Mean targeting estimator for the integer-valued GARCH(1, 1) model

Qi Li and Fukang Zhu ()
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Qi Li: Jilin University
Fukang Zhu: Jilin University

Statistical Papers, 2020, vol. 61, issue 2, No 7, 659-679

Abstract: Abstract The integer-valued GARCH model is commonly used in modeling time series of counts. Maximum likelihood estimation (MLE) is used to estimate unknown parameters, but numerical results for MLE are sensitive to the choice of initial values, which also occurs in estimating the GARCH model. To alleviate this numerical difficulty, we propose an alternative to MLE and name it as mean targeting estimation (MTE), which is an analogue to variance targeting estimation used in the GARCH model. Consistency and asymptotic normality for MTE are established. Comparisons with the standard MLE are provided and the merits of the mean targeting method are discussed. In particular, it is shown that MTE can be superior to MLE for estimating parameters or prediction when the model is well specified and misspecified. We conduct numerical studies to confirm our theoretical findings and illustrate the practical utility of our proposals.

Keywords: GARCH model; Mean targeting estimator; MLE; Numerical simplicity; Time series of counts (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0958-9

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