INAR-hidden Markov chains to deal with misreported count data

Since McKenzie presented the classical non-negative integer-valued autoregressive (INAR)
model, the analysis of count time series has been rapidly growing in the past years, and many
authors have been actively contributing to its improvement. However, many issues remain to
be addressed in this field.
In the present work, the authors introduce new models of count time series that accommodate
potential misreporting in data. Misreporting in count data is a widespread concern that is
responsible for reporting inaccurate levels of data. This phenomenon can appear in terms of
under-reporting (less than the actual amount of data) or over-reporting (more than the actual
amount of data). However, the believability of such data significantly decreases when both
phenomena are present.