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.
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- 1.
\(Z_t=\frac {Y_t-\mathrm {E}[Y_t | Y_{t-1}]}{\sqrt {\mathrm {Var}(Y_t | Y_{t-1})}}\).
- 2.
Masking occurs when one outlier prevents others from being detected.
- 3.
Available from the authors.
- 4.
In the performed simulation study, the detail coefficients present a large variability. Therefore, as a compromise between correct and false detection of outliers, it is found that a reasonable acceptance envelope is constructed from the 0.01th and 99.99th extreme percentiles.
- 5.
Available from the authors.
- 6.
Since 241 is not a power of two, by default Matlab extends the signal by using symmetric-padding (symmetric boundary value replication).
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Acknowledgements
The authors would like to thank the referees for their comments which helped to improve the paper and to Aurea Grané for supplying the programs of the paper [8]. This work is partially supported by Portuguese funds through the CIDMA and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013.
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Silva, I., Silva, M.E. (2018). Wavelet-Based Detection of Outliers in Poisson INAR(1) Time Series. In: Oliveira, T., Kitsos, C., Oliveira, A., Grilo, L. (eds) Recent Studies on Risk Analysis and Statistical Modeling. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-76605-8_13
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DOI: https://doi.org/10.1007/978-3-319-76605-8_13
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