Periodic integer-valued bilinear time series model. (English) Zbl 1360.62091
Summary: This paper deals with the study of some probabilistic and statistical properties of a periodic integer-valued diagonal bilinear model. The existence of a periodically strict stationary integer-valued process is shown. Sufficient conditions for the periodically stationary, both in the first and second orders, are established. The closed-forms of the mean and the second moment are obtained. The closed-form of the periodic autocovariance function is established. The Yule-Walker estimations of the underlying parameters are obtained. A simulation study is provided.
MSC:
62F12 | Asymptotic properties of parametric estimators |
62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
periodic integer-valued diagonal bilinear model; periodically causal model; periodically correlated integer-valued process; strictly and second moment periodically correlated integer-valued process; Yule-Walker estimationsReferences:
[1] | DOI: 10.1111/j.1467-9892.1987.tb00438.x · Zbl 0617.62096 · doi:10.1111/j.1467-9892.1987.tb00438.x |
[2] | DOI: 10.2307/3214650 · Zbl 0704.62081 · doi:10.2307/3214650 |
[3] | DOI: 10.1239/aap/1151337085 · Zbl 1096.62082 · doi:10.1239/aap/1151337085 |
[4] | DOI: 10.1111/j.1467-9892.2006.00496.x · Zbl 1150.62046 · doi:10.1111/j.1467-9892.2006.00496.x |
[5] | DOI: 10.1137/1108016 · Zbl 0138.11003 · doi:10.1137/1108016 |
[6] | DOI: 10.1111/j.1467-9892.1995.tb00251.x · Zbl 0834.62077 · doi:10.1111/j.1467-9892.1995.tb00251.x |
[7] | DOI: 10.1111/j.1467-9892.1991.tb00073.x · Zbl 0727.62084 · doi:10.1111/j.1467-9892.1991.tb00073.x |
[8] | DOI: 10.1002/sim.4336 · doi:10.1002/sim.4336 |
[9] | DOI: 10.1111/j.1467-9892.2004.01685.x · Zbl 1062.62167 · doi:10.1111/j.1467-9892.2004.01685.x |
[10] | DOI: 10.1214/aop/1176994950 · Zbl 0418.60020 · doi:10.1214/aop/1176994950 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.