A bivariate first-order signed integer-valued autoregressive process |
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Authors: | Jan Bulla Christophe Chesneau Maher Kachour |
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Institution: | 1. Department of Mathematics, University of Bergen, Bergen, Norway;2. Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse-Normandie, Campus II, Caen, France;3. Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen Basse-Normandie, Campus II, Caen, France;4. Ecole supérieure de commerce IDRAC, rue Sergent Michel Berthet CP, Lyon Cedex, France |
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Abstract: | Bivariate integer-valued time series occur in many areas, such as finance, epidemiology, business etc. In this article, we present bivariate autoregressive integer-valued time-series models, based on the signed thinning operator. Compared to classical bivariate INAR models, the new processes have the advantage to allow for negative values for both the time series and the autocorrelation functions. Strict stationarity and ergodicity of the processes are established. The moments and the autocovariance functions are determined. The conditional least squares estimator of the model parameters is considered and the asymptotic properties of the obtained estimators are derived. An analysis of a real dataset from finance and a simulation study are carried out to assess the performance of the model. |
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Keywords: | Bivariate integer-valued time series INAR models SINAR models |
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