条件自回归极差模型的对数正态拟极大似然估计

Lognormal quasi-maximum likelihood estimate of CARR

为了解决在估计条件自回归极差模型(CARR)中的分布厚尾性问题,采用尾部呈幂函数衰减的对数正态分布估计CARR模型.在新息序列具有有限的12阶矩条件下,利用M估计的大样本性质和鞅的泛函中心极限定理,允许模型包含一个单位根的情况下,证明了对数正态分布下的拟极大似然估计是局部相合和渐近正态的,并且对数正态分布的厚尾性也较好地解决了异常值问题.相对于目前广泛采用的指数似然估计方法,提高了参数估计的效率.

In order to circumvent the heavy-tailed problem in estimating the conditional autoregressive range model（CARR）, the lognormal distribution is considered. Under conditions that the innovations have a finite 12th moment, which allows the model to have a unit root,we show that the quasi-maximum likelihood estimator which uses the lognormal distribution as the likelihood is locally consistent and asymptotically normal by the properties of the M-estimator and functional central limit theorem for martingale. Meanwhile the efficiency of the estimator can also be improved by the heavier tail of lognormal distribution than the exponential likelihood methods currently used in the literature.