Underreporting in gender-based violence data is a worldwide problem leading to the underestimation of the magnitude of this social and public health concern. This problem deteriorates the data quality, providing poor and biased results that lead society to misunderstand the actual scope of this domestic violence issue. The present work proposes time series models for underreported counts based on a latent integer autoregressive of order 1 time series with Poisson distributed innovations and a latent underreporting binary state, that is, a first-order Markov chain. Relevant theoretical properties of the models are derived, and the moment-based and maximum-based methods are presented for parameter estimation. The new time series models are applied to the quarterly complaints of domestic violence against women recorded in some judicial districts of Galicia (Spain) between 2007 and 2017. The models allow quantifying the degree of underreporting. A comprehensive discussion is presented, studying how the frequency and intensity of underreporting in this public health concern are related to some interesting socioeconomic and health indicators of the provinces of Galicia (Spain).
KEYWORDSinteger autoregressive models, intimate partner violence, public health, state-dependent underreporting, underrecorded data 4404
The present paper introduces a new model used to study and analyse the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration process with Poisson immigration, Po-INAR(1), together with a mechanism that allows the estimation of the under-reporting in non-stationary count time series. A novelty of the model is that the expectation of the unobserved process’s innovations is a time-dependent function defined in such a way that information about the spread of an epidemic, as modelled through a Susceptible-Infectious-Removed dynamical system, is incorporated into the model. In addition, the parameter controlling the intensity of the under-reporting is also made to vary with time to adjust to possible seasonality or trend in the data. Maximum likelihood methods are used to estimate the parameters of the model.
Background
Genital warts are a common and highly contagious sexually transmitted disease. They have a large economic burden and affect several aspects of quality of life. Incidence data underestimate the real occurrence of genital warts because this infection is often under-reported, mostly due to their specific characteristics such as the asymptomatic course.
Methods
Genital warts cases for the analysis were obtained from the Catalan public health system database (SIDIAP) for the period 2009-2016. People under 15 and over 94 years old were excluded from the analysis as the incidence of genital warts in this population is negligible. This work introduces a time series model based on a mixture of two distributions, capable of detecting the presence of under-reporting in the data. In order to identify potential differences in the magnitude of the under-reporting issue depending on sex and age, these covariates were included in the model.
Results
This work shows that only about 80% in average of genital warts incidence in Catalunya in the period 2009-2016 was registered, although the frequency of under-reporting has been decreasing over the study period. It can also be seen that this issue has a deeper impact on women over 30 years old.
Conclusions
Although this study shows that the quality of the registered data has improved over the considered period of time, the Catalan public health system is underestimating genital warts real burden in almost 10,000 cases, around 23% of the registered cases. The total annual cost is underestimated in about 10 million Euros respect the 54 million Euros annually devoted to genital warts in Catalunya, representing 0.4% of the total budget.
We propose a methodology for clustering financial time series of stocks' returns, and a graphical set-up to quantify and visualise the evolution of these clusters through time. The proposed graphical representation allows for the application of well known algorithms for solving classical combinatorial graph problems, which can be interpreted as problems relevant to portfolio design and investment strategies. We illustrate this graph representation of the evolution of clusters in time and its use on real data from the Madrid Stock Exchange market.
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