Testing continuous time models in financial markets

The aim of the thesis is to provide a wide range of statistical methods designed to test parametric assumptions about the evolution of continuous time processes in financial markets. The main focus is on the statistical methodology and the investigation of the properties of the proposed methods when applied to finite samples. The latter aspect is particularly important for empirical applications. All chapters include an empirical analysis of financial data using the developed methods.

[1]  H. E. Hurst,et al.  Long-Term Storage Capacity of Reservoirs , 1951 .

[2]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[3]  M. Taqqu.  Weak convergence to fractional brownian motion and to the rosenblatt process , 1975, Advances in Applied Probability.

[4]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[5]  J. Hannay,et al.  Topography of random surfaces , 1978, Nature.

[6]  R. Sayles,et al.  Surface topography as a nonstationary random process , 1978, Nature.

[7]  L. Rogers,et al.  Diffusions, Markov processes, and martingales , 1979 .

[8]  S. Karlin,et al.  A second course in stochastic processes , 1981 .

[9]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[10]  D. Siegmund,et al.  A diffusion process and its applications to detecting a change in the drift of Brownian motion , 1984 .

[11]  Peter Hall.  Resampling a coverage pattern , 1985 .

[12]  R. Davies,et al.  Tests for Hurst effect , 1987 .

[14]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[15]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[16]  M. Yor.  DIFFUSIONS, MARKOV PROCESSES AND MARTINGALES: Volume 2: Itô Calculus , 1989 .

[17]  W. Härdle.  Applied Nonparametric Regression , 1991 .

[18]  Fern Y. Hunt.  Error analysis and convergence of capacity dimension algorithms , 1990 .

[19]  A. Owen.  Empirical Likelihood Ratio Confidence Regions , 1990 .

[20]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[21]  Leonard M. Adleman,et al.  Proof of proposition 3 , 1992 .

[22]  E. Platen,et al.  Option Pricing under Incompleteness and Stochastic Volatility , 1992 .

[23]  Ming-Deh A. Huang,et al.  Proof of proposition 1 , 1992 .

[24]  M. Chavance.  [Jackknife and bootstrap]. , 1992, Revue d'epidemiologie et de sante publique.

[25]  Campbell R. Harvey,et al.  An Empirical Comparison of Alternative Models of the Short-Term Interest Rate , 1992 .

[26]  Andrew T. A. Wood,et al.  On the performance of box-counting estimators of fractal dimension , 1993 .

[27]  E. Mammen,et al.  Comparing Nonparametric Versus Parametric Regression Fits , 1993 .

[28]  D. Florens-zmirou.  On estimating the diffusion coefficient from discrete observations , 1993, Journal of Applied Probability.

[29]  Hans Föllmer,et al.  A Microeconomic Approach to Diffusion Models For Stock Prices , 1993 .

[30]  Peter Hall,et al.  On the Relationship Between Fractal Dimension and Fractal Index for Stationary Stochastic Processes , 1994 .

[31]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[32]  P. Hall,et al.  Characterizing surface smoothness via estimation of effective fractal dimension , 1994 .

[33]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[34]  Edgar E. Peters.  Fractal Market Analysis: Applying Chaos Theory to Investment and Economics , 1994 .

[35]  A. Wood,et al.  Simulation of Stationary Gaussian Processes in [0, 1] d , 1994 .

[36]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[37]  M. Sørensen,et al.  Martingale estimation functions for discretely observed diffusion processes , 1995 .

[38]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[39]  Yacine Aït-Sahalia.  Nonparametric Pricing of Interest Rate Derivative Securities , 1995 .

[40]  D. Duffie,et al.  A Yield-factor Model of Interest Rates , 1996 .

[41]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[42]  S. Haberman.  Independence and Dependence , 1996 .

[43]  E. Platen,et al.  Principles for modelling financial markets , 1996, Journal of Applied Probability.

[44]  Algorithms for Analyzing Nonstationary Time Series with Fractal Noise , 1996 .

[45]  Denis Bosq,et al.  Nonparametric statistics for stochastic processes , 1996 .

[46]  G. J. Jiang,et al.  A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model , 1997, Econometric Theory.

[47]  Laurent E. Calvet,et al.  A Multifractal Model of Asset Returns , 1997 .

[48]  John T. Kent,et al.  Estimating the Fractal Dimension of a Locally Self-similar Gaussian Process by using Increments , 1997 .

[49]  E. Mammen.  The Bootstrap and Edgeworth Expansion , 1997 .

[50]  Wolfgang Karl Härdle,et al.  Local polynomial estimators of the volatility function in nonparametric autoregression , 1997 .

[51]  Richard Stanton.  A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk , 1997 .

[52]  Y. Kutoyants,et al.  Efficient Density Estimation for Ergodic Diffusion Processes , 1998 .

[53]  L. Rogers,et al.  Complete Models with Stochastic Volatility , 1998 .

[54]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[55]  Michael H. Neumann,et al.  Regression-type inference in nonparametric autoregression , 1998 .

[56]  Keith A. Baggerly,et al.  Empirical likelihood as a goodness-of-fit measure , 1998 .

[57]  Wolfgang Härdle,et al.  XploRe-The Statistical Computing Environment , 1999 .

[58]  Marc Hoffmann,et al.  Adaptive estimation in diffusion processes , 1999 .

[59]  Peter Hall,et al.  Fractal analysis of surface roughness by using spatial data , 1999 .

[60]  W. Fleming,et al.  Optimal long term growth rate of expected utility of wealth , 1999 .

[61]  D. Ahn,et al.  A Parametric Nonlinear Model of Term Structure Dynamics , 1999 .

[62]  C. LareÂdo,et al.  Stochastic volatility models as hidden Markov models and statistical applications , 2000 .

[63]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[64]  Efstathios Paparoditis,et al.  The Local Bootstrap for Kernel Estimators under General Dependence Conditions , 2000 .

[65]  Risk premia and financial modelling without measure transformation , 2000 .

[66]  W. Härdle,et al.  Semiparametric diffusion estimation and application to a stock market index , 2008 .

[67]  Yongmiao Hong,et al.  Nonparametric Specification Testing for Continuous-Time Models with Application to Spot Interest Rates , 2002 .

[68]  W. Härdle,et al.  An Empirical Likelihood Goodness-of-Fit Test for Diffusions , 2002 .

[69]  Enno Mammen,et al.  Properties of the nonparametric autoregressive bootstrap , 2002 .

[70]  Wolfgang Karl Härdle,et al.  An empirical likelihood goodness‐of‐fit test for time series , 2003 .

[71]  R. Pape,et al.  APPENDIX A: APPENDIX A , 1988, Xunzi.

[72]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.