Shared analysis2026-05-08

^GSPC · daily cycle analysis

Random Walk regime · Hurst 0.542 · 79-bar daily cycle. Snapshot captured 2026-05-08 from a live FractalCycles analysis.

Hurst exponent

0.542

random-walk

Regime

Random Walk

Confidence 98%

Dominant cycle

79.0 bars

Next peak in 8 · trough in 48

Significant cycles

Out of 20 candidates

Price + composite cycle

Detrended composite of 4 selected cycles, scaled and overlaid on the most recent 600 bars. The dashed segment shows the cycle composite projected forward 341 bars.

Detected cycles

Cycles ranked by spectral power. Statistical significance is tested against the Bartels distribution against the platform default threshold; only cycles below that threshold are flagged significant.

Rank	Period (bars)	Bartels p	Significant	In composite	Phase	Next peak	Next trough
1	79.00	100.000	Yes	Yes	Approaching peak	8	48
2	35.00	100.000	Yes	No	Falling toward zero	26	9
3	51.00	100.000	Yes	No	Just past peak	48	22
4	8.00	100.000	Yes	No	Just past peak	8	4
5	11.00	100.000	Yes	No	Just past peak	10	4
6	59.00	100.000	Yes	No	Just past peak	58	28
7	120.00	100.000	Yes	Yes	Rising toward zero	40	100
8	26.00	100.000	Yes	No	Approaching trough	14	1
9	30.00	100.000	Yes	No	Falling below zero	19	4
10	341.00	100.000	Yes	Yes	Falling below zero	246	75
11	17.00	100.000	Yes	No	Just past peak	16	7
12	41.00	100.000	Yes	No	Falling toward zero	35	14
13	73.00	100.000	Yes	No	Approaching peak	5	41
14	86.00	100.000	Yes	No	Rising from trough	12	55
15	49.00	100.000	Yes	No	Just past peak	45	20

Power spectrum

Goertzel-DFT power across the analyzed period range. Peaks indicate candidate cycle lengths; statistical significance is tested separately via Bartels.

How this snapshot was produced

Detrend method: hodrick-prescott. Sampling cadence: daily. Total bars analyzed: 1200.

FractalCycles applies the Goertzel discrete Fourier transform across a candidate period range, tests each peak against the Bartels distribution for statistical significance, and classifies the current regime via the Hurst exponent (rescaled-range analysis). This snapshot represents the analysis output at the moment of sharing and does not update as new bars print.