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The empirical likelihood for first-order random coefficient integer-valued autoregressive processes. (English) Zbl 1208.62143

Summary: This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62G15 Nonparametric tolerance and confidence regions
62F10 Point estimation
62F03 Parametric hypothesis testing
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