A monte-carlo study on the linear difussion process with time delay

Abstract

본 논문에서는 시차를 갖는 확률미분방정식에 의해 정의된 비정상 확률과정의 모수를 추정하는데 있어서 pivotal quantity 이 Gaussian 분포를 갖는 새로운 instrumental variable estimator을 소개하고 새로운 instrumental variable estimator을 이용한 confidence interval 과 tests를 제시한다. 그리고 Monte-Carlo simulation을 통해 시차를 갖는 선형 비정상 확률과정에서는 기존의 최소제곱추정량보다 새로 제안된 instrumental variable estimator가 더 효과적임을 확인하였다. ; For estimating parameters of possibly non-stationary processes defined by stochastic differential equation with time delay, we made a simulation study on the finite sample performance of a new instrumental variable (IV) method whose the pivotal quantity has an approximate Gaussian distribution. Using the normal distribution of the pivotal quantity, we construct the approximate confidence intervals and the tests for the parameter. Monte-Carlo simulation shows that the performance of the tests and confidence intervals based on the proposed estimator is locally better than those of the tests based on the traditional OLSE.