Conditional Moments of Noncausal Alpha-Stable Processes and the Prediction of Bubble Crash Odds
Bibliographic Data
| ID | 19419877 |
|---|---|
| Authors | Sébastien Fries (0000-0003-1204-5532, Vrije Universiteit Amsterdam, corresponding author) |
| Year | 2022 |
| Volume | 40 |
| Issue | 4 |
| Pages | 1596-1616 |
| Publication date | 2022-10-02 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Journal of Business and Economic Statistics (JOURNAL) |
| Journal identifiers | ISSN: 0735-0015 • E-ISSN: 1537-2707 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/07350015.2021.1953508 |
| OpenAlex | W2992057657 |
| Language | EN |
| Citations received | 1 |
| References cited | 35 |
Noncausal, or anticipative, heavy-tailed processes generate trajectories featuring locally explosive episodes akin to speculative bubbles in financial time series data. For (Xt) a two-sided infinite α-stable moving average (MA), conditional moments up to integer order four are shown to exist provided (Xt) is anticipative enough, despite the process featuring infinite marginal variance. Formulas of these moments at any forecast horizon under any admissible parameterization are provided. Under the assumption of errors with regularly varying tails, closed-form formulas of the predictive distribution during explosive bubble episodes are obtained and expressions of the ex ante crash odds at any horizon are available. It is found that the noncausal autoregression of order 1 (AR(1)) with AR coefficient ρ and tail exponent α generates bubbles whose survival distributions are geometric with parameter ρ^α. This property extends to bubbles with arbitrarily shaped collapse after the peak, provided the inflation phase is noncausal AR(1)-like. It appears that mixed causal–noncausal processes generate explosive episodes with dynamics à la Blanchard and Watson which could reconcile rational bubbles with tail exponents greater than 1
Bubble · Conditional probability distribution · Economics · Explosive material · Exponent · Mechanics · Physics · Statistical physics · Statistics · Complex Systems and Time Series Analysis · Financial Risk and Volatility Modeling · Market Dynamics and Volatility · Mathematics · Applied Mathematics · Finance
| Citations per year | 1 |
|---|---|
| Citation span | 2025 - 2025 (1) |
| Highly cited | No |