Detection of additive outliers in bilinear time series

Abstract

Outliers are commonplace in applied time series analysis. Additive outliers could happen in linear time series as well as nonlinear time series. However, their existence is often ignored and their impact overlooked in nonlinear processes. The problem of detecting additive outliers in bilinear time series is considered in this work. We show how Gibbs sampler can be applied to detect aberrant observations in bilinear processes. We also discuss some major problems encountered in practice, such as how one can distinguish between ARMA model with outliers and a bilinear model without outliers. The methodology proposed is illustrated using some generated examples and the US monthly retail price of regular unleaded gasoline. The results obtained by the proposed procedure are informative. The major strength of this procedure is that it can identify those observations which would require more careful scrutinizing.