Wavelet-Based Detection of Outliers in Poisson INAR(1) Time Series

Abstract

The presence of outliers or discrepant observations has a negative impact in time series modelling. This paper considers the problem of detecting outliers, additive or innovational, single, multiple or in patches, in count time series modelled by first-order Poisson integer-valued autoregressive, PoINAR(1), models. To address this problem, two wavelet-based approaches that allow the identification of the time points of outlier occurrence are proposed. The effectiveness of the proposed methods is illustrated with synthetic as well as with an observed dataset.