Path-Explosive Behaviour in Economic Time Series: A Realization-Centred Exploratory Framework

We propose a descriptive, realization-centred framework for detecting and characterising explosive and co-explosive behaviour in economic time series, which we term path-explosive behaviour. Departing from the data-generating-process (DGP) perspective that underlies recursive unit root testing, the approach operates directly on observable path properties of the realised series. Four diagnostic layers -- level geometry, growth rate dynamics, normalised curvature, and log-space behaviour -- yield statistics that discriminate between genuine self-reinforcing multiplicative growth and I(2) dynamics without distributional assumptions or asymptotic critical values. Two theoretically motivated absolute gate thresholds screen detected episodes before a composite intensity score is assigned. Co-explosive behaviour between pairs of series is assessed at the episode level through a Jaccard co-occurrence index and non-parametric intensity concordance measures. The theoretical motivation draws on the path dependence and planning irreversibility literatures to argue that, in settings where discrete institutional decisions shape growth trajectories, a realization-centred characterisation is epistemically more appropriate than a DGP-based test. A simulation study across four DGP regimes validates the framework's discriminating power and conservatism. An empirical application to real house prices, commodity prices, public debt, and Spanish tourism destinations illustrates the empirical content of the path-explosive concept and distinguishes it from speculative bubble detection.