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Asymptotic normality and parameter change test for bivariate Poisson INGARCH models

Youngmi Lee (), Sangyeol Lee () and Dag Tjøstheim ()
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Youngmi Lee: Seoul National University
Sangyeol Lee: Seoul National University
Dag Tjøstheim: University of Bergen

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 1, 52-69

Abstract: Abstract In this paper, we consider the problem of testing for a parameter change in bivariate Poisson integer-valued GARCH(1, 1) models, constructed via a trivariate reduction method of independent Poisson variables. We verify that the conditional maximum-likelihood estimator of the model parameters is asymptotically normal. Then, based on these results, we construct CMLE- and residual-based CUSUM tests and derive that their limiting null distributions are a function of independent Brownian bridges. A simulation study and real data analysis are conducted for illustration.

Keywords: Time series of counts; Bivariate Poisson INGARCH model; Test for a parameter change; CUSUM test; 62M10; 62G20 (search for similar items in EconPapers)
Date: 2018
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