DISCRETE-TIME STATISTICAL INFERENCE FOR MULTISCALE DIFFUSIONS

被引:8
作者
Gailus, Siragan [1 ]
Spiliopoulos, Konstantinos [1 ]
机构
[1] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA
关键词
multiscale diffusions; slow fast; homogenization; averaging; parameter estimation; PARAMETRIC-ESTIMATION; POISSON EQUATION; ASYMPTOTICS; VOLATILITY; APPROXIMATION;
D O I
10.1137/17M1147408
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization regimes, based on an appropriate misspecified model motivated by a second-order stochastic Taylor expansion of the slow process with respect to a function of the time-scale separation parameter. In the case of a fixed number of observations, we establish consistency, asymptotic normality, and asymptotic statistical efficiency of a minimum contrast estimator (MCE), the limiting variance having been identified explicitly; we furthermore establish consistency and asymptotic normality of a simplified MCE, which is, however, not, in general, efficient. These results are then extended to the case of high-frequency observations under a condition restricting the rate at which the number of observations may grow vis-a-vis the separation of scales. Numerical simulations illustrate the theoretical results.
引用
收藏
页码:1824 / 1858
页数:35
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