ΣL Cycle Summary

After the Easter break we return to Bitcoin and what has been a subdued up leg of the lovely 80 day cycle during March. This has been somewhat surprising given the 40 week feature is also now powering up but there are some analogies in the past for this in Bitcoin, notably mid 2024. Amplitude of a cycle (or the volatility / price move amount per leg) is much harder to predict than timing, although we can possibly infer price moves nearer nowtime from the most recent leg. Focusing on what we do know about a financial market’s spectra is optimal (frequency tends to modulates slowly), let price take care of itself, so to speak.

Bulls will be hoping now the sideways price action continues or begins to shape mildly upward, indicating the 40 week is supporting with increased power as the 80 day pushes down simultaneously.

Mid May is the next inflection point (trough) for the 80 day cycle and if price does indeed remain sideways we could see an explosive move up at that point. This would take us just past mid 2026, as the two main periodic features align in phase once 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 - Bitcoin 18th February 2026
Entry: 18th February 2026 @ 66419.79
Exit: 7th April 2026 @ 68650.37
Gain: 3.36%

Time Frequency Analysis

Read more

ΣL Cycle Summary

Those who followed the time prediction from the January update will be well satisfied — the crunchpoint flagged for mid to late February has arrived precisely on cue, with the 80 day cycle now in its trough phase and Bitcoin having shed a substantial ~25% from the peak near $90,000. The confluence of the 80 day and the larger 280 day cycle exerting their combined downside influence has played out much as anticipated, and the short trade closed out with an excellent result.

The trough is now upon us, with the frequency modulation running at +/- 5 days from the current position — a relatively tight window that lends reasonable confidence to the timing. With 17 completed iterations since June 2022 at an average wavelength of 83 days, this remains one of the more dependable cyclical features in the cryptocurrency space, and the upgraded ‘A’ class signal classification reflects that robustness. The cumulative component yield over the sample period stands at an impressive 387.71%, a testament to the consistency of this feature over time.

Looking ahead, the next peak range is projected between the 30th March and 8th April 2026, with the central time target falling around the 3rd of April. Bulls will note that this gives a window of approximately six weeks for the up leg to develop — and with the powerful 280 day cycle now set to shift from headwind to tailwind, the conditions for a more meaningful advance are considerably more favourable than they were entering the January trough.

Charts below show a variety of phasings over and above the ~ 80 day feature. Included are some screenshots of our new MT5 EA, due to be released soon. For the latest update on that please take a look at the article here.

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 - Bitcoin 10th January 2026
Entry: 10th January 2026 @ 90385.54
Exit: 18th February 2026 @ 67349.26
Gain: 25.49%

Time Frequency Analysis

Read more

Extrapolation

One of the most requested and often well discussed features is now live. Sigma-MT uses a sinusoidal tuned Kalman filter to decompose the bandpass-filtered cycle into trend and oscillatory components, then projects forward. The extrapolation respects the detected wavelength and current phase, producing a natural continuation rather than a naive repetition. A short cross-fade at the boundary prevents discontinuities where historical data meets the forecast.

Each enabled timeframe — short, medium, and long-term — extrapolates independently, with the projection length configurable in terms of forward cycles.

Inflection Points and Uncertainty

Building on extrapolation, the system identifies upcoming inflection points — peaks and troughs in the projected cycle — and marks them on the chart with estimated timing. The information panel displays a countdown to the next expected inflection alongside phase status.

Since any projection carries uncertainty, the inflection markers include a time window rather than a single bar, giving a realistic range for when the turn is expected. UTC and broker time display are both supported.

Envelopes

Amplitude envelopes now wrap each cycle component, calibrated so that approximately 95% of price action falls within the bands. The envelope width is driven by the instantaneous magnitude from the wavelet transform rather than a fixed offset, so the bands widen and narrow as cycle strength fluctuates. These extend through the extrapolation region, providing a projected price range alongside the cycle forecast. This concept, first espoused by JM Hurst in ‘Profit Magic for Stock Transaction Timing’, is a useful way to visualise the volatility in an instrument defined by the cycle feature driving it

Trade Boxes

Trade zones highlight regions around upcoming inflection points where the cycle is expected to reverse. Each box spans the uncertainty window of the inflection and uses the envelope amplitude to set price bounds. Red boxes mark projected peaks, green boxes mark projected troughs. These provide a quick visual for where the cycle analysis suggests actionable zones may develop.

Yield Mode

Pressing Y activates yield mode, which walks through historical cycle inflections and calculates what a systematic approach of buying troughs and selling peaks (and vice versa) would have produced over the analysis window. The chart displays individual trade legs with percentage gains, a running total, win rate and expectancy. Each enabled timeframe calculates its own yield independently, letting you compare how different cycle horizons have performed on the same instrument.

Composite Instruments

A new cross-instrument analysis mode examines multiple related markets simultaneously. Define a basket of instruments — for example the major USD pairs — and Sigma-MT z-score normalises each price series independently, then averages them in the time domain to produce a single composite series. This averaged series is then fed through the standard wavelet convolution pipeline — the same CFAR detection, bandpass filtering, and phase analysis that runs on any individual chart. By convolving the average rather than averaging individual convolutions, the process identifies periodicity that is genuinely shared across the basket rather than artefacts of summing unrelated cycles.

The composite average line overlays the primary chart, rescaled back into the chart instrument’s price space.

Once the dominant cycle is detected from the composite, Sigma-MT calculates a Cycle Amplitude Ratio (CAR) for each instrument in the basket. CAR measures how much of an instrument's actual price movement falls within the detected cycle band, expressed as bandpass amplitude relative to mean price. The instruments are then ranked by CAR in a volatility ranking displayed alongside the composite line. Higher CAR means a larger proportion of that instrument's price action is cyclical at the shared frequency — making it the better candidate to trade if the wavelength range around the composite cycle is your target signal.

Cycle Band Lock and Manual Selection

The detected dominant frequency band can now be locked, preventing it from jumping to any transient higher frequency power as time progresses. A lock indicator in the info panel shows the current state, toggled by clicking the box or pressing 0.

Beyond locking the auto-detected band, you can now manually define your own frequency range by shift-clicking twice on the spectrogram — once for each boundary. A dashed marker line provides visual feedback after the first click. The selection auto-locks immediately, and an Auto/User indicator next to the lock box shows whether the current band was detected algorithmically or chosen manually. A minimum bandwidth of 5% of total frequencies is enforced to ensure meaningful results

Expanded Keyboard Interface

The beta introduces a comprehensive keyboard-driven workflow. A dedicated shortcuts panel (K key) documents everything, organised into sections:

Interface: F flips the spectrogram position, G toggles spectrogram visibility, P toggles the info panel, < > adjusts panel width, C takes a screenshot.

Analysis Control: W/S adjusts sample size, A/D shifts through history, Q/E changes the increment, L/O/H/I adjusts frequency bounds, Ctrl+Click centres on a bar, and shift+click selects a custom band.

Cycle Visibility: 1/2/3 toggle short/medium/long-term cycles, 0 toggles band lock, X toggles envelopes, B toggles trade boxes.

Modes: Y activates yield mode.

Score Threshold Filtering

A configurable score threshold now filters longer-term cycles, suppressing medium and long-term overlays when their detection score falls below a chosen level (700, 800, or 900). This keeps the chart clean when only the short-term cycle has strong evidence, avoiding visual clutter from marginal detections on higher timeframes.

What’s Next

The beta is currently with founding members for testing. As we work toward a stable release, the focus is on refinement — edge cases, performance, and ensuring everything behaves predictably across instruments and timeframes. Sigma-MT will be listed on the MetaTrader market at release, and for future founding members of Sigma-L.

More to follow.

David

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

Since the initial alpha announcement, development on Sigma-MT, a Meta-Trader 5 expert advisor, has progressed steadily and is nearing beta. This update covers some improvements to the underlying time-frequency analysis, visual refinements, and how the tool integrates with the recently announced scanner.

Time-Frequency Engine Updates

The multi-timeframe analysis system performs independent wavelet convolutions for each enabled timeframe - short, medium, and long-term. Each process transforms the price series into the frequency domain, applies a rapid convolution process and returns a time-frequency power matrix showing how spectral energy evolves across the analysis window.

When analysing higher timeframes, the system retrieves the appropriate bar data, performs the full convolution at that resolution, then interpolates the resulting bandpass signal back to the chart timeframe for overlay. This interpolation maps the higher timeframe’s filtered output onto the short-term bar structure, accounting for the timeframe ratio. A cycle detected on H4 while viewing an M15 chart will display correctly aligned with the underlying price bars.

Dominant cycle detection begins by using CFAR (Constant False Alarm Rate) as the default method - the same adaptive thresholding technique used in radar systems. Rather than applying a fixed SNR threshold across all frequencies, CFAR calculates a local threshold for each frequency bin based on the surrounding spectral energy. Reference cells on either side of each bin establish the local noise floor, with guard cells preventing the signal itself from contaminating the estimate. The detection threshold adapts to the spectral shape, maintaining consistent false alarm probability regardless of whether you’re examining a flat spectrum or one with significant slope.

The ranking score combines multiple metrics: peak prominence above the CFAR threshold, spectral isolation from neighbouring frequencies, amplitude stability across the recency window, and consistency of the instantaneous frequency estimate. A high score indicates a cycle that stands clearly above the noise, maintains stable characteristics, and persists through the analysis period rather than appearing transiently.

Wavelength display throughout the interface now uses adaptive unit conversion. The base unit is determined by your chart timeframe - minutes for M1-M30, hours for H1-H12, days for daily charts. Values then convert upward when they exceed natural thresholds: minutes to hours beyond 120, hours to days beyond 24, days to weeks beyond 100. This ensures the Y-axis labels, information panel, and cycle readouts all express wavelengths in immediately meaningful terms.

Workflow with Sister Scanner App

Sigma-MT and the Sigma-MT Scanner serve different analytical needs within the same workflow.

The scanner processes your entire market watch, applying the same wavelet convolution engine across every instrument and ranking results by cycle strength. It answers the question of where to focus attention. Which markets are exhibiting periodicity now?

Sigma-MT provides the detailed examination. The full spectrogram reveals how cycle strength evolves through time, the bandpass filter isolates the dominant component and the information panel displays phase status, wavelength, and detection score. A cycle flagged by the scanner will appear with identical characteristics when examined in Sigma-MT - the underlying detection will be consistent across both tools.

Keyboard Configuration

So far we have added some very useful keyboard shortcuts to help the user navigate the spectra in an analysis.

Analysis Window:

• A / D - Shift analysis left/right through price history

• W / S - Increase/decrease sample size (N)

• Q / E - Decrease/increase increment value

• Ctrl + Click - Centre analysis on clicked bar

Frequency Bounds:

• L / O - Decrease/increase lowest frequency of analysis

• I / H - Increase/decrease highest frequency of analysis

Display:

• F - Flip spectrogram/bandpass to top or bottom of chart

• P - Toggle information panel

• Left click on spectrogram - show spectral summation and detection threshold at the clicked timepoint

• < / > - Increase/decrease panel width

Cycles:

• 1 / 2 / 3 - Toggle short/medium/long-term cycle visibility

• 4 - Toggle composite cycle overlay
  

Availability

Sigma-MT remains available to a small group of founding members for testing and I thank them for their help. As we approach a stable release, it will also be listed on the Meta-Trader market for all, in addition to being available for all new founding members of Sigma-L at release.

More updates to follow and exciting features to add, not least extrapolation, which everyone seems to love!

David

The scanner applies the same robust wavelet convolution engine that powers Sigma-MT across every instrument in your market watch, simultaneously analysing multiple timeframes and ranking results by cycle strength. In seconds, you have a prioritised list of instruments exhibiting the most statistically significant cyclical behaviour.

Under the Hood: Time-Frequency

Under the hood, the scanner leverages the same frequency-domain convolution that makes Sigma-MT so fast in MT5. Each instrument undergoes a full wavelet transform, with automatic cycle detection using either a simple SNR (Signal-to-Noise Ratio) and filter or CFAR (Constant False Alarm Rate) algorithms - the same detection methods used in radar systems for picking signals out of noise.

The cycle ranking score then combines multiple factors: peak prominence above the noise floor, spectral isolation, amplitude stability, frequency consistency, and persistence across the analysis window. To be clear this isn’t just finding any cycle - it’s finding cycles that exhibit the characteristics of genuine periodic phenomena rather than random fluctuations.

A scan of several hundred instruments across multiple timeframes completes in seconds.

Intelligent Phase Grouping

This is where the scanner becomes more than just a ranking tool. When analysing multiple timeframes, the scanner can automatically identify phase confluence - instruments showing aligned cycle phases across different time horizons.

When the same symbol exhibits similar phase, these groups lock to the top of the results, immediately drawing your attention to potential multi-timeframe confluence setups.

However, matching phases alone isn’t enough. To ensure meaningful alignment rather than the same cycle detected at different resolutions, the scanner validates that each higher timeframe shows a wavelength greater than at least 1.5 times the previous timeframes’ detected cycle. This filters for genuine nested cycle structures - the kind of fractal patterns that Hurst and others identified as characteristic of market behaviour.

Multi-Timeframe Analysis

The scanner has capacity for up to five timeframes running at simultaneous analysis. The scanner will evaluate every market watch instrument against each timeframe, giving you a comprehensive view of cyclical activity from intraday through to longer-term structures, if required.

Results display the detected wavelength (automatically formatted in minutes, hours, days, or weeks), the cycle rank score, timeframe, and current phase status. Click any row to instantly open a chart with that symbol and timeframe - ready for deeper analysis with the main Sigma-MT EA.

Filtering & Configuration

Focus your attention with built-in filtering (more features to come):

• Minimum Rank Threshold - Hide weak cycles below a specified score

• Minimum Wavelength - Filter out very short cycles that may represent noise rather than tradeable features

• Recency Bias - Weight the analysis toward recent price action

All active parameters display clearly at the top of the interface, so you always know exactly what you’re looking at:

Bars: 500 | Frequency Range: 5-40 | Detection: CFAR | Recency Bias: 50% | Analysis on Median Price | Min Wavelength: 30 min | Timeframes: M1, M15, H1

The Workflow

The scanner and Sigma-MT EA are designed to work together although one can use the scanner standalone if you have a system already setup to identify periodicities in markets.

1. Scan - Run the Scanner to identify instruments with strong cyclical behaviour. Set the scan to loop continuously after completion, manually by pressing ‘R’ or at set intervals.

2. Filter - Use phase grouping and rank thresholds to surface the most interesting opportunities

3. Click - Open a chart directly from the scanner results

4. Analyse - Apply Sigma-MT for detailed time-frequency analysis, phase projection, extrapolation and cycle visualisation. Automatic trading will also be in place further along the development process.

This workflow transforms cycle analysis from a manual, instrument-by-instrument process into a systematic scan of the entire market.

The scanner is currently in development alongside the main Sigma-MT EA and will be available to new founding members on Sigma-L in addition to being directly available on the MQL store. I believe this combination of tools - broad market scanning paired with deep individual analysis - represents something genuinely new for retail cycle analysts. I am excited to finally be able to share the insight I have been using for the past few years with others.

More updates to follow as development progresses. Thank you for your continued support.

David

So many people have asked me over the last few years whether they can use my software and I am always flattered by this. I developed it initially for myself to examine the claims by Hurst and others of the existence of periodic features in financial markets. I never really intended it to be used by others although we successfully built a multi instrument live scanner which was somewhat useful! Since then I am grateful to have shared many analyses with subscribers here and on X for those who are interested in this rather niche but fascinating area.

I am pleased to say, therefore, over the holiday period and just before, I began development work on porting over the familiar time frequency analysis readers have seen over many years on Sigma-L, to Metatrader’s MQL language. The main question was one of speed. I wanted to ensure that this new version would be fast enough to use intraday (it updates on every new bar) and also flexible enough to perform the many computations required for a robust time frequency analysis. The underlying process is already highly optimised, performing the calculations and wavelet formation all in the frequency domain.

Fortunately, with MQL’s C based language the vectorisation present in the python/numpy version was fairly easily transferred and has produced excellent results. A convolution over 1000 points and 100 frequencies takes less than a quarter of a second.

Enhancements

Over the last few years I have collated a large list of enhancements I want to bring to this kind of market analysis, both from a user experience point of view and from a signal processing point of view. Some of the expectations for features on this expert advisor, as we move toward release, will be (non exhaustive):

• Ability to shift analysis anywhere on the chart (currently live in alpha 1.0)

• Ability to quickly move up and down the frequency spectra to inspect any features of interest (currently live in alpha 1.0)

• Automatic intraday updating (currently live in alpha 1.0, updates on each new bar)

• Time frequency analysis on return series

• Multi length analysis and composite lines, combining multiple cycles of influence and true, numerically evidenced based compositing / extrapolation

• Auto detection at all timeframes

• Tuned Kalman filter extrapolation

• Composite analysis of many instruments for phase correlation

• Aesthetic configuration (colours, spectrogram etc)

• High pass filtering at the touch of a button

• Future time phase estimation for all detected features

• Social media sharing

Currently the alpha is available for testing to founding members only but as we draw closer to something I feel is ready, we will likely list it on the Metatrader shop and also make it available to future founding members here. The exact format remains to be decided.

I can’t wait to see lots of very cool cycle charts coming up on my X feed over 2026 as you guys get your hands on one of the most powerful analysis techniques out there!

Do continue to watch this space for updates, thank you all for your continued support.

David

ΣL Cycle Summary

Happy new year to all!

In this much anticipated update we take a look, once again, at one of the few markets providing cyclical dominance at the moment, the ubiquitous 80 day cycle in Bitcoin and the wider spectra going forwards.

The up leg from late November was a damp squib of a move, suggesting the now more apparent ~ 280 day cycle (shown below) is still exerting downside influence. This much larger wave is considerably more powerful than the 80 day feature, such is the nature of power distribution in financial markets. Over the course of the last few years it has featured a rather wide and therefore unpredictable, practically speaking, modulation. For that reason it has not featured on Sigma-L before although I have mentioned it briefly on X. That modulation has diminished somewhat recently and even more so when the addition of other liquid cryptocurrencies is analysed in a composite, also shown below.

The crunchpoint appears to be ahead of us in mid - late February with troughs of the 80 day and 280 day broadly aligning in phase. That said, the modulation is still quite wide in the larger feature so it may well be a case of sideways until then, which is even better for bulls. The 30 day carries on regardless, making excellent undulations at the lower resolution and is easily discerned by our time frequency method, see below. Useful for traders with a shorter time horizon I have no doubt.

In summary, not long to wait for the more bullish crypto enthusiasts with the powerful 280 day cycle set to provide an excellent guide in 2026. Alongside that the 80 day looks to be maintaining it’s power, providing even more granularity to the swings.

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 - Bitcoin 17th November 2025
Entry: 17th November 2025 @ 92100.60
Exit: 10th December 2025 @ 90646.30
Gain: - 1.58%

Time Frequency Analysis

Read more

ΣL Cycle Summary

In this sample of Gold (XAUUSD) over the last 12 years we reveal a periodic feature that has been present throughout, exhibiting excellent spectral spacing within a bandwidth spanning ~ 1000 to 100 days. Sporting a wavelength around 500 days (or 16 months) this feature has maintained it’s power even through the tremendous and linear uptrend since early 2024. The phase is currently peaking with the next trough due late 2026. Indeed this feature is also clearly present in PHYS and GDX (shown below via composite), something that may be obvious but is not always the case at the shorter wavelengths.

The highpass filtered series below also reveals the spectacular amplitude increase passed through to the cycle around 500 days from underlying trend. A breach of the red standard deviation line is a high probability reversal signal and indicative of a peak for this wave.

Time Frequency Analysis

Read more

ΣL Cycle Summary

Much gnashing of teeth and surprised sentiment has been doing the rounds on X recently in the crypto space, many caught unaware by the powerful nature of the 80 day cycle in this recent downturn.

So, we return to this feature, slightly early, to update the phase and look to the next stage. The other cycle of interest in Bitcoin below 100 days is the ~ 30 day cycle, which is currently troughing. This is the reason, mainly, for the earlier update in the 80 day cycle phase as we may see yet another battle here between these two.

The two main cyclic components are out of phase and have been for many months, producing consolidations prior to syncing and exploding in the prevailing direction. This was seen recently in the mid phase of the bearish 80 day leg and entire bearish leg of the 30 day. Whilst the cycle low of the 80 day feature (currently late down) is due toward the back end of November/early December, there may be enough power in the 30 day to produce sideways price action prior to the larger degree low. Charts below display both components in detail.

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 - Bitcoin 22nd October 2025
Entry: 22nd October 2025 @ 107585.98
Exit: 17th November 2025 @ 94002.67
Gain: 12.63%

Time Frequency Analysis

Read more

Although Tradingview’s pinescript language is, unfortunately, limited for the purpose of performing frequency domain analysis on market data, one can implement time domain filters to a decent degree, given some verbose coding (compared to optimal python/numpy/C and vectorisation).

Below is a fairly simple implementation of a Butterworth bandpass filter (on close prices) for your analysis pleasure. The price series is first detrended prior to filtering using a quadratic (order 2) or cubic (order 3) polynomial fit.

Copy and paste the code into the Tradingview code area to use on your charts, remembering to configure the upper and lower bounds of the filter (the cutoffs) according to your desired cycle target.

It is important to consider when configuring the cutoffs that Tradingview does not interpolate for weekends / holidays as we do in the main time frequency analysis. Therefore cycles identified in the main time frequency analysis will be slightly longer than the cutoffs needed for this Butterworth filter. I recommened experimenting yourself to discover the best parameters for optimal correlation to the time frequency result.

//@version=6
indicator(”Sigma-L BW Sweep”, overlay=false)

// Inputs
low_per = input.int(40, “Low Cutoff Period”, minval=10)
high_per = input.int(80, “High Cutoff Period”, minval=10)
filter_length = input.int(100, “Number of Bars for Filter/Detrend”, minval=20)
detrend_order = input.int(2, “Detrend Order (2 or 3)”, minval=1, maxval=3)
src = input.source(close, “Source”)

// Polynomial Detrend Function (least squares fit for order 2 or 3)
poly_detrend(src_in, len, order) =>
    if len <= order
        src_in
    else
        n = len
        x_mean = (n - 1) / 2.0
        sum_y = 0.0
        sum_z_y = 0.0
        sum_z2_y = 0.0
        sum_z3_y = 0.0
        sum_z2 = 0.0
        sum_z4 = 0.0
        sum_z6 = 0.0
        for i = 0 to n - 1
            xi = float(n - 1 - i)
            zi = xi - x_mean
            yi = src_in[i]
            sum_y += yi
            sum_z_y += zi * yi
            sum_z2_y += zi * zi * yi
            sum_z2 += zi * zi
            sum_z4 += zi * zi * zi * zi
            sum_z3_y += zi * zi * zi * yi
            sum_z6 += zi * zi * zi * zi * zi * zi
        y_mean = sum_y / n
        denom_even = sum_z4 - sum_z2 * sum_z2 / n
        b2 = (sum_z2_y - y_mean * sum_z2) / denom_even
        b0 = y_mean - (sum_z2 / n) * b2
        b1 = 0.0
        b3 = 0.0
        z_current = float(n - 1) - x_mean
        if order == 2
            b1 := sum_z_y / sum_z2
        else
            det = sum_z2 * sum_z6 - sum_z4 * sum_z4
            b1 := (sum_z6 * sum_z_y - sum_z4 * sum_z3_y) / det
            b3 := (sum_z2 * sum_z3_y - sum_z4 * sum_z_y) / det
        trend = b0 + b1 * z_current + b2 * z_current * z_current + b3 * z_current * z_current * z_current
        src_in - trend

// Detrended source
detrended_src = poly_detrend(src, filter_length, detrend_order)

// 3-Pole Butterworth Low-Pass Function
butterLP(src_in, len_in) =>
    cf = 2 * math.tan(math.pi / len_in)
    cf2 = cf * cf
    cf3 = cf2 * cf
    a0 = 8 + 8 * cf + 4 * cf2 + cf3
    a1 = -24 - 8 * cf + 4 * cf2 + 3 * cf3
    a2 = 24 - 8 * cf - 4 * cf2 + 3 * cf3
    a3 = -8 + 8 * cf - 4 * cf2 + cf3
    c = cf3 / a0
    d0 = -a1 / a0
    d1 = -a2 / a0
    d2 = -a3 / a0
    out = 0.0
    out := nz(c * (src_in + src_in[3]) + 3 * c * (src_in[1] + src_in[2]) + d0 * out[1] + d1 * out[2] + d2 * out[3], src_in)
    out

// Band-Pass on detrended series: High-Pass (detrended - LP(high_per)) then LP(low_per)
lp_high = butterLP(detrended_src, high_per)
hp = detrended_src - lp_high
bp_full = butterLP(hp, low_per)

// Plot in indicator window
plot(bp_full, “Butterworth Band-Pass (Detrended)”, color=color.blue, linewidth=2)
hline(0, “Zero Line”, color=color.gray, linestyle=hline.style_dashed)

The Cycle Hunt is On

If, in the course of using this indicator, you discover what you believe to be a metronomic signal (mostly stationary amplitude and frequency!), please let me know so I can run the TFA across it and share it to subscribers. Many pairs of eyes are better than one!

Thanks in advance.

David

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

Whilst the superb 30 day cycle has been ‘making all the headlines’ in Bitcoin for it’s wonderful correlation to price action over the last 6 months, the 80 day feature bubbles under the surface. In the latest iteration of the up leg during late September and October price has moved largely sideways, battling with the aforementioned little brother for correlation. It is also interesting to note the power around 60 days, likely a harmonic (see chart below), picked up by the time frequency analysis in response to the relatively high amplitude of the 30 day. The fact that the 80 day is not harmonically related (at least not in an integer multiple) to the 30 day suggests these two (80 & 30) are the distinct and notable periodic features.

Taking this phasing on the evidence, it looks bearish for Bitcoin. Bulls will hope the 30 day (troughing) continues to battle hard with it’s larger brother and push price a little further up against the 80 day’s down pressure over the next week or two. However, it is a fundamental feature of financial markets that power is distributed in a ~ 1/f manner in the frequency domain, so the 80 day will exert it’s dominance in time.

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 - Bitcoin 22nd September 2025
Entry: 22nd September 2025 @ 112736.59
Exit: 22nd October 2025 @ 108329.60
Gain: - 3.91%

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

Arguments constantly seem to rage over which is the better investment, Gold or Silver, in the investment zeitgeist. The truth, at least from a cycles point of view, is that one should pay very close attention to a remarkable periodic feature of around 260 days in order to switch between the two!

In the below sample the cycle in question is shown clearly over a 10 year period. Featuring 13 + iterations and with no significant power in neighbouring frequencies (or indeed anywhere in the bandwidth), this cycle is an example of highly stationary, non random price action. Silver has recently had one of it’s best runs of the last decade, a run which is now ending, or at least until the start of March 2026, according to the current phasing (see details below). Gold and silver bugs should always keep this extraordinary feature in mind.

Time Frequency Analysis

Read more

ΣL Cycle Summary

We have held off, slightly, updating the 80 day cycle in Bitcoin (the ‘big brother’) due to the continued influence of it’s feisty little brother around 30 days. That smaller cycle continues to be out of phase with it’s more powerful and larger sibling, producing the fairly choppy price action we see as these two battle. The 80 day has likely now troughed and is starting to influence to the upside. Whilst the 30 day is still turned down the result is likely to be sideways price action. When these two combine and are both bullish then price should trend more smoothly. The 30 day trough is due toward the end of September so bullish traders may wish to sit on their hands until then.

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 - Bitcoin 18th July 2025
Entry: 28th July 2025 @ 119273.69
Exit: 22nd September 2025 @ 112045.48
Gain: 6.06%

Time Frequency Analysis

Read more

For more on how we detect periodic features in financial markets please see Hacking the Uncertainty Principle: Time Frequency. You may also wish to read our guide on how to interpret charts on Sigma-L, below is the first part:

With that pre-amble out of the way, below are 10 of the most coherent, daily resolution signals in financial markets at the moment, presented in no particular order!

There are many more very good signals and it was a hard task to distill into just 10. I have tried to include instruments across a wide range of sectors to reflect the remarkable ubiquity of coherent cycles in all markets. All of these were detected by our cycle scanner in the first instance, which is available for intraday trading (live stream) and individual posted analysis in our discord. Membership of which can be obtained by contacting me on X (@tradinghurst) via DM.

The charts below all display a full time frequency analysis showing the detected dominant cycle within the bandwidth of the spectrogram.

1. Johnson & Johnson (JNJ) | ~ 200 Day Cycle

Component Average Wavelength: ~ 215 days
Current Phase: Hard Up / Late Up
Timeframe: January 2019 - Now
Completed Iterations: 12
Next Cycle Peak: ~ 2nd November - 14th November 2025
Next Cycle Trough: ~ 17th February - 3rd March 2026
Component Yield Over Timeframe: 139.63%

2. Bitcoin (BTC/USD) | ~ 30 Day Cycle

Component Average Wavelength: ~ 30 days
Current Phase: Peaking / Peaked
Timeframe: June 2024 - Now
Completed Iterations: 15
Next Cycle Peak: ~ 16th - 18th October, 2025
Next Cycle Trough: ~ 2nd - 4th October, 2025
Component Yield Over Timeframe: 186.16%

3. US Stock Markets (via SPY/QQQ/IWM) | ~ 258 Day Cycle

Component Average Wavelength: ~ 258 days
Current Phase: Peaking / Peaked
Timeframe: August 2015 - Now
Completed Iterations: 14
Next Cycle Peak: ~ 1st - 21st May, 2026
Next Cycle Trough: ~ 21st December 2025 - 11th January, 2026

4. Tesla (TSLA) | ~ 166 Day Cycle

Component Average Wavelength: ~ 166 days
Current Phase: Trough / Hard Up
Timeframe: November 2020 - Now
Completed Iterations: 11
Next Cycle Peak: ~ 3rd November - 2nd December 2025
Next Cycle Trough: ~ 23rd January - 23rd February 2026
Component Yield Over Timeframe: 612.41%

5. Copper (XG/USD) | ~ 144 Day Cycle

Component Average Wavelength: ~ 144 days
Current Phase: Troughing
Timeframe: January 2022 - Now
Completed Iterations: 10
Next Cycle Peak: ~ 8th - 16th December 2025
Next Cycle Trough: ~ 27rd September - 5th October 2025
Component Yield Over Timeframe: 150.86%

6. Wells Fargo (WFC) | ~ 265 Day Cycle

Component Average Wavelength: ~ 265 days
Current Phase: Peaking / Peaked
Timeframe: March 2018 - Now
Completed Iterations: 11
Next Cycle Peak: ~ 6th - 16th June, 2026
Next Cycle Trough: ~ 26th January - 5th February, 2026
Component Yield Over Timeframe: 248.61%

7. iShares 20 Year Treasury Bond ETF (TLT) | ~ 524 Day Cycle

Component Average Wavelength: ~ 524 days
Current Phase: Hard Up
Timeframe: August 2008 - Now
Completed Iterations: 12
Next Cycle Peak: ~ 2nd March - 12th April, 2026
Next Cycle Trough: ~ 24th November - 28th December, 2026
Component Yield Over Timeframe: 188.20%

8. Litecoin (LTC/USD) | ~ 85 Day Cycle

Component Average Wavelength: ~ 85 days
Current Phase: Troughing / Troughed
Timeframe: March 2023 - Now
Completed Iterations: 12
Next Cycle Peak: ~ 1st - 3rd November, 2025
Next Cycle Trough: ~ 13th - 15th December, 2025
Component Yield Over Timeframe: 321.25%

9. Honeywell (HON) | ~ 187 Day Cycle

Component Average Wavelength: ~ 187 days
Current Phase: Troughing / Troughed
Timeframe: October 2020 - Now
Completed Iterations: 9
Next Cycle Peak: ~ 3rd - 11th January, 2026
Next Cycle Trough: ~ 2nd - 12th October, 2025
Component Yield Over Timeframe: 133.20%

10. Rio Tinto (RIO) | ~ 77 Day Cycle

Component Average Wavelength: ~ 77 days
Current Phase: Troughing / Troughed
Timeframe: June 2022 - Now
Completed Iterations: 16
Next Cycle Peak: ~ 17th - 23rd October, 2025
Next Cycle Trough: ~ 24th - 30th November, 2025
Component Yield Over Timeframe: 130.21%

ΣL Cycle Summary

Here we return to look at the excellent ~ 30 day cycle in Bitcoin, a smaller, less powerful but no less stationary brother of the 80 day cycle we have covered many times on the site. It is another interesting period because these two features are out of phase at the troughing zone of the larger feature. In the past, interactions between these two will result in general sideways price action as the two fight for dominance. The 80 day phase wins over time (1/f power distribution in freq domain) but at the outset of the initial move up the 30 day has recently shown enough power to push price around until it’s own phase is aligned. Some examples of this are highlighted below in the charts.

The 30 day cycle itself is phased to be peaking here with a trough at the end of the month. If price moves generally sideways until then expect an explosion of bullish pressure as big and little brother combine at the next trough of the 30 day.

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

ΣL Cycle Summary

Although some volatility has crept into the excellent cycle around 90 days of late, courtesy of high frequency power (see burst around 30 days below!), this wave is still fairly stationary and just about qualifies for a ‘C’ category rating in our system. Overall, price has grinded sideways for a couple of years now with this feature defining the price action within the consolidation. Worth noting and trading with the anticipation of increased volatility to the upside during the forthcoming up leg.

Time Frequency Analysis

Read more