Abstract
To better capture the features of time series of counts such as the counting of elements of variable character and piecewise phenomenon, this paper proposes a class of mixed-thinning threshold integer-valued autoregressive model where the distribution of the innovation sequence is unknown. Strict stationarity ergodicity property is proved. The unknown parameters in the model are estimated by conditional least squares and modified quasi-likelihood methods, as well as their asymptotic normality, are established for the case that the threshold variable is known. The performances of the estimators are investigated in simulation, which manifests that the modified quasi-likelihood estimation performs better. Finally, a set of COVID-19 data on critical cases imported from outside China is analyzed to illustrate the application of developed model.
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