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A non-stationary integer-valued autoregressive model. (English) Zbl 1148.62074

Summary: It is frequent to encounter a time series of counts which are small in value and show a trend having relatively large fluctuations. To handle such a non-stationary integer-valued time series with a large dispersion, we introduce a new process called integer-valued autoregressive process of order p with signed binomial thinning (INARS(p)). This INARS(p) uniquely exists and is stationary under the same stationary conditions as in the AR(p) process.

We provide the properties of the INARS(p) as well as the asymptotic normality of the estimates of the model parameters. This new process includes previous integer-valued autoregressive processes as special cases. To preserve the integer-valued nature of the INARS(p) and to avoid difficulties in deriving the distributional properties of the forecasts, we propose a bootstrap approach for deriving forecasts and confidence intervals. We apply the INARS(p) to the frequency of new patients diagnosed with the acquired immunodeficiency syndrome (AIDS) in Baltimore, Maryland, U.S., during the period of 108 months from January 1993 to December 2001.

MSC:
62M10Time series, auto-correlation, regression, etc. (statistics)
62G20Nonparametric asymptotic efficiency
62G09Nonparametric statistical resampling methods
62F12Asymptotic properties of parametric estimators
62P10Applications of statistics to biology and medical sciences
62G05Nonparametric estimation
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