Journal
Stochastic Processes and their Applications
Volume 150
(2022),
p. 886
Anchovy (Engraulis ringens) and Pacific sardine (Sardinops sagax) variability changes in northern Chile associated with the environment and inter species synchronicity: GARCH model with exogenous variable and hybrid Bayesian deep learning estimation approach
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.
On Lamperti transformation and AR(1) type characterisations of discrete random fields
Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2022 (MATHTECH 2022): Navigating the Everchanging Norm with Mathematics and Technology