Pure Math Trading Lab

Signal processing and statistical physics applied to ASX price series: a Baum–Welch hidden Markov model for market regime, Kalman-filtered trend, Fourier spectral analysis, Hurst/DFA long-memory exponents, and Marchenko–Pastur random matrix theory for separating real correlation from noise. Method notes in docs/PUREMATH_RESEARCH.md.

Read this before trusting anything below. Every backtest here carries a deflated Sharpe ratio — the probability the result survives once you account for how many strategy variants were tried (Bailey & López de Prado). A beautiful equity curve with a low DSR is luck, not skill, and the table says so in plain English. Renaissance's edge came from high-frequency data, execution infrastructure and leverage that daily Yahoo bars cannot reproduce — what transfers is the method and the discipline, not the returns. Research tooling, not financial advice.

Model workbench — run any model on any stock

Last computed 2 Oct 2026 21:31 · Pure-math signal panel over 60 liquid names

Market regime — Gaussian HMM fitted by Baum–Welch

P(turbulent regime) today

72.7%

State means (% p.a.)

-39.48 · 16.68

State vols (% p.a.)

19.48 · 9.45

Expected turbulent spell

10.2 days

The filtered probability that the ASX 200 is in its low-return, high-volatility state. The transition matrix (0.9024, 0.0976 / 0.0325, 0.9675) shows how sticky each regime is — this persistence is the volatility clustering that makes regime models work at all.

Composite signal — walk-forward backtest & honesty test

Variant	Final equity	Ann. Sharpe	PSR	Deflated Sharpe	Verdict
Signal + HMM regime overlay	1.5402×	0.813	94.8%	24.2%	indistinguishable from luck
Signal only (no regime overlay)	1.5499×	0.714	92.3%	18.4%	indistinguishable from luck
ASX 200 (buy & hold)	—	0.488	83.7%	—	single strategy, no deflation needed

60 liquid names, top 10 held equal-weighted, monthly rebalance, 25bps costs, 1026 daily observations, deflated against 60 trials (skew -0.302, kurtosis 6.42). The overlay variant spent 168 days in cash.
Caveat: the regime model is fitted on the full sample, so the overlay row is optimistic — that is exactly why the un-overlaid row is shown beside it.

Market structure — random matrix theory

Real factors detected

out of 118 assets

Variance that is pure noise

62.4%

market mode: 16.3%

Eigenvalue spectrum of the correlation matrix. The red line is the Marchenko–Pastur edge λ₊ = 2.252: everything to its left is statistically indistinguishable from random noise. Only 6 eigenvalues carry genuine structure — the honest answer to "how many independent bets does the ASX really offer?"

Per-stock signal panel

Ticker	Score	Kalman %	Hurst	Regime	Entropy	Cycle	5d rev %
PME Pro Medicus Limited	100	-96.5	0.70	trend	0.91	252	2.9
CPU Computershare Limited	98	6.0	0.63	trend	0.93	252	1.6
CDA Codan Limited	97	615.9	0.62	trend	0.92	252	-29.1
SOL Washington H. Soul Pa…	95	76.7	0.57	trend	0.93	252	2.7
SUN Suncorp Group Limited	93	-45.0	0.62	trend	0.93	252	1.1
ALL Aristocrat Leisure Li…	91	-45.4	0.65	trend	0.93	252	-2.3
MEZ Meridian Energy Limit…	90	24.1	0.38	revert	0.88	252	-2.1
RHC Ramsay Health Care Li…	88	37.9	0.58	trend	0.94	168	1.6
IFT Infratil Limited	86	-53.2	0.59	trend	0.92	252	2.4
CSL CSL Limited	84	39.9	0.59	trend	0.93	252	0.9
CSC Capstone Copper Corp.	83	-89.3	0.59	trend	0.93	252	2.6
S32 South32 Limited	81	-32.5	0.60	trend	0.93	252	0.6
ASX ASX Limited	79	102.8	0.55	random	0.92	252	-2.8
WES Wesfarmers Limited	78	44.4	0.63	trend	0.93	252	-3.5
IAG Insurance Australia G…	76	-47.5	0.57	trend	0.93	252	1.4
BSL BlueScope Steel Limit…	74	-8.9	0.58	trend	0.92	252	-0.8
NWSLV News Corporation	72	-83.2	0.57	trend	0.93	252	0.1
ANZ ANZ Group Holdings Li…	71	14.4	0.60	trend	0.93	252	1.2
JHX James Hardie Industri…	69	-146.7	0.58	trend	0.94	126	2.5
AIA Auckland Internationa…	67	-7.0	0.56	trend	0.93	252	1.6
GMG Goodman Group	66	-10.4	0.62	trend	0.92	252	1.8
FPH Fisher & Paykel Healt…	64	70.4	0.52	random	0.92	126	-1.3
MQG Macquarie Group Limit…	62	12.9	0.59	trend	0.93	168	-2.5
COL Coles Group Limited	60	-23.4	0.54	random	0.93	252	0.7
BHP BHP Group Limited	59	-41.8	0.55	trend	0.93	252	-0.8
APA APA Group	57	-40.8	0.56	trend	0.93	126	-0.4
NWS News Corporation	55	-62.4	0.60	trend	0.94	252	-0.9
WOW Woolworths Group Limi…	53	-12.9	0.58	trend	0.95	252	0.3
SCG Scentre Group	52	-45.4	0.59	trend	0.93	252	0.9
QAN Qantas Airways Limited	50	-13.0	0.60	trend	0.93	252	1.6
STO Santos Limited	48	0.5	0.60	trend	0.93	168	0.2
SIG Sigma Healthcare Limi…	47	-24.6	0.53	random	0.93	84	-1.2
XYZ Block, Inc.	45	-70.4	0.61	trend	0.92	252	1.6
TLS Telstra Group Limited	43	6.5	0.57	trend	0.93	252	-1.1
AMC Amcor plc	41	-1.4	0.56	trend	0.92	126	-1.3
EVN Evolution Mining Limi…	40	-127.8	0.58	trend	0.90	252	4.5
NEM Newmont Corporation	38	-107.5	0.59	trend	0.93	252	3.2
ORI Orica Limited	36	57.6	0.65	trend	0.92	252	-1.4
NAB National Australia Ba…	34	2.7	0.64	trend	0.92	252	0.1
MPL Medibank Private Limi…	33	-31.7	0.54	random	0.93	252	0.2
WDS Woodside Energy Group…	31	-75.5	0.63	trend	0.93	168	1.5
RIO Rio Tinto Group	29	-71.6	0.51	random	0.92	252	0.0
ALQ ALS Limited	28	-53.9	0.57	trend	0.93	252	-1.6
WBC Westpac Banking Corpo…	26	0.2	0.56	trend	0.93	252	0.5
QBE QBE Insurance Group L…	24	53.9	0.51	random	0.94	252	-3.8
RMD ResMed Inc.	22	13.4	0.58	trend	0.92	252	-0.7
TCL Transurban Group	21	-66.0	0.55	random	0.91	126	-0.8
TLC The Lottery Corporati…	19	-6.5	0.52	random	0.92	252	-1.0
REA REA Group Limited	17	-67.6	0.55	trend	0.91	252	-4.7
LYC Lynas Rare Earths Lim…	16	-203.1	0.59	trend	0.92	168	8.9
FMG Fortescue Ltd	14	-75.5	0.52	random	0.92	252	1.1
CBA Commonwealth Bank of …	12	-46.9	0.55	random	0.92	252	-0.4
SGH SGH Limited	10	-19.0	0.57	trend	0.93	84	-2.9
PLS PLS Group Limited	9	-390.7	0.58	trend	0.92	252	3.6
NST Northern Star Resourc…	7	112.1	0.61	trend	0.93	252	-8.6
ORG Origin Energy Limited	5	-117.1	0.52	random	0.92	252	-0.6
BXB Brambles Limited	3	25.7	0.51	random	0.93	252	-2.5
WTC WiseTech Global Limit…	2	-88.6	0.55	random	0.92	252	-6.7
AAI Alcoa Corporation	0	-207.1	0.62	trend	0.94	252	1.3

Score is the cross-sectional percentile of the weighted ensemble (Kalman slope, Hurst-weighted momentum, short-horizon reversal, spectral concentration). Individually every one of these signals is weak — that is the point of an ensemble, and also why the deflated Sharpe above matters more than any single row here.