On the Estimation of Parameters in Observation-driven Time Series Models PDF Download

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ISBN: 9789036107174
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Languages : en
Pages : 0

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Book Description
This thesis concerns parameter estimation for observation-driven time-series models. In particular, the focus is on deriving asymptotic properties of (quasi) maximum likelihood estimators for the parameters of (quasi) score-driven models. Before moving to this novel research, Chapter 2 offers an accessible introduction to score-driven models, with a focus on time-varying conditional location and scale models. Then, Chapter 3 establishes conditions for consistency and asymptotic normality of the maximum likelihood estimator for a general class of stationary score-driven models, which is the first main contribution of the thesis. The asymptotic results are global and are also derived under potential misspecification. Importantly, the conditions are formulated in terms of the basic building blocks of score-driven models, which allows anyone to apply them to their own score-driven models of choice. The other main contribution is the proposal of two novel unit-root non-stationary (quasi) score-driven location models and the derivation of the asymptotic properties of the proposed estimators of these models in Chapters 4 and 5. Thus far, no rigorous asymptotic theory was available for non-stationary score-driven models of this type. In particular, Chapter 4 concerns a univariate score-driven location model, with a unit root location process, and with innovations from a mixture of normals distribution. This distribution offers considerable flexibility, and has not been considered for score-driven models before. We establish consistency and asymptotic normality of the maximum likelihood estimator, and examine the model's filtering ability in a Monte Carlo simulation study and an application to electricity spot prices. Chapter 5 considers a multivariate model where the observations are driven by a common univariate quasi score-driven location process with unit root dynamics. We propose a two-step estimation procedure, where the loading coefficients are estimated in the first step and the remaining parameters are estimated in the second step through quasi maximum likelihood estimation. We establish consistency of this two-step estimator and use a Monte Carlo simulation study to investigate its small-sample properties. To illustrate the model's use in practice, we consider an empirical application to diesel prices in different markets.