This paper introduces a new approach to the modelling of a stationary long run component, which is an autoregressive process with near unit root and small sigma innovation. We show that a combination of a noise and a long run component can explain the long run predictability puzzle pointed out...

Newey, Steigerwald (1997) considered a univariate conditionally heteroscedastic model, with independent and identically distributed errors. They showed that the parameters characterizing the serial dependence are consistently estimated by any pseudo maximum likelihood approach, whenever two...

In a transformation model $\by_t = c [\ba(\bx_t,\bbeta), \bu_t]$, where the errors $\bu_t$ are i.i.d and independent of the explanatory variables $\bx_t$, the parameters can be estimated by a pseudo-maximum likelihood (PML) method, that is, by using a misspecified distribution of the errors, but...

We prove the uniqueness of linear i.i.d. representations of heavy-tailed processes whose distribution belongs to the domain of attraction of an $\alpha$-stable law, with $\alpha2$. This shows the possibility to identify nonparametrically both the sequence of two-sided moving average coefficients...

The noncausal autoregressive process with heavy-tailed errors possesses a nonlinear causal dynamics, which allows for %unit root, local explosion or asymmetric cycles often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly...