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Testing the compounding structure of the CP-INARCH model

Christian H. Weiß (), Esmeralda Gonçalves () and Nazaré Mendes Lopes ()
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Christian H. Weiß: Helmut Schmidt University
Esmeralda Gonçalves: Universidade de Coimbra
Nazaré Mendes Lopes: Universidade de Coimbra

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 5, 571-603

Abstract: Abstract A statistical test to distinguish between a Poisson INARCH model and a Compound Poisson INARCH model is proposed, based on the form of the probability generating function of the compounding distribution of the conditional law of the model. For first-order autoregression, the normality of the test statistics’ asymptotic distribution is established, either in the case where the model parameters are specified, or when such parameters are consistently estimated. As the test statistics’ law involves the moments of inverse conditional means of the Compound Poisson INARCH process, the analysis of their existence and calculation is performed by two approaches. For higher-order autoregressions, we use a bootstrap implementation of the test. A simulation study illustrating the finite-sample performance of this test methodology in what concerns its size and power concludes the paper.

Keywords: Count-data time series; Compound Poisson distribution; INGARCH model; Diagnostic tests; Inverse moments; 60J10; 62M02; 62M10 (search for similar items in EconPapers)
Date: 2017
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