ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain and Fourier integral methods that have been used in other recent work on these problems.

[1]  Robert M. de Jong,et al.  ADDENDUM TO “ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES” , 2004, Econometric Theory.

[2]  B. M. Pötscher.  NONLINEAR FUNCTIONS AND CONVERGENCE TO BROWNIAN MOTION: BEYOND THE CONTINUOUS MAPPING THEOREM , 2004, Econometric Theory.

[3]  NONPARAMETRIC ESTIMATION IN NULL RECURRENT TIME SERIES BY HANS ARNFINN KARLSEN AND DAG TJ STHEIM , 2006 .

[4]  Jacques Akonom,et al.  Comportement asymptotique du temps d'occupation du processus des sommes partielles , 1993 .

[5]  CONVERGENCE OF INTEGRAL FUNCTIONALS OF STOCHASTIC PROCESSES , 2006, Econometric Theory.

[6]  Peter C. B. Phillips,et al.  Nonlinear Regressions with Integrated Time Series , 2001 .

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

[8]  P. Phillips,et al.  Nonstationary Density Estimation and Kernel Autoregression , 1998 .

[9]  E. J. Hannan,et al.  The central limit theorem for time series regression , 1979 .

[10]  P. Phillips.  Econometric Analysis of Fisher's Equation , 2005 .

[11]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[12]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[13]  Emmanuel Guerre,et al.  Design-Adaptive Pointwise Non-Parametric Regression Estimation for Recurrent Markov Time Series , 2004 .

[14]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[15]  P. Hall,et al.  Martingale Limit Theory and Its Application , 1980 .

[16]  Miljenko Huzak,et al.  Characteristic Functions , 2011, International Encyclopedia of Statistical Science.

[17]  A. Borodin,et al.  Limit theorems for functionals of random walks , 1995 .

[18]  Peter C. B. Phillips,et al.  Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach , 2002 .

[19]  P. Phillips,et al.  Nonstationary Discrete Choice , 2002 .

[20]  Hans Arnfinn Karlsen,et al.  Nonparametric estimation in a nonlinear cointegration type model , 2007, 0708.0503.

[21]  P. Phillips,et al.  Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity , 2005 .

[22]  Qiying Wang,et al.  Strong Approximation for Long Memory Processes with Applications , 2003 .

[23]  Chien-Ho Wang,et al.  FURTHER RESULTS ON THE ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES , 2005, Econometric Theory.

[24]  Peter C. B. Phillips,et al.  ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES , 1999, Econometric Theory.

[25]  P. Jeganathan.  Convergence of functionals of sums of r.v.s to local times of fractional stable motions , 2004, math/0410097.

[26]  J. Doob.  Stochastic processes , 1953 .

[27]  Peter C. B. Phillips,et al.  Fully Nonparametric Estimation of Scalar Diffusion Models , 2001 .

[28]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[29]  Garey Ramey,et al.  Cowles Foundation for Research in Economics at Yale University , 1995 .

[30]  Joon Y. Park.  The Spatial Analysis of Time Series , 2005 .

[31]  Dag Tjøstheim,et al.  Nonparametric estimation in null recurrent time series , 2001 .

[32]  F. Bandi.  On persistence and nonparametric estimation (with an application to stock return predictability) , 2004 .

[33]  Qiying Wang,et al.  ASYMPTOTICS FOR GENERAL FRACTIONALLY INTEGRATED PROCESSES WITH APPLICATIONS TO UNIT ROOT TESTS , 2003, Econometric Theory.