Dennis Kristensen, PhD-student

Department of Economics/Financial Markets Group

London School of Economics

PhD-studies at the LSE, Department of Economics

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Job market paper:

"Estimation in Two Classes of Semiparametric Diffusion Models"
ABSTRACT: In this paper we propose an estimation method for two classes of semiparametric scalar diffusion models driven by a Brownian motion: In the first class, only the diffusion term is parameterised while the drift is unspecified; in the second, the drift term is specified while the diffusion is of unknown form. A MLE-like estimator for the parametric part and a kernel estimator of the nonparametric part are defined for a discrete sample with a fixed time distance between the observations. We show that the parametric part of the estimator is root-n-consistent while the nonparametric part has a slower convergence rate. Also, the asymptotic distribution of the estimator is derived. To illustrate the usefulness of these two classes, we fit a specific model from the first class to a proxy of the Eurodollar short-term interest rate. We find non-linearities in both the drift and diffusion function that standard parametric models are unable to capture.

Other papers:

“Semi-nonparametric Estimation of Shape Invariant Engel Curves under Endogeneity” (with R. Blundell & X. Chen), Cemmap working paper WP15/03, submitted to Econometrica.
ABSTRACT: This paper concerns the identification and estimation of a shape-invariant Engel curve system with endogenous total expenditure. The shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of Engel curves. We present a new identification condition and propose an estimation procedure based on conditional moment restrictions allowing for endogeneity. Mean squared convergence rate for the nonparametric IV regression, and root-n asymptotic normality and semiparametric efficiency of the parametric components is established. The method is applied to UK Family Expenditure Survey data, and shows the importance of adjusting for endogeneity in terms of both the curvature and demographic parameters.

“Asymptotics of the QMLE for a Class of ARCH(q) Models” (with A. Rahbek), under revision at Econometric Theory.
ABSTRACT: Consistency and asymptotic normality is established for the quasi-maximum likelihood estimator for a class of ARCH(q) models. The conditions are that the ARCH process is geometrically ergodic with a moment of arbitrarily small order. Furthermore for consistency, the assumption is that the second order moment exists for the non-degenerate rescaled errors and, similarly, that the fourth order moment exists for asymptotic normality to hold. Contrary to existing literature on (G)ARCH models the parameter space is not assumed to be compact. It is demonstrated that the general conditions are satisfied for a range of specific models.

“Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach” (with A. Jeffrey, O. Linton, T. Nguyen, & P.C.B. Phillips), under revision at Journal of Financial Econometrics.
ABSTRACT: We propose a new nonparametric estimator for the volatility structure of the zero coupon yield curve inside the Heath-Jarrow-Morton framework. The estimator incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which can arise from estimation of the yield curve from noisy data. The estimates are implemented with daily CRSP bond data.

"Nonparametric Estimation of Partial Differential Equations with Applications to Asset Pricing", under revision.
ABSTRACT: We consider the estimation of solutions to linear 2nd order partial differential equations (PDE’s) of the elliptic type is considered, when preliminary estimators of the coefficients of the system are available. Making use of the link between this class of PDE’s and stochastic differential equations, we give conditions for consistency, and also derive the asymptotic distribution of the solutions in three leading cases. These general results are applied to the pricing of financial derivatives.

"Mixing Conditions for a Nonlinear State Space Model with Applications to Time Series Models", under revision.
ABSTRACT: We give general conditions for a class of Markov chains on state space form to be geometrically ergodic. We apply this result to various time series models. In particular, sufficient conditions for a broad class of univariate GARCH models to be geometrically ergodic without having a 2nd moment are derived. In certain cases, the condition is also necessary. We also consider various multivariate GARCH models and give conditions for stationarity with 2^nd moment.