LOG - NORMAL ERROR INNOVATIONS AUTOREGRESSIVE TIME SERIES MODEL

Abstract

In order to develop dynamic time series models, the error terms were assumed to have regular
white noise when data deviate from gussian assumption and does not follow normal distribution,
this frequently leads to parameter estimations error and inflated forecast performance. Hence, in
this study, the estimation of parameters for the Autoregressive model with Lognormal error
innovations was accomplished through a maximum likelihood approach. To evaluate the
effectiveness of these Lognormal error innovations, the parameters of the AR(2) model were
compared against those of a standard model with regular error innovations, using criteria such
as the Akaike information criterion (AIC) and forecast performance measures, including the
Root Mean Squared Error and Mean Absolute Error. The models were Furthermore subjected
to validation across various sample sizes. The results of this analysis consistently indicate that
the Autoregressive model (AR(2)) with Lognormal error innovations outperforms its counterpart
with regular error innovations, making it a more effective and suitable choice for modeling non-
normal time series processes.