Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional moments of noncausal alpha-stable processes and the
  prediction of bubble crash odds   Noncausal, or anticipative, heavy-tailed processes generate trajectories
featuring locally explosive episodes akin to speculative bubbles in financial
time series data. For $(X_t)$ a two-sided infinite $\alpha$-stable moving
average (MA), conditional moments up to integer order four are shown to exist
provided $(X_t)$ is anticipative enough, despite the process featuring infinite
marginal variance. Formulae of these moments at any forecast horizon under any
admissible parameterisation are provided. Under the assumption of errors with
regularly varying tails, closed-form formulae 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 $\rho$ and tail exponent
$\alpha$ generates bubbles whose survival distributions are geometric with
parameter $\rho^{\alpha}$. 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 \`a la Blanchard and Watson (1982) which could
reconcile rational bubbles with tail exponents greater than 1. Applications of
the conditional moments to bubble modelling by noncausal processes are
discussed and the use of the closed-form crash odds is illustrated on the
Nasdaq and S&P500 series.

24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th