The Sigma-MT Suite is available now for new VIP Cycle Analysts (founding members). Please contact me (on X or Substack chat) once you have joined or upgraded from standard membership to receive the software.

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Prerequisites: the quick start guide. You should already have Sigma-MT on a chart and recognise the spectrogram, bandpass panel and info panel by sight.

The quick start guide told you what the spectrogram is. This guide tells you what it means, and why a picture built from wavelet convolution is a fundamentally more honest way to look at market cycles than counting peaks on a chart. Everything that follows in the course (detection, projection, yield, composites, the Scanner) is built on the foundation laid here, so this is the one guide worth reading twice.

The problem with counting cycles..

Classical cycle analysis, the kind you find in most trading literature and some descending from the work of J.M. Hurst, begins by simple counting of visually apparent inflection points. You find two lows, measure the bars between them, and declare a cycle of that length. The trouble is that this is subjective and brittle. Two analysts looking at the same chart can pick different lows and arrive at different cycles, and a single noisy swing can throw the count off entirely. Indeed higher frequency features can often have bursts in power than exceed the power of the longer cycle, influencing price in a transitory and misleading (to the cycle counter) manner. Worse, it assumes a cycle has one fixed length, when real market rhythms drift in period (frequency modulation) and fade in and out of strength (amplitude modulation) over time. The real marker of a quality cycle is the minimisation of any modulation (or a high degree of stationarity), since modulation is a constant in financial market cycles.

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A reminder before the list. Several inputs have a keyboard twin, so anything you adjust live with the keys (sample size, frequency edges, panel toggles) only persists for that chart session. The inputs are where you set the values that load every time the EA attaches.

Time Series

SampleN (default 500) — The number of bars in the analysis window. Range 64 …

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Sigma-MT is driven almost entirely from the keyboard. There are no buttons cluttering the chart and no menus to dig through; once the key map is in your fingers, reshaping an entire analysis takes seconds. The keys fall into four groups, mirroring the in-app panel: analysis controls that change what the engine computes, cycle visibility toggles, display…

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What is Sigma-MT?

Sigma-MT is an advanced Expert Advisor for the trading platform MetaTrader 5, available exclusively to VIP cycle analyst members on Sigma-L (founding members).

It is a direct port and enhancement of the python/numpy version I have developed over the last few years and has been seen previously in posts on Sigma-L. It is a bespoke, unique and powerful way to detect, analyse and act upon statistically significant periodic features in financial markets. It abstracts away many of the more technical aspects of this approach but retains a great degree of adaptability, alongside a streamlined interface and fast computation (processor dependent!). I hope you will enjoy using it as much as I do and discover some cyclic gems in the process.

Sigma-MT is not an indicator/expert advisor in the usual Meta Trader sense. It is a time-frequency analysis engine, drawn from the same family of mathematics used in radar and seismology, pointed at price. Rather than smoothing price and hoping a crossover means something, it decomposes the series into its component frequencies, watches how their power evolves through time, and tells you which cycle is dominant right now, where that cycle sits in its phase, and how much confidence the detection deserves.

This guide takes you from a fresh install to reading that information. Everything deeper, from the detection mathematics through projection, yield statistics, composites and the Sigma-MT Scanner, has its own guide in this series. Here we simply get you on the chart.

For a complete reference to all of the controls for analysis navigation see Sigma-MT keyboard reference.

See also: Sigma-MT v1.0 Input Reference for a complete guide to all input parameters in the EA

1. Install

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ΣL Cycle Summary

Here we have a coherent periodic feature that is highly conspicuous across multiple stock markets, including here in the S&P 500, Nikkei and Dax, amongst others. Running at a trading day wavelength of around 82 days, it is peaking now.

The low back in February of this year was likely of larger magnitude, although cycles at this scale are currently fairly noisy and not worthy of posting, yet. However, we can assume the phase of the larger feature is up so a flatter retrace is likely for this smaller cycle.

We will keep an eye on this one going forward, it appears to span the globe in terms of it’s stationarity across multiple major stock market averages and that in itself is remarkable.

Time Frequency Analysis

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ΣL Cycle Summary

As we return to look at the beautiful 80 day cycle feature in Bitcoin we can observe, in this instance, that the larger and exponentially more powerful 40 week wave has influenced the latest down leg significantly. This is standard behaviour for financial markets where the power in the frequency domain is distributed in a 1/f manner, larger features providing much more influence, especially in their acceleration phases. Smaller features can shine through but it is generally when the larger component is at or near an inflection point (a peak or trough of the larger feature, therefore neutral power).

Such is the case here where we have seen a fairly grinding period of price action with an upward bias, courtesy of the bending power of the 40 week cycle. Certainly not the explosive move that is usually characterised by two coherent features that are in phase. This more volatile characteristic is now anticipated here with the two aligned in a bullish manner toward the end of June to early July.

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 7th April 2026
Entry: 7th April 2026 @ 71910.20
Exit: 18th May 2026 @ 77432.02
Gain: -7.68%

Time Frequency Analysis

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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

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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

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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

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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

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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

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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

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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

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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

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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

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