Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Parameter Estimation in a Complex Non-Stationary and Nonlinear Diffusion Process

  • Published : 2000.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.

Keywords

References

  1. Soviet. Math. Dokl. v.3 Evaluation of the parameters of a complex stationary Gauss-Markov process Arato, M.;Kolmogorov, A.N.;Sinai, Ya. G.
  2. Statistical inference for stochactic processes Basawa, I.V.;Prakasa Rao, B.L.S.
  3. Philosophical Magazine v.8 On a new formula for solving the problem of interpolation in a manner applicable to physical investigations Cauchy, A.L.
  4. Martingale limit theory and its applications Hall, P.;Heyde, C. C.
  5. In Mathematical Programming Studies v.5 On continuous and discrete sampling for parameter estimaition in diffusion type processes Le Breton, A.
  6. Statistics of random processes II;Applications Liptser, R.S.;Shiryayev, A.N.
  7. Stochastic Processes and Their Applications v.17 Girsanov's theorem in Hillbert space and an appicaltion to the statistics of Hilbert space valued stochastic differential equations Loges, W.
  8. Econometric Theory v.15 Cauchy estimatiors for autoregressive processes with applications to unit root tests and confidence intervals So, B. S.;Shin, D. W.
  9. IEEE transactions on Information Theory v.31 Continuous-time system identification on compact parameter sets. Tugnait, J.K.
  10. Principles of coherent communications Viterbi, A.J.