ursigma.org / research memorandum

Asymmetric Tail Dependence as a Market Signal Layer

A research interface for downside co-movement, event clustering, and the $URSIG attention tape.

The claim is not that one market mechanically controls another. The claim is narrower: downside tails may have their own dependence structure.

visual identity

Ursigma Research Desk

The bear is the paper-facing identity: slower, more academic, less terminal noise. It frames $URSIG as a research tape, not a price oracle.

Abstract

Ursigma studies cross-asset stress through asymmetric tail dependence: the possibility that joint downside moves synchronize more strongly than ordinary returns or upside moves.

The instrument avoids hard causal language. Each venue is treated as an event stream. Lower-tail events, volatility bursts, and attention shocks become a neutral public readout. The $URSIG token is the social layer attached to that readout, not the source of the move.

The goal is a live stress surface: a compact interface that tracks when tails cluster, whether lower-tail dependence exceeds upper-tail dependence, and how quickly event intensity decays after shock.

Object

Tail events

Dependence

Asymmetric

Dynamics

Self-exciting

Tape

$URSIG

Research Questions

Does lower-tail co-movement exceed upper-tail co-movement after returns are mapped into standardized quantiles?

Do tail events arrive independently, or do they cluster after an initial shock?

Can clustered event intensity become a public signal without pretending to be a directional forecast?

Once the stress tape is public, does attention itself behave like a secondary self-exciting process?

K-line Diagnostic Panel

The panel below is a diagnostic schematic, not a price forecast. Candles become return observations. Observations beyond a lower-quantile threshold become downside tail events. Those events feed the Hawkes intensity and the attention surface.

green/red candles = raw OHLCdashed line = lower-tail thresholdpink bars = extracted tail eventsgold curve = event intensity

Mathematical Framework

The framework combines return normalization, copula separation, empirical tail-dependence estimation, quantile-response checks, and multivariate Hawkes event dynamics.

Log returnr_i,t = log(P_i,t) - log(P_i,t-delta)

Lower-tail eventD_i,t(q) = 1{ r_i,t <= Q_i(q) }

Upper-tail eventU_i,t(q) = 1{ r_i,t >= Q_i(1-q) }

Empirical lower-tail dependencelambda_L(q) = sum 1{D_x=1, D_y=1} / sum 1{D_x=1}

Empirical upper-tail dependencelambda_U(q) = sum 1{U_x=1, U_y=1} / sum 1{U_x=1}

Asymmetry scoreA(q) = lambda_L(q) - lambda_U(q)

Copula decompositionH(x,y) = C(F_x(x), F_y(y))

Quantile responseQ_y(tau | x) = beta_0(tau) + beta_1(tau)x + beta_2(tau)x^2

Multivariate Hawkeslambda_i(t) = mu_i + sum_j integral phi_ij(t-s)dN_j(s)

Exponential kernelphi_ij(u) = alpha_ij exp(-beta_ij u), u > 0

Stability conditionspectral_radius( integral_0^infinity Phi(u)du ) < 1

Attention surfacelambda_URSIG(t) = nu + rho lambda_tail(t) + integral eta exp(-kappa(t-s)) dN_URSIG(s)

Estimation Stack

1. Clean returns

Use log returns, missing-candle handling, winsorization checks, and rolling volatility normalization.

2. Define tails

Estimate rolling thresholds at q = 1%, 2.5%, and 5%. Threshold choice stays visible instead of being buried in the backend.

3. Estimate dependence

Compute lambda_L(q), lambda_U(q), and A(q). A positive A(q) supports lower-tail asymmetry; it does not prove causality.

4. Fit event intensity

Fit Hawkes kernels on timestamped event indicators, then compare them against a Poisson baseline to test whether clustering is real.

5. Publish state

Expose only interpretable outputs: tail state, clustering intensity, decay speed, and model confidence.

Protocol Design

Convert raw OHLC candles into standardized return events.
Separate normal-state correlation from tail-state dependence.
Track lower-tail and upper-tail dependence independently.
Use a Hawkes kernel to measure whether stress events self-excite or quickly decay.
Publish the live state as a neutral stress-and-attention readout.
Keep the token layer honest: it is an attention tape, not an oracle.

Limitations And Non-Claims

No causal pathway is asserted. The model observes dependence and event clustering, not mechanical control.

Tail dependence can be regime-specific and unstable. A relationship visible in one window can disappear in another.

A statistically interesting signal is not automatically tradable after slippage, fees, latency, and model error.

Copula and Hawkes models are sensitive to threshold selection, time aggregation, and non-stationarity.

The $URSIG layer is a public attention wrapper around the readout, not a pricing oracle or investment recommendation.

References / Concepts

Tail dependenceCo-movement in distribution tails; ordinary correlation can miss it.

Extreme value theoryA statistical toolkit for rare events, threshold exceedances, and tail behavior.

CopulaA way to separate marginal distributions from dependence structure.

Quantile regressionA method for studying conditional behavior at different parts of a distribution.

Hawkes processA self-exciting point process where events temporarily raise future event intensity.

Branching ratioA stability diagnostic for whether event cascades decay or become explosive.

Tail dependence Copula Hawkes process