<p>We introduce <i>Drift Radar</i>, an anytime-valid detector of distributional shifts in multivariate financial streams. The method compares adjacent (or seasonality-matched) windows using a panel of nonparametric two-sample functionals—random Fourier features (RFF) MMD, energy distance, sliced Wasserstein, rank-based dependence (Spearman), and short-lag autocorrelation—each standardized on a stable baseline. Standardized scores are aggregated at every update into a test martingale (e-process), triggering segment-wise calibrated alarms when the evidence exceeds <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1/\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mi>α</mi> </mrow> </math></EquationSource> </InlineEquation>. Two design elements make the approach operational: (i) <i>mixtures across scales</i> (e-values averaged over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L\in \{60,200,600\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>60</mn> <mo>,</mo> <mn>200</mn> <mo>,</mo> <mn>600</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>) to capture both fast and slow drift; and (ii) <i>scheduled restarts</i> (e.g., every 6&#xa0;h, yielding segment-wise anytime validity at level <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) to localize evidence and prevent carryover across segments. On five stylized scenarios (mean, volatility, correlation, tail index, AR(1) shifts), Drift Radar detects promptly where appropriate and, at higher sensitivity, responds to temporal and dependence reconfigurations that elude mean-only detectors. In a BTC/USD 1-minute study around the April 2024 Bitcoin halving, we observe repeated <i>post-event</i> alarms under 6-hour restarts, attribution indicates that the dominant deviations are captured by distance-based components (energy distance, MMD, and sliced <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(W_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>), with smaller contributions from rank-dependence and short-lag autocorrelation. Compared to KS/PSI, variance–CUSUM/Page–Hinkley, and an RFF–KCUSUM baseline, Drift Radar provides calibrated, interpretable, and streaming-friendly detection with <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(O(Ld+d^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mi>L</mi> <mi>d</mi> <mo>+</mo> <msup> <mi>d</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> memory per active scale.</p>

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Anytime nonparametric detection of distributional shifts in financial data via e-process mixtures

  • Tomislav Kesić,
  • Goran Oblaković,
  • Mato Njavro,
  • Andrej Novak

摘要

We introduce Drift Radar, an anytime-valid detector of distributional shifts in multivariate financial streams. The method compares adjacent (or seasonality-matched) windows using a panel of nonparametric two-sample functionals—random Fourier features (RFF) MMD, energy distance, sliced Wasserstein, rank-based dependence (Spearman), and short-lag autocorrelation—each standardized on a stable baseline. Standardized scores are aggregated at every update into a test martingale (e-process), triggering segment-wise calibrated alarms when the evidence exceeds \(1/\alpha \) 1 / α . Two design elements make the approach operational: (i) mixtures across scales (e-values averaged over \(L\in \{60,200,600\}\) L { 60 , 200 , 600 } ) to capture both fast and slow drift; and (ii) scheduled restarts (e.g., every 6 h, yielding segment-wise anytime validity at level \(\alpha \) α ) to localize evidence and prevent carryover across segments. On five stylized scenarios (mean, volatility, correlation, tail index, AR(1) shifts), Drift Radar detects promptly where appropriate and, at higher sensitivity, responds to temporal and dependence reconfigurations that elude mean-only detectors. In a BTC/USD 1-minute study around the April 2024 Bitcoin halving, we observe repeated post-event alarms under 6-hour restarts, attribution indicates that the dominant deviations are captured by distance-based components (energy distance, MMD, and sliced \(W_1\) W 1 ), with smaller contributions from rank-dependence and short-lag autocorrelation. Compared to KS/PSI, variance–CUSUM/Page–Hinkley, and an RFF–KCUSUM baseline, Drift Radar provides calibrated, interpretable, and streaming-friendly detection with \(O(Ld+d^2)\) O ( L d + d 2 ) memory per active scale.