Functionals of complex Ornstein-Uhlenbeck processes

Abstract The exact distribution of the sufficient statistics and distribution of the maximum likelihood estimator of the drift (damping) parameter in a stationary complex Ornstein-Uhlenbeck process, given by (1.1), is investigated. Complete tables of the distribution function for different levels are given by the help of MATLAB. The comparison with the earlier calculations are discussed. The relation of the famous model of Chandler Wobble proposed by Kolmogorov is investigated [1].

[1]  James D. Hamilton.  Time Series Analysis , 1994 .

[2]  David R. Brillinger,et al.  The calculation of cumulants via conditioning , 1969 .

[3]  T. W. Anderson.  On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations , 1959 .

[4]  J. Dickey,et al.  Earth's Variable Rotation , 1991, Science.

[5]  The variation of latitude , 1940 .

[6]  E. Müller,et al.  Rotation of the Earth , 1977 .

[7]  C. Z. Wei,et al.  Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes , 1988 .

[8]  Nearly unstable multidimensional AR processes , 1997 .

[9]  R. Laha.  Probability Theory , 1979 .

[10]  G.Ye. Shilov,et al.  Mathematical Analysis , 1965, Nature.

[11]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[12]  A. Wald,et al.  On the Statistical Treatment of Linear Stochastic Difference Equations , 1943 .

[13]  A. M. Walker,et al.  Further Results on the Analysis of the Variation of Latitude , 1957 .

[14]  The Analysis of the Observations of the Variation of Latitude , 1955 .

[15]  Parameter Estimation with Exact Distribution for Multidimensional Ornstein-Uhlenbeck Processes , 1996 .

[16]  G. Pap,et al.  Asymptotic inference for nearly unstable multidimensional AR processes@@@Asymptotic inference for nearly unstable multidimensional AR processes , 1996 .

[17]  M. Arató.  Linear Stochastic Systems with Constant Coefficients , 1982 .

[18]  Walter Munk,et al.  The rotation of the earth , 1960 .