Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes
Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes
复制标题
DOI：
10.1198/073500102288618397
复制
发表时间：
2002-07-01
影响因子：
3
通讯作者：
Gallant, AR
中科院分区：
文献类型：
--
作者：
Durham, GB;Gallant, AR
随机微分方程通常提供了一种方便的方法来描述经济和金融数据的动态，并且已经花费了大量的努力来寻找基于它们来估计模型的有效方法。最大似然是典型的估计选择;然而，由于转移密度通常是未知的，人们被迫近似它。Pedersen（1995）提出的基于模拟的方法具有很大的理论吸引力，但以前可用的实现计算成本很高。我们研究了各种数值技术，旨在提高这种方法的性能。使用Cox-Ingersoll-Ross模型生成的合成数据作为测试案例，该模型的参数经过校准以匹配美国短期利率的月度观测值。由于该过程的似然函数是已知的，因此可以容易地评估近似的质量。在具有1，000个观测值的数据集上，我们能够在1分钟内近似最大似然估计，误差可以忽略不计。与没有这些增强功能的实现相比，这意味着计算工作量减少了10，000倍。通过其他旨在强调方法的参数设置，性能仍然很强。这些想法很容易推广到多变量设置和（与一些额外的工作）的潜变量模型。为了说明，我们估计了一个简单的美国短期利率随机波动模型。
Stochastic differential equations often provide a convenient way to describe the dynamics of economic and financial data, and a great deal of effort has been expended searching for efficient ways to estimate models based on them. Maximum likelihood is typically the estimator of choice; however, since the transition density is generally unknown, one is forced to approximate it. The simulation-based approach suggested by Pedersen (1995) has great theoretical appeal, but previously available implementations have been computationally costly. We examine a variety of numerical techniques designed to improve the performance of this approach. Synthetic data generated by a Cox-Ingersoll-Ross model with parameters calibrated to match monthly observations of the U.S. short-term interest rate are used as a test case. Since the likelihood function of this process is known, the quality of the approximations can be easily evaluated. On datasets with 1,000 observations, we are able to approximate the maximum likelihood estimator with negligible error in well under 1 min. This represents something on the order of a 10,000-fold reduction in computational effort as compared to implementations without these enhancements. With other parameter settings designed to stress the methodology, performance remains strong. These ideas are easily generalized to multivariate settings and (with some additional work) to latent variable models. To illustrate, we estimate a simple stochastic volatility model of the U.S. short-term interest rate.