Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models
针对非高斯非线性密度函数中依赖潜变量高斯长记忆过程的参数估计，提出一种精确极大似然方法，通过重要性采样和线性高斯近似模型实现，并应用于S&P 500指数日对数收益率的单变量和多变量长记忆随机波动率模型。
An exact maximum likelihood method is developed for the estimation of parameters in a non-Gaussian nonlinear density function that depends on a latent Gaussian dynamic process with long-memory properties. Our method relies on the method of importance sampling and on a linear Gaussian approximating model from which the latent process can be simulated. Given the presence of a latent long-memory process, we require a modification of the importance sampling technique. In particular, the long-memory process needs to be approximated by a finite dynamic linear process. Two possible approximations are discussed and are compared with each other. We show that an autoregression obtained from minimizing mean squared prediction errors leads to an effective and feasible method. In our empirical study, we analyze ten daily log-return series from the S&P 500 stock index by univariate and multivariate long-memory stochastic volatility models. We compare the in-sample and out-of-sample performance of a number of models within the class of long-memory stochastic volatility models.