Sébastien FRIES (Vrije Universiteit Amsterdam) FORECASTING HEAVY-TAILED NONCAUSAL PROCESSES AND BUBBLE CRASH ODD
December 10, 11:30 am - 12:30 pm
FINANCIAL ECONOMETRICS SEMINAR
Date: 10th of December 2020
Sébastien FRIES (Vrije Universiteit Amsterdam) “Forecasting Heavy-Tailed Noncausal Processes and Bubble Crash Odd”
Abstract : 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 alpha-stable moving average, conditional moments up to integer-order four are shown to exist provided Xt is anticipative enough. Formulae of these moments at any forecast horizon are provided. Under the assumption of errors with regularly varying tails, closed-form formulae of the crash odds during explosive bubble episodes are obtained. 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 ρα. 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 could reconcile rational bubbles with tail exponents greater than 1. The use of the conditional moments is illustrated in a bubble-timing portfolio allocation framework, and an application of the closed-form predictive crash odds to the Nasdaq and S&P500 series is provided.
Jean-Michel ZAKOIAN (CREST )
CREST and ILB
Address : ENSAE ParisTech
5, avenue Henry Le Chatelier
How to come?