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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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[1] DOI: 10.1080/03610929208830925 · Zbl 0775.62225 · doi:10.1080/03610929208830925
[2] DOI: 10.1111/j.1467-9892.1987.tb00438.x · Zbl 0617.62096 · doi:10.1111/j.1467-9892.1987.tb00438.x
[3] DOI: 10.1111/j.1467-9574.1988.tb01521.x · Zbl 0647.62086 · doi:10.1111/j.1467-9574.1988.tb01521.x
[4] Billingsley P., Statistical Inference for Markov Process (1961) · Zbl 0106.34201
[5] Chan N. H., Econometric Theor. 22 pp 403– (2006)
[6] DOI: 10.1016/j.jeconom.2006.12.002 · Zbl 1418.62191 · doi:10.1016/j.jeconom.2006.12.002
[7] DOI: 10.1111/1467-9868.00408 · Zbl 1063.62064 · doi:10.1111/1467-9868.00408
[8] Chuang C. S., Statistica Sinica 12 pp 387– (2002)
[9] Hall P., Martingale Limit Theory and Its Application (1980) · Zbl 0462.60045
[10] DOI: 10.1214/aos/1069362388 · Zbl 0881.62095 · doi:10.1214/aos/1069362388
[11] DOI: 10.2307/1427362 · Zbl 0664.62089 · doi:10.2307/1427362
[12] DOI: 10.1093/biomet/84.2.395 · Zbl 0882.62082 · doi:10.1093/biomet/84.2.395
[13] DOI: 10.1214/aos/1176324527 · Zbl 0877.62004 · doi:10.1214/aos/1176324527
[14] DOI: 10.1093/biomet/75.2.237 · Zbl 0641.62032 · doi:10.1093/biomet/75.2.237
[15] DOI: 10.1214/aos/1176347494 · Zbl 0712.62040 · doi:10.1214/aos/1176347494
[16] DOI: 10.1214/aos/1176348368 · Zbl 0799.62048 · doi:10.1214/aos/1176348368
[17] DOI: 10.1214/aos/1176325370 · Zbl 0799.62049 · doi:10.1214/aos/1176325370
[18] DOI: 10.1214/aop/1176994950 · Zbl 0418.60020 · doi:10.1214/aop/1176994950
[19] DOI: 10.1111/j.1467-9892.2006.00472.x · Zbl 1126.62086 · doi:10.1111/j.1467-9892.2006.00472.x
[20] DOI: 10.1016/j.jspi.2005.12.003 · Zbl 1098.62117 · doi:10.1016/j.jspi.2005.12.003
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