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HYPERLIQUID · PERPETUAL FUTURES

AXS

AXS-USD perpetual · 24/7 trading on Hyperliquid

▸ Advanced metrics · M2M bundle

hyperliquid · perp-axs · fresh · feed 3s old
24h sparkline · 60 pts▲ 19.23%
realized vol (ann.)
377.55%
max drawdown
4.30%
sharpe
-3.44
ulcer index
2.85%
RMS drawdown
pain index
2.48%
mean drawdown
mod. VaR 95%
0.14%
Cornish-Fisher
martin ratio
-454.78
ret / ulcer
CDaR 95%
4.15%
cond. drawdown
gain/pain
0.99
Σgain / Σ|loss|
sterling
-312.87
ret / CDaR
omega (θ=0)
0.99
upside/downside
roll spread
0.0 bps
implied (price-only)
bars used
615
store
spread
—
24h Δ
19.23%
flow lean
—
carry
shorts_pay
-12.82%
signalLONGconfidence 43%suggested side: BUY
  • 24h change +19.23%
  • funding: shorts pay — perp longs get paid to wait
  • mark cheap vs HL oracle by 15.1bps — long bias
Same bundle via M2M API: /api/m2m/hl-axs/bundle · venue execution: hyperliquid →
LIVEPOLL0SRCFRESH3.5s⏱--:--:-- UTC8NEXT8.0sUP0s--:--HIST0/30
▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·▶ STREAMING·HYPERLIQUID·POLYMARKET·0 POLLS·SRC FRESH·UPTIME 0s·NEXT POLL 8.0s·CC0 OPEN DATA·HYPO.MARKETS·
MARK · live
$1.121
24h Δ · live
19.23%
24h vol · live
$1.9M
AXS · live 24h price
n=25 · μ=0.9958 · σ=0.0856 · range [0.9348, 1.1671] · R²=0.660▲ RISING +19.55%σ HIGH 8.59%LAST 1.12101.16711.10901.05100.99290.9348μ = 0.9958max 1.1671min 0.9348dataMA(5)OLS R²=0.66μ lineμ ± σ bandmaxminlive endpoint
25 closes · last $1.12
Funding direction · live
Long fee 48.3%Short fee 51.7%SHORT FEE51.7%
Σ = 0.0%
Σ-sides total = 0.00% (100.00pp arb gap)
H(p) entropy = 0.999 / 1.00 bits (100%) · max uncertainty (~50/50)
Long fee
48.3%▬ +0.00pp
Short fee
51.7%▬ +0.00pp
1h funding -0.001463% · shorts pay
Hourly contract volume · live
n=25 · Σ=1,739,691 · μ=69587.6 · σ=123544.4 · CV=1.78BURSTY · concentratedcumulative energy ↗ · 50% by h=21096,775193,550290,326387,101μ = 69588387,100.750%h1h5h9h13h17h21h25#1 peak#2-3> μactivequietμ linecum energy
peak 387101 contracts
Live numerics · pulse on poll
LIVE NUMERICS9 metrics·POLL 0
⏱snapshot age
3.5s
$mark $
$1.1205
$mid $
$1.1195
◉prev-day close
$0.9398
Δ24h Δ %
+19.234%
$24h vol $
$1.90M
◐open interest $
$684.94k
%funding (1h)
-0.001463%
%funding (yr)
-12.82%/yr

§1 · 24h time-series

Close price · hourly
n=25 · μ=0.9958 · σ=0.0856 · range [0.9348, 1.1671] · R²=0.660▲ RISING +19.55%σ HIGH 8.59%LAST 1.12101.16711.10901.05100.99290.9348μ = 0.9958max 1.1671min 0.9348dataMA(5)OLS R²=0.66μ lineμ ± σ bandmaxmin
mark $1.1205 · 24h 19.23% · range $[0.9348, 1.1671]
OHLC candles · hourly
n=25 · up 13 · down 12 (52% up) · range [0.9290, 1.1807] · σ=0.0856 · CV=0.09 · bodyµ=51%BULLISH +18.78%CLOSE 1.1210 vs OPEN 0.9437 (+18.78%)&#9650; CLOSE 1.12101.18071.11781.05480.99190.9290μ close = 0.9958O0.944 H0.944 L0.935 C0.938 (-0.64%)O0.944 H0.944 L0.935 C0.938 (-0.64%)O0.940 H0.944 L0.940 C0.940 (+0.04%)O0.940 H0.944 L0.940 C0.940 (+0.04%)O0.941 H0.941 L0.937 C0.938 (-0.35%)O0.941 H0.941 L0.937 C0.938 (-0.35%)O0.938 H0.938 L0.934 C0.937 (-0.12%)O0.938 H0.938 L0.934 C0.937 (-0.12%)O0.938 H0.938 L0.933 C0.935 (-0.29%)O0.938 H0.938 L0.933 C0.935 (-0.29%)O0.935 H0.941 L0.929 C0.941 (+0.68%)O0.935 H0.941 L0.929 C0.941 (+0.68%)O0.943 H0.951 L0.939 C0.950 (+0.71%)O0.943 H0.951 L0.939 C0.950 (+0.71%)O0.949 H0.951 L0.943 C0.944 (-0.47%)O0.949 H0.951 L0.943 C0.944 (-0.47%)O0.945 H0.948 L0.943 C0.944 (-0.05%)O0.945 H0.948 L0.943 C0.944 (-0.05%)O0.946 H0.949 L0.941 C0.943 (-0.31%)O0.946 H0.949 L0.941 C0.943 (-0.31%)O0.942 H0.950 L0.941 C0.947 (+0.51%)O0.942 H0.950 L0.941 C0.947 (+0.51%)O0.947 H0.947 L0.939 C0.942 (-0.62%)O0.947 H0.947 L0.939 C0.942 (-0.62%)O0.942 H0.944 L0.937 C0.939 (-0.31%)O0.942 H0.944 L0.937 C0.939 (-0.31%)O0.941 H0.943 L0.936 C0.943 (+0.19%)O0.941 H0.943 L0.936 C0.943 (+0.19%)O0.943 H0.945 L0.939 C0.939 (-0.38%)O0.943 H0.945 L0.939 C0.939 (-0.38%)O0.940 H0.945 L0.938 C0.944 (+0.49%)O0.940 H0.945 L0.938 C0.944 (+0.49%)O0.944 H0.953 L0.944 C0.951 (+0.67%)O0.944 H0.953 L0.944 C0.951 (+0.67%)O0.951 H1.022 L0.951 C0.985 (+3.56%)O0.951 H1.022 L0.951 C0.985 (+3.56%)10.6%O0.986 H1.092 L0.978 C1.091 (+10.64%)O0.986 H1.092 L0.978 C1.091 (+10.64%)O1.088 H1.161 L1.082 C1.119 (+2.84%)O1.088 H1.161 L1.082 C1.119 (+2.84%)O1.117 H1.164 L1.078 C1.125 (+0.69%)O1.117 H1.164 L1.078 C1.125 (+0.69%)O1.126 H1.170 L1.098 C1.167 (+3.69%)O1.126 H1.170 L1.098 C1.167 (+3.69%)O1.167 H1.181 L1.125 C1.126 (-3.51%)O1.167 H1.181 L1.125 C1.126 (-3.51%)O1.127 H1.171 L1.116 C1.148 (+1.86%)O1.127 H1.171 L1.116 C1.148 (+1.86%)O1.149 H1.168 L1.113 C1.121 (-2.45%)O1.149 H1.168 L1.113 C1.121 (-2.45%)#1#5#9#13#17#21#25up bar (C≥O)down bar (C<O)MA(5) closeμ closedoji (~no body)biggest body
25 bars
Hourly volume (base units)
n=25 · Σ=1,739,691 · μ=69587.6 · σ=123544.4 · CV=1.78BURSTY · concentratedcumulative energy &nearr; · 50% by h=21096,775193,550290,326387,101μ = 695883,693.6 · 1.0% peak3,693.6 · 1.0% peak5,237 · 1.4% peak5,237 · 1.4% peak3,522.4 · 0.9% peak3,522.4 · 0.9% peak6,428.3 · 1.7% peak6,428.3 · 1.7% peak10,009.8 · 2.6% peak10,009.8 · 2.6% peak5,671 · 1.5% peak5,671 · 1.5% peak2,577.1 · 0.7% peak2,577.1 · 0.7% peak2,293.3 · 0.6% peak2,293.3 · 0.6% peak2,078.6 · 0.5% peak2,078.6 · 0.5% peak2,164.9 · 0.6% peak2,164.9 · 0.6% peak3,715.9 · 1.0% peak3,715.9 · 1.0% peak2,212 · 0.6% peak2,212 · 0.6% peak2,736.4 · 0.7% peak2,736.4 · 0.7% peak3,337.5 · 0.9% peak3,337.5 · 0.9% peak1,939.9 · 0.5% peak1,939.9 · 0.5% peak6,013.7 · 1.6% peak6,013.7 · 1.6% peak4,225.9 · 1.1% peak4,225.9 · 1.1% peak46,441.8 · 12.0% peak46,441.8 · 12.0% peak313,810.8 · 81.1% peak313,810.8 · 81.1% peak336,804.6 · 87.0% peak336,804.6 · 87.0% peak387,100.7387,100.7 · 100.0% peak387,100.7 · 100.0% peak102,047.5 · 26.4% peak102,047.5 · 26.4% peak112,652.3 · 29.1% peak112,652.3 · 29.1% peak63,085.1 · 16.3% peak63,085.1 · 16.3% peak309,891.1 · 80.1% peak309,891.1 · 80.1% peak50%#1#5#9#13#17#21#25#1 peak#2-3> μactivequietμ linecum energy
Σ vol 1739691 · peak 387101 · CV 1.78

§2 · Returns distribution (log-returns)

Histogram of rₜ = ln(pₜ/pₜ₋₁)
n=24 · 12 bins · μ=0.0068 · σ=0.0241 · skew=2.10 (right-skewed) · kurt=5.47 (leptokurtic (fat tails))108530 1-299.47bpbin -299.47bp · n=1 · 10.0% peakbin -299.47bp · n=1 · 10.0% peak 1-184.96bpbin -184.96bp · n=1 · 10.0% peakbin -184.96bp · n=1 · 10.0% peak 7-70.45bpbin -70.45bp · n=7 · 70.0% peakbin -70.45bp · n=7 · 70.0% peak 1044.06bpbin 44.06bp · n=10 · 100.0% peakbin 44.06bp · n=10 · 100.0% peak 1158.57bpbin 158.57bp · n=1 · 10.0% peakbin 158.57bp · n=1 · 10.0% peak 1273.08bpbin 273.08bp · n=1 · 10.0% peakbin 273.08bp · n=1 · 10.0% peak 2387.59bpbin 387.59bp · n=2 · 20.0% peakbin 387.59bp · n=2 · 20.0% peak502.10bp616.61bp731.12bp845.63bp 1960.14bpbin 960.14bp · n=1 · 10.0% peakbin 960.14bp · n=1 · 10.0% peakμΔ < 0 · loss barsΔ ≈ 0 · flatΔ > 0 · gain barsN(μ,σ²) referenceμ line · ±σ band shaded
n=24 · positive 14 · negative 10
Q-Q plot · standardised rₜ vs N(0,1)
n=24 · skew=2.09 · kurt=6.24 · near 10 / mid 13 / far 1 · OLS slope=0.88 intercept=-0.00LEPTOKURTIC — FAT TAILSMILDLY HEAVY UPPERLOWER TAIL NORMAL-3σ-3σ-2σ-2σ-1σ-1σ+0σ+0σ+1σ+1σ+2σ+2σ+3σ+3σΔ=+1.75σsample ↓marginal: sample bars + theoretical N(0,1) curve →theoretical Φ⁻¹(p) →↑ sample z-quantile|Δ| < 0.3σ · on the line|Δ| < 1σ · moderate|Δ| ≥ 1σ · outliery = x refOLS fit

§3 · Spot quote

Mark price
$1.1205
Mid price
$1.1195
24h change
+19.23%
Mark–mid spread
8.92 bps
Prev-day close
$0.9398

§4 · Sample moments (prices)

Descriptive statistics · 5-number summary · shape diagnostics
SAMPLE MOMENTS · N=25RIGHT-SKEWED (G₁=0.95)
μ MEAN0.9958$95% CI: [0.9623$, 1.0294$]
σ STD DEV0.0856$σ² = 73.229×10⁻⁴ · CV = 8.59%
med MEDIAN0.9443$Q₁ 0.9402$ · Q₃ 1.0905$
FIVE-NUMBER SUMMARY · BOX PLOTrange 0.2323$ · IQR 0.1503$ (1.349σ→0.1154$)
min 0.9348$Q₁ 0.9402$med 0.9443$Q₃ 1.0905$max 1.1671$μ
SKEWNESS · G₁0.951right-skewed
−3−10+1+3
EXCESS KURTOSIS · G₂-1.009platykurtic · thin tails
−30+2+4+6
μ ↔ medianμ > med · right-tailed|μ−med| / σ = 0.60
σ × 1.349 ↔ IQRdiverges from normalratio = 0.77
range ↔ σconcentrated (range < 4σ)range / σ = 2.71
μ = mean · σ = standard deviation · CV = coefficient of variation. Skew (G₁): >0 right-skewed. Kurt (G₂, excess): >0 leptokurtic. 95% CI = μ ± 1.96·SE.

§5 · Returns analytics (log-returns)

Risk-adjusted performance · log-returns
RETURNS · RISK-ADJUSTEDEXCEPTIONAL EDGE · SR=27.38
μᵣ MEAN / h+0.743854%drift is positive per h · |μ|/σ = 0.293
σᵣ STD / h2.542453%σ²ᵣ = 6.464×10⁻⁴ · CV = 3.42×
σ ANNUALISED237.96%/yrscaled by √8760 (hourly→yearly) · 2.542%/h base
RISK-ADJUSTED PERFORMANCEhigher = better edge per unit risk
SHARPE (annualised)27.38excellent · top-decile
-2-10+1+2+3+4
SORTINO (annualised)50.09strong downside-adjusted
-2-10+1+2+3+4
CALMAR (return / max-DD)100.00exceptional DD control
-20+2+4+6
RETURN-DISTRIBUTION SHAPE|skew| < 0.5 ≈ symmetric · |kurt| < 1 ≈ mesokurtic
SKEWNESS · G₁2.23right-skewed · heavy positive tail
-3-10+1+3
EXCESS KURTOSIS · G₂8.06leptokurtic · fat tails
-30+2+4+6
SORTINO vs SHARPEdownside vol < total vol · favourableSoR / SR = 1.83
CALMAR · DD CONTROLdrawdown control exceptionalCR = 100.00
EXPECTED EDGE+6516.16%/yr driftμ × 8760 = annualised expectation
rₜ = ln(pₜ/pₜ₋₁). σ × √8760 = annualised. Sharpe = μ/σ scaled; Sortino uses downside-only vol; Calmar = annual return / max drawdown.

§6 · Risk metrics

Tail risk + drawdown · downside diagnostics
TAIL & DRAWDOWN RISKHIGH · 95% VaR 2.10%
VaR₉₅ (h)2.099%5% prob of larger adverse h move
VaR₉₉ (h)3.292%1% prob · extreme-tail threshold
ES₉₅ (CVaR)2.969%expected loss given 5% tail event
MAX DRAWDOWN3.95%3h from peak to trough
TAIL-RISK LADDER (h losses)larger negative = worse · markers show severity
0 · no lossVaR₉₅−2.099%VaR₉₉−3.292%ES₉₅−2.969%worst tail ←→ zero loss
MAX DRAWDOWN PROFILEmoderate drawdown · 3h duration
PEAK116.71$
−3.95% drawdown over 3h
112.10$TROUGH
ES / VaR · TAIL THICKNESSmild tail heaviness|ES₉₅| / |VaR₉₅| = 1.41× (normal ≈ 1.25)
VaR₉₉ / VaR₉₅ · CONCENTRATIONmoderate extreme-tail concentrationratio = 1.57× (normal ≈ 1.41)
DRAWDOWN · CAPITAL DURATIONmoderate drawdownrecovery needed: +4.11% (compounding)
VaR = quantile loss · ES (CVaR) = expected loss conditional on tail · DD = peak-to-trough decline. Under normality ES₉₅/VaR₉₅ ≈ 1.25; ratio > 1.5 ⇒ fat-tail regime.

§7 · Technicals

RSI(14)
71.5 · overbought
Bollinger %B
0.807 · within band
Bollinger upper
$1.1907
Bollinger MA
$1.0104
Bollinger lower
$0.8301

§8 · Time-series structure

Regime & autocorrelation diagnostics
TIME-SERIES STRUCTUREREGIME: TRENDING · variance ratio > 1
ρ(1) AUTOCORR+0.189within white-noise band
ρ(2) AUTOCORR+0.208lag-2 not significant
H · HURST EXPONENT1.039strongly persistent
OLS TREND · t-STAT+6.678significant @ α=0.05
HURST EXPONENT [0, 1]strongly persistent · H = 1.039
H = 1.039STRONGLY PERSISTENT
0
anti-persistent0.45
mean-reverting0.5
random walk0.55
persistent1
strongly trending
AUTOCORRELATION FUNCTION · ρ(k) for k=1..5WHITE NOISE · no significant lags
k=1+0.189k=2+0.208k=3+0.067k=4-0.242k=5-0.0650+1−1+0.41−0.41+ momentum (ρ > +0.41)− reversal (ρ < −0.41)noise (within band)±2/√n threshold
OLS TREND · t-STAT · [-5, +5]SIGNIFICANT @ 1% (|t|=6.68)
−5 reject−1.960 retain H₀+1.96+5 reject
REGIME CLASSIFICATIONTRENDING · variance ratio > 1from Hurst + ρ(1) joint diagnosis
PREDICTABILITY · score 1.00very high · strong structure|ρ(1)| + 2·|H − 0.5| heuristic
TREND SIGNIFICANCESIGNIFICANT @ 1% (|t|=6.68)α=0.05 critical |t|=1.96 · α=0.01 |t|=2.58
ρ(k) = lag-k sample autocorrelation · H = R/S Hurst exponent · t = OLS-trend t-statistic. Significance bands at ±2/√n approximate the 95% white-noise envelope. α=0.05 critical |t|=1.96; α=0.01 |t|=2.58.

§9 · Microstructure

24h volume (USD)
$1.90M
Open interest (USD)
$684.94k
Vol / OI (turnover)
2.77x
1h funding
-0.001463%
Funding (annualised)
-12.82%/yr

§10 · Position sizing

Continuous Kelly (μ/σ²)
10.000× leverage · optimal log-utility leverage
Half-Kelly
5.000× · industry-standard conservative
Quarter-Kelly
2.500×

§11 · Hourly return heatmap

24-hour signed Δln-r grid · green = up · red = down
HOURLY RETURN HEATMAP · n=24 bars · best 10.17% · worst -3.57% · typical |Δ| 1.45%MILD BULLISH +17.85%BEST+10.17%01hWORST-3.57%05hTYPICAL |Δ|1.45%mean absoluteCUMULATIVE+17.85%Σ signed ΔSTREAK↘ 1down-runASIA · 00-08 UTCμ +2.06% · Σ +16.48%EUROPE · 08-16 UTCμ +0.09% · Σ +0.71%US · 16-24 UTCμ +0.08% · Σ +0.66%CUMULATIVE Δ PATH · final +17.85%+21.88%-0.31%0.26% · 08h0.26% · 08h0.26%08h-0.28% · 09h-0.28% · 09h-0.28%09h-0.09% · 10h-0.09% · 10h-0.09%10h-0.20% · 11h-0.20% · 11h-0.20%11h0.69% · 12h0.69% · 12h0.69%12h0.87% · 13h0.87% · 13h0.87%13h-0.55% · 14h-0.55% · 14h-0.55%14h0.02% · 15h0.02% · 15h0.02%15h-0.17% · 16h-0.17% · 16h-0.17%16h0.41% · 17h0.41% · 17h0.41%17h-0.54% · 18h-0.54% · 18h-0.54%18h-0.30% · 19h-0.30% · 19h-0.30%19h0.42% · 20h0.42% · 20h0.42%20h-0.34% · 21h-0.34% · 21h-0.34%21h0.52% · 22h0.52% · 22h0.52%22h0.66% · 23h0.66% · 23h0.66%23h3.55% · 00h3.55% · 00h3.55%00h10.17% · 01h10.17% · 01h10.17%01h★ BEST2.60% · 02h2.60% · 02h2.60%02h0.52% · 03h0.52% · 03h0.52%03h3.67% · 04h3.67% · 04h3.67%04h-3.57% · 05h-3.57% · 05h-3.57%05h▼ WORST1.91% · 06h1.91% · 06h1.91%06h-2.37% · 07h-2.37% · 07h-2.37%07hTIME PATTERNAsia-led (+16.48%)RUNSup max 7 · down max 3BREADTH58% up · 42% down
14 up bars · 10 down · best 10.17% · worst -3.57% · typical |Δ| 1.446%

§12 · Equity curve & underwater drawdown

Cumulative compounded return + running peak-to-trough
EQUITY & DRAWDOWN ANALYSIS · n=25 barsPROFITABLE +18.62%FINAL+18.62%MAX DD-4.06%RECOVERYONGOING · 3 barsMAX RUN-UP+23.64%UNDERWATER15/25 (60%)STREAK↘ 1EQUITY CURVE · end 1.1862 · peak 1.2364 · range [0.9969, 1.2364]1.23640.9969break-even = 1★ PEAK 1.2364UNDERWATER DRAWDOWN · max -4.06% · moderate0%-4.06%▼ TROUGH -4.06%TOP DRAWDOWN PERIODS · 3 total#1 -4.06%bar 23-25 · 3 bars · ONGOING#2 -1.14%bar 8-16 · 9 bars · recovered#3 -0.57%bar 3-5 · 3 bars · recoveredDD SEVERITYmoderate (max -4.06%)RECOVERYongoing · 3 barsTIME UNDER WATER60% of session · 15/25 bars
final equity 1.1862 (18.62%) · max DD -4.06% · time-under-water 15/25 bars

§13 · Rolling-window statistics (w = 6 bars)

Rolling annualised Sharpe ratio · green positive · red negative
n=19 · +16 / −3 (84% positive) · μ=28.58 · σ=35.67PROFITABLE STRATEGYLAST 14.98 (-0.38σ vs μ)93.5846.790.00-46.79-93.58μ = 28.5840.2940.2911.8511.8520.8720.8718.4918.4936.3336.330.830.83-48.88-48.88-6.70-6.70-20.18-20.185.235.2312.4712.4748.9648.9658.5658.5669.3069.3075.3075.3093.5893.5858.6758.6753.0253.0214.9814.98v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest 14.984 · range [-48.88, 93.58] · μ 28.578 · positive Sharpe = excess-return-per-risk earned by buying-and-holding through this window
Rolling annualised volatility (%)
n=19 · μ=166.7405 · σ=156.8738 · range [34.1699, 421.6893] · R²=0.687▲ RISING +493.22%σ EXTREME 94.08%LAST 268.7853421.6893324.8095227.9296131.049834.1699μ = 166.7405max 421.6893min 34.1699dataMA(3)OLS R²=0.69μ lineμ ± σ bandmaxmin
latest 268.79% · range [34.17%, 421.69%] · μ 166.74% · σ̂ scaled to annualised (×√8760)
Rolling lag-1 autocorrelation ρ(1)
n=19 · +6 / −13 (32% positive) · μ=-0.111 · σ=0.263MEAN-REVERSIONLAST -0.547 (-1.66σ vs μ)0.5470.2740.000-0.274-0.547μ = -0.1110.3120.312-0.044-0.044-0.082-0.082-0.100-0.100-0.026-0.026-0.503-0.503-0.338-0.338-0.361-0.361-0.490-0.490-0.439-0.4390.0230.0230.0720.0720.2670.2670.1910.1910.0940.094-0.060-0.060-0.031-0.031-0.049-0.049-0.547-0.547v > 0 · positivev < 0 · negativeμ mean lineμ ± σ bandlatest bar (outlined)
latest -0.547 · |ρ| > 0.3 ⇒ regime with persistence (ρ > 0) or reversal (ρ < 0) · |ρ| ≤ 0.1 = consistent with random walk

§14 · Hypothesis tests (α = 0.05)

Formal inference at 5% significance
2 of 6 REJECT · mixed evidence2 reject·4 pass·α = 0.05
𝒩

Jarque-Bera

REJECT H₀***

H₀: Δln-r ~ Normal(μ, σ²)

STATISTIC
84.9191
p-VALUE (log scale)
< 0.0001
α
10⁻⁴10⁻³10⁻²10⁻¹1
p < α · rejection zonenon-normal · fat tails or skew present
ρ

Ljung-Box(h=5)

FAIL TO REJECTns

H₀: No serial autocorrelation up to lag 5

STATISTIC
4.2884
p-VALUE (log scale)
0.5103
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedconsistent with white noise
Ψ

Dickey-Fuller (τ_μ)

FAIL TO REJECTns

H₀: p has a unit root (non-stationary)

STATISTIC
-0.1770
p-VALUE (log scale)
0.9355
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedrandom-walk behaviour (crit ≈ -2.86)
±

Wald-Wolfowitz runs

FAIL TO REJECTns

H₀: Sign sequence of Δ is random

STATISTIC
0.5732
p-VALUE (log scale)
0.5665
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedsigns appear random (14 runs)
χ

KPSS (μ stationarity)

REJECT H₀*

H₀: p IS level-stationary

STATISTIC
0.6752
p-VALUE (log scale)
0.0158
α
10⁻⁴10⁻³10⁻²10⁻¹1
p < α · rejection zonenon-stationary (crit 0.463)
χ

Variance ratio q=3

FAIL TO REJECTns

H₀: Δln-r is a random walk · VR = 1

STATISTIC
1.5686
p-VALUE (log scale)
0.1167
α
10⁻⁴10⁻³10⁻²10⁻¹1
p ≥ α · null retainedVR 1.477 ≈ 1 (RW behaviour)
Each row states an explicit null H₀, the test statistic, an approximated p-value, and the decision. REJECT means evidence against H₀. KPSS complements ADF (rejecting both ⇒ ambiguous; rejecting one ⇒ clean verdict).

§15 · Spectral analysis (DFT periodogram)

Power spectrum of Δln-r · ‖X̂(k)‖²/n
n=12 bins · noise floor μ=6.27e-4 · top T=12.00h (21.7%) · top-3 cover 50.9%2 SIGNIFICANT CYCLEScumulative energy ↗ (2 bins above 2× noise)1.6e-31.2e-38.2e-44.1e-40.0e+0μ noise floor2× noise (significance)period 24.0 · power 1.37e-3 · 18.2% energyperiod 24.0 · power 1.37e-3 · 18.2% energyperiod 12.0 · power 1.63e-3 · 21.7% energyperiod 12.0 · power 1.63e-3 · 21.7% energyperiod 8.0 · power 6.89e-4 · 9.2% energyperiod 8.0 · power 6.89e-4 · 9.2% energyperiod 6.0 · power 4.17e-4 · 5.5% energyperiod 6.0 · power 4.17e-4 · 5.5% energyperiod 4.8 · power 2.07e-4 · 2.7% energyperiod 4.8 · power 2.07e-4 · 2.7% energyperiod 4.0 · power 4.21e-4 · 5.6% energyperiod 4.0 · power 4.21e-4 · 5.6% energyperiod 3.4 · power 1.38e-4 · 1.8% energyperiod 3.4 · power 1.38e-4 · 1.8% energyperiod 3.0 · power 4.73e-4 · 6.3% energyperiod 3.0 · power 4.73e-4 · 6.3% energyperiod 2.7 · power 8.29e-4 · 11.0% energyperiod 2.7 · power 8.29e-4 · 11.0% energyperiod 2.4 · power 7.28e-4 · 9.7% energyperiod 2.4 · power 7.28e-4 · 9.7% energyperiod 2.2 · power 4.40e-4 · 5.8% energyperiod 2.2 · power 4.40e-4 · 5.8% energyperiod 2.0 · power 1.87e-4 · 2.5% energyperiod 2.0 · power 1.87e-4 · 2.5% energy50% by T=6.0h#1 dominantT=12.00h#2T=24.00h#3T=2.67hT=2hT=3hT=4hT=6hT=8hT=12hT=16hT=24h← shorter cycle (high freq · Nyquist=½) · period T (bars per cycle) · longer cycle (low freq · 1/n) →#1 dominant#2 peak#3 peak> 2× noisenoiseμ floor2μ sig.cum energy
dominant period ≈ 12.00h (freq 0.083) · concentrates 21.7% of total energy · Σ|X̂|²/n = 7.527e-3

▸ Depth section using sovereign-store price series (4731 bars · effective 5249975 bars/year) — annualisation reflects native polling cadence, not upstream timeframes.

§16 · NOSTRADAMUS continuous quant — perp leverage & bootstrap MC

Continuous-price extension of the prediction-market quant module. Kelly growth on observed returns (Merton μ/σ² parametric vs argmax empirical), Monte-Carlo equity fan bootstrapped from the historical return distribution at quarter-Kelly leverage, and an annualized return decomposition. Sweep parameters in the simulator.

§17 · Continuous Kelly

Continuous-Kelly growth · g(f) = E[ln(1 + f·r)]
f★ empirical 7.43× · g(f★) 0.012%/barparametric μ/σ² 3.98× · μ 0.004% · σ 0.32%
μ per barmean
0.004%
σ per barvol
0.32%
Empirical f★argmax g(f)
7.43×
from observed distribution
Parametric f★μ/σ²
3.98×
Merton continuous-time
Half-Kelly½ f★
3.72×
~⅔ of full growth, half the variance
Quarter-Kelly¼ f★
1.86×
industry default — survives model error
0.00%0.00%0.01%0.01%0.01%0.0×1.6×3.2×4.8×6.4×8.0×f★ empμ/σ²leverage fraction fexpected log-growth per bar
g(f) empiricalf★ argmaxparametric f★
Maximum expected log-growth from leveraging the historical return distribution. Empirical f★ argmaxes the sample expectation; parametric f★ = μ/σ² is Merton's continuous-time optimum.

§18 · MC equity fan

Bootstrapped equity fan at 1.00× leverage
Median CAGR/bar 0.001% · annualized Sharpe 32.37400 paths × 720 bars · leverage 1.00× · bootstrap from 4730 observed returns
Sharpe / barμ/σ
0.014
annualized 32.37
μ per barafter L
0.005%
σ per barafter L
0.33%
VaR 95%5%
0.07%
per-bar worst-case
CVaR 95%ES
0.25%
mean tail loss
Max DD (median)MDD
-0.3%
0.90×0.98×1.06×1.14×1.21×1.29×0120240360480600720startbar #equity multiple
median25/75 band5/95 band
Median path with 25/75 and 5/95 percentile bands across 400 simulated careers. Bars resample with replacement from the observed return distribution — preserves fat tails the parametric model misses.

§19 · Annualized breakdown

Annualized return components
APR 1000% · APY 1000% · Sharpe 28.82σ ann 724% · Sortino 61.10 · n 4730 · ⚠ capped (n=4730 too small to support 8760-bar projection)
0%1467%2933%4400%5866%7333%1000.0%APR (simple)1000.0%APY (compound)723.9%Ann. vol σ2881.9%Sharpe (ann)6110.5%Sortino (ann)
Simple APR vs compounded APY · annualized volatility · risk-adjusted Sharpe and Sortino. All scaled by √(periods/yr).

§20 · GARCH(1,1) volatility band

GARCH(1,1) · conditional vol envelope (±2σ)
GARCH persistence α+β = 0.980· σ̂ₜ = 1.002% · long-run σ = 2.236%
0.8460.9321.0191.1051.1921.278t-4730t-3942t-3153t-2365t-1577t-788t-0

Persistence near 1 ⇒ vol clusters strongly (slow mean reversion). Long-run σ is the unconditional target the conditional vol orbits. The ±2σ band reflects time-varying scale, unlike a flat-vol band.

Time-varying volatility band fitted to the price series. Persistence α+β > 0.98 means vol shocks decay slowly — recent moves stay relevant.

§∞ · Provenance & attestation

Upstream
api.hyperliquid.xyz
Snapshot fetched
2026-06-20 07:57:07 UTC
Snapshot age
3.5s
History points
25 hourly closes
Page rendered
2026-06-20 07:57:11 UTC
Storage policy
no persistence — fetched on every request
SHA-256 attestation
fd4cdeac5d359a5816ee10e40867db835e7e09ff82fd69defda8d28a5a9596b6 · deterministic hash of the source snapshot — proves this page was rendered from this exact data
Open data licence
CC0 / public domain · free to mirror, syndicate, analyse

§∞-2 · Related markets · explore more

HL PREDSpain88.4¢HL PREDEcuador86.5¢HL PREDUruguay67.8¢HL PERPBTC-USD perpetual$63,676HL PERPHYPE-USD perpetual$70.12HL PERPETH-USD perpetual$1,725.3

Also see: /arb opportunities · RSS feed

Market depth

▸ live order book · Hyperliquid perp
Depth within 1bp
$0
bid $0 · ask $0
Depth within 5bp
$3.15K
bid $2.83K · ask $314
Depth within 10bp
$6.26K
bid $5.06K · ask $1.20K
Depth within 50bp
$39.23K
bid $27.69K · ask $11.55K
Mid price
1.119350
(best bid + best ask) / 2
Spread
9.8bp
(bestAsk − bestBid) / mid
Imbalance (whole book)
+0.417
bid-heavy
Imbalance (top-5)
+0.480
bid-heavy top-of-book

Slippage scenarios

▸ live book walk · Hyperliquid perp

Simulating a market order at three notionals against the live book. Slippage = avg execution price vs. mid, in basis points. Worst fill = price of the deepest level touched. Live JSON: /api/asset/hl-axs/slippage?size=10000&side=buy

SideNotionalAvg fillSlippageWorst fillLevelsStatus
BUY$1.00K1.12005.53bp1.12002FILLED
BUY$10.00K1.122023.56bp1.123416FILLED
BUY$100.00K1.122225.87bp1.124820PARTIAL
SELL$1.00K1.11884.91bp1.11881FILLED
SELL$10.00K1.118012.05bp1.11639FILLED
SELL$100.00K1.115930.49bp1.113420PARTIAL

Funding carry

▸ SHORTS PAY · longs receive
Hourly funding
-1.463e-5
-0.00146% / hr
Annualised APR
-12.828%
hourly · 24 · 365.25
Long: days to 1% carry
28.5d
longs receive
Short: days to 1% carry
28.5d
shorts pay
SideDirectionAnnualised carryDays → 1%Days → 10%
LONGRECEIVE12.828%28.5d284.7d
SHORTPAY-12.828%28.5d284.7d

/api/asset/hl-axs/carry · same metrics, JSON

Volume profile

▸ real volume · Hyperliquid candlesstep $ 1 · 25 records
Price binBarsVolumeDistribution
$1.0000–$2.0000★7$1.63M
$0.000000–$1.000018$114.30K

★ POC = Point of Control (highest-volume bin). Live JSON: /api/asset/hl-axs/volprofile?priceStep=1

Order flow

▸ BID-LEAN · +0.477 · Hyperliquid candles
Bars (buy / sell)
14 / 10
1 unclassified
Buy weight
$1.28M
real volume
Sell weight
$453.85K
real volume
Net delta
$828.30K
buyers net
Imbalance
47.71%
(buy − sell) / (buy + sell)
Toxicity (VPIN)
47.7%
two-sided / balanced
Impact (|Δp|/vol)
—
needs real volume

Sparkline = cumulative delta over the 25-record window./api/asset/hl-axs/flow?rollingWindow=30

Cascade clusters

▸ DOWN · 4 found · deepest 3.95% · Hyperliquid candles

Price-only proxy for forced-unwind clusters. No exchange liquidation feed is wired — read each row as a candidate event, not a confirmed liquidation.

#WindowDurationPeak → TroughDrawdownBars
#12026-06-20 05:00:00Z2.0h1.1671→1.12103.950%3
#22026-06-19 18:00:00Z1.0h0.946680→0.9387200.841%2
#32026-06-19 14:00:00Z2.0h0.949520→0.9428500.702%3

/api/asset/hl-axs/cascades?windowMs=10800000&minDrawdownPct=0.005 · full list + parameters in JSON

Risk metrics

▸ sovereign store · 4,731 barsperiods/year ≈ 5.25M
Realized vol (annualised)
723.87%
σ per bar = 0.003159
Mean return (annualised)
20861.06%
μ per bar = 0.000040
Sharpe (rf=0)
28.82
annualised; risk-free assumed zero
Max drawdown
8.76%
peak 1.02 → trough 0.93 over 3981 bars

/api/asset/hl-axs/risk · same metrics, JSON