which very accurately reflect any periodic features within the wider market.

Although superbly stationary and well isolated in the period 2015-2020, subsequently there has been a emergent (2020 - now) area of power at higher frequencies. This has influenced price action correlation, resulting in an overall ‘C’ rating across the sample using our ranking criteria. Undoubtedly if this report had been written around the time of December 2018, for example, the spectra, and this component, would have drawn at least a ‘B’ rating. We attempt to demonstrate the difference below.

In addition, thanks to X (known back then as Twitter!), we can take a look at the phasing at that point with a Sentient Trader chart, used before developing the current, more robust software. We have also included a phasing of the 40 week nominal wave (for the FTSE 100) from a very early version of software development, on metatrader 4. This used a static FFT as a crude insight into the periodic features of price action.

At nowtime, this component is phased as peaking with the next trough iteration due late in the 1st quarter 2025.

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white.

Current Signal Detail & Targets

Here we give more detail on the signal relative to speculative price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample (learn more).

Detected Signal Class: C - learn more
Average Wavelength: 254.25 Days (36.32 Weeks)
Completed Iterations: 15

Phase: Peaking / Peaked
FM: +- 53 Days
Next Trough Range: 16th February - 11th April, 2025
Next Peak Range: 21st June - 14th August, 2025

Sigma-L Recommendation: Sell
Time Target: ~ 15th March, 2025

Current Signal Phase

This is ‘how far along’ the cycle is in it’s period at now time and is related to the predicted price action direction.

Current Signal Frequency Modulation (FM)

This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency usually modulates relatively slowly and over several iterations.

Current Signal Amplitude Modulation (AM)

This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.

ΣL Cycle Summary

Power continued to seep away from the nominal 80 day wave in stockmarkets worldwide, modulating very obviously to the shorter 40 day nominal wave, most notably in August. It is this wave we look at here and it has shown some quite outstanding periodicity from our sample since mid 2023. A clear spectral spacing in the area of interest within the frequency domain (shown below in both daily and hourly formats) features a large falloff around the power spike, centred at 36 days average wavelength. This is a sublime feature over many years and is a central reason for the signal receiving an ongoing ‘A’ category rating. The current phase is classed as peaking and it will be fascinating to see whether power is retained once again in the down leg. If it is, we can expect a similar price move range as the recent up leg from the trough earlier in September.

Time Frequency Analysis

Read more

ΣL Cycle Summary

This report is interesting in the fact that the 80 day nominal wave has continued to lose power to the shorter component, namely the 40 day nominal wave, through August and September, as noted in our last report. Indeed so much so that the recent price low in early September was likely the 80 day nominal low even though it did not breach the previous 40 day nominal low. The shorter component commanding price action with absolute authority it seems and providing the larger price swings. The scenario where the price low is not the cycle low does happen and illustrates why an alternative approach to simply counting all price lows/peaks as cycle lows/peaks is flawed. Although generally power is contained in a 1/f structure across the spectra of financial markets there are periods of transitory shifts in power distribution (via amplitude modulation), this being one example. It can be misleading if one can’t see where the modulation is coming from.

As is shown below, the power of the 80 day nominal wave is now heavily suppressed. This means the phase is also uncertain, rendering peak and trough date extrapolation highly variable. This uncertainty is reflected in the signal detail section. This one will be interesting to revisit in mid October.

Time Frequency Analysis

Read more

ΣL Cycle Summary

This superbly stable, long term cycle in the S&P 500 (and in others, Russell 2000 and DJIA, shown below) is testament to the non random nature of financial markets to some degree. We are excited to finally report on it as the peak approaches, although this report is somewhat early for the peak, subscribers should take note. It is quite incredible to see such a long term signal stand out in the bandwidth from around 2000 - 200 days wavelength and retain such clarity with relatively low frequency modulation (it’s duration varies very little over time). This is our archetypal ‘A’ category signal, with clear spectral spacing from surrounding frequencies. The implication being that there is no power (to drive price action) comparable to it in any significant statistical sense, anywhere near it.

As far as Hurst Cycles nomenclature is concerned, the common assumption is that there is a long term periodic component running at around 54 months, at least according to the nominal model. It was the discovery of the below wave several years ago, whilst applying an early version of our wavelet convolution, that prompted us to abandon that model in favour of a more evidenced and data driven approach, making conclusions from what we see. The stationarity of the wave, at around 1275 days from this particular sample, or ~ 41 months, is the only periodic feature of note over the last 30 years in this bandwidth range.

Readers should note that this periodic component is present in almost all global stock markets to a greater or lesser degree. US examples shown below.

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white.

High-Pass Filtered Price

Our high-pass filter isolates the component of interest from underlying trend and presents buy and sell threshold envelopes (green and red). The envelopes are based upon the amplitude envelope of the bandpass filter +- 2 standard deviations. Breaches of either by high-passed price is a strong reversal action signal.

Current Signal Detail & Targets

Here we give more detail on the signal relative to speculative price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample (learn more).

Detected Signal Class: A - learn more
Average Wavelength: 1274.54 Days (~ 3.49 Years)
Completed Iterations: 9
Component Yield Over Sample: 262.18% - learn more

Phase: Peaking
FM: +- 86 Days
AM: 173.01661
Next Trough Range: September 1st, 2026 - November 26th, 2026
Next Peak Range: December 5th, 2024 - February 9th, 2025

Sigma-L Recommendation: Early Sell
Time Target: ~ 14th October, 2026

Current Signal Phase

This is ‘how far along’ the cycle is in it’s period at now time and is related to the predicted price action direction.

Current Signal Frequency Modulation (FM)

This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency usually modulates relatively slowly and over several iterations.

Current Signal Amplitude Modulation (AM)

This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.