IRSFPThe study PSI: Predicting Instability and Critical Transitions in Financial Markets (Martin Petrásek, 24 May 2026) investigates whether the risk of a financial-regime shift can be described jointly by volatility and the rate at which market fluctuations relax. Here, PSI stands for Perturbation Susceptibility Index. The result is a research indicator of susceptibility to rising volatility, not a model predicting price direction or investment advice.
Abstract and research question
Financial markets exhibit volatility clustering, nonlinear responses to information and abrupt transitions between calm and unstable regimes. The manuscript asks whether current volatility alone adequately captures loss of stability, or whether a measure of slowing system response should be added. Its practical question is whether high PSI precedes subsequent increases in realised volatility and intraday regime changes.
Mathematical definition
The manuscript's fundamental relation is PSI = σ / λ². Here, σ denotes realised volatility, used as a proxy for the intensity of market perturbations. The parameter λ describes relaxation inferred from the time series' autocorrelation structure. Dividing by λ squared means that weaker relaxation raises the indicator even at a comparable amplitude of price fluctuations. This relation defines the proposed model; it is not, by itself, evidence of predictive value.
Empirical material and methods
The author describes historical-data analysis across cryptocurrency futures, commodity and energy markets, index futures and stock indices. Particular attention is given to intraday series at one-, five-, fifteen-minute and hourly resolution. The manuscript compares extreme PSI values with subsequent realised volatility, tests conditional differences at similar current volatility, examines regime transitions and presents multiscale variants. It also discusses window-length sensitivity, walk-forward evaluation and comparisons with baseline indicators.
What the paper actually reports
According to the results section, the strongest associations occurred in liquid intraday markets, particularly index futures, SPY and bitcoin futures; energy futures were also analysed. In some intraday datasets, future realised volatility after extreme PSI states exceeded twice the usual intraday average. For selected intraday index and futures data, conditional comparisons report approximately 15–30% higher subsequent volatility at high PSI than in regimes with similar current volatility and lower PSI. These figures are reported in the preprint, rather than independently recalculated here.
An important negative finding is that some daily, low-frequency datasets supplied no consistent additional information beyond realised volatility alone. The manuscript also acknowledges that a volatility-only model may sometimes match or outperform basic one-dimensional PSI. The study therefore does not establish universal validity for the indicator.
Interpretation and limits
The paper interprets PSI as a supplementary measure of structural susceptibility to instability. It does not establish an ability to predict price direction or justify claims of guaranteed trading advantage. An overlap between rising PSI and subsequent volatility does not establish general causality: financial data are non-stationary, and results depend on temporal resolution, liquidity, market microstructure and the computational window.
Requirements for further validation
Independent assessment requires reproducing the individual data subsets and parameters, comparing PSI against volatility models specified in advance on equal terms, monitoring false alarms and evaluating stability across new market regimes. These are requirements for subsequent replication, not results already achieved. The framework's scientific value depends on whether the extra information from relaxation persists in previously unused data.
Publications and related studies
Martin Petrásek (2026), PSI: Predicting Instability and Critical Transitions in Financial Markets, a preprint by the author. DOI: 10.5281/zenodo.20364144 ↗. Public full text ↗. This page provides a scholarly interpretation of the manuscript, not evidence of external peer review.
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