Adaptive Student's t-distribution with method of moments moving estimator for nonstationary time series

Abstract

The real life time series are usually nonstationary, bringing a difficult question of model adaptation. Classical approaches like ARMA-ARCH assume arbitrary type of dependence. To avoid their bias, we will focus on recently proposed agnostic philosophy of moving estimator: in time t finding parameters optimizing e.g. F_t=_<t (1-)^t- (_ (x_)) moving log-likelihood, evolving in time. It allows for example to estimate parameters using inexpensive exponential moving averages (EMA), like absolute central moments m_p=E[|x-|^p] evolving for one or multiple powers pR^+ using m_p,t+1 = m_p,t + (|x_t-_t|^p-m_p,t). Application of such general adaptive methods of moments will be presented on Student's t-distribution, popular especially in economical applications, here applied to log-returns of DJIA companies. While standard ARMA-ARCH approaches provide evolution of and , here we also get evolution of describing (x) |x|^--1 tail shape, probability of extreme events - which might turn out catastrophic, destabilizing the market.

Tasks

Reproductions