digital signal processing, applied to financial time series
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Cycle charts: the dominant cycles of each market and their next projected turns

SPY time series, with the cycle's turns markedctrl + scroll to zoom · drag to pan · double-click to reset

price
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Cycles detected tick to add

Each row is one cycle on its own. The card at the top adds the ticked cycles into one wave, which has its own turns, so its phase and turns are not an average of the rows.

How to read this

The cycles table. strength, all is how far a cycle stands out over the whole history analysed, strength, recent the same over recent months (below 1.0 it has faded and is left out; the card at the top shows this one). The page usually opens on the top two added together (on volatility markets, the top one alone). The order is chosen on strength plus further checks, so a slightly stronger cycle can sit lower. phase is how far a cycle has travelled from its last turn to its next. Tick several to add them together.

Cycle component ctrl + scroll to zoom · drag to pan · double-click to reset

How to read this

Solid is measured, dotted is projected. Past troughs (green) and peaks (red) use data from before and after each bar: they show where the cycle was, not what was knowable on the day. The latest turn, when it falls in the last half-cycle, is provisional (shaded box) and still looks small. Hollow dots are projected turns, where the wave would turn if its rhythm holds; the shaded box and its ± in trading days (td) show how early or late such turns have typically come — measured from past turns; the windows of later turns are wider and estimated. Not a guarantee.

The gold typical range (off at first) is the middle half of the ticked cycles' past shapes, cut at turns found with hindsight; past today it shows how the rhythm would run if it holds. Click a key entry to show or hide it.

cycle waveprojected wavetypical range
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Next turns the hollow dots on the cycle component · projections, not forecasts

Cycles, one by one each ticked cycle on its ownctrl + scroll to zoom · drag to pan · double-click to reset

← swipe for earlier years

Where each cycle stands the ticked cycles

How to read this

Each cycle runs clockwise round its own ring: down the right side from peak to trough, up the left side back to the peak.

Scalogram bright = a strong cycle · right: the whole period against recent monthsctrl + scroll to zoom · drag to pan · double-click to reset

How to read this

Scalogram and surface. The same analysis as a map: time across, cycle length down, colour for strength. A bright band reaching the right-hand edge is a cycle still active.

The glow on the right. Around each ticked cycle's length, a glow in its colour marks the band of lengths that belong to that cycle: where the curves peak inside it, the strength measured across the whole series lines up with the cycle on the charts.

wavelet scalogram
← swipe for earlier years

Surface the scalogram in 3D: the high ridges are the strong cycles, cyan: the ones selected in the table · drag to turn

What this is. Signal processing on a financial time series: the daily data split into cycles, each measured against the background noise. How it works
Signal processing, not advice. This site applies signal processing to financial time series and projects possible future turning points. It does not trade and gives no trading signals. Past turns are located with hindsight, using data that came after them, which is impossible in real time. Projected turns are extrapolation, not prediction. Nothing on this site is investment advice, and the operator is not a registered adviser. Markets carry a substantial risk of loss; past performance guarantees nothing. Data is third-party and supplied as is. We accept no responsibility for any loss arising from the use of this site. Full disclaimer and risk disclosure