Generalized structural time series model

Doctoral thesis English OPEN
Djennad, Abdelmadjid;
  • Subject: dewey510

new class of univariate time series models is developed, the Generalized Structural (GEST) time series model. The GEST model extends Gaussian structural time series models by allowing the distribution of the dependent variable to come from any parametric distribution, i... View more
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    1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Research motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    4 Random e ect models 44 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Gaussian linear mixed models . . . . . . . . . . . . . . . . . . . . . . 47 4.3 Estimation of the xed parameters . . . . . . . . . . . . . . . . . . . 48 4.4 Estimation of the random e ects . . . . . . . . . . . . . . . . . . . . 49 4.5 Computing the hyperparameters via ^ and ^ . . . . . . . . . . . . . . 50 4.6 Estimation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.7 Several random e ects . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7.2 The GEST process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.3 Properties of the GEST process . . . . . . . . . . . . . . . . . . . . . 111 7.3.1 Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.3.2 Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.4 Simulation of the GEST process . . . . . . . . . . . . . . . . . . . . . 113 7.4.1 GEST process with normal distribution . . . . . . . . . . . . . 114 7.4.2 GEST process with Poisson distribution . . . . . . . . . . . . 126 7.4.3 GEST process with negative binomial type I distribution . . . 130 7.4.4 GEST process with Student t distribution . . . . . . . . . . . 134 7.4.5 GEST process with skew Student t distribution . . . . . . . . 138

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