Inference for locally stationary processes is often based on some local Whittle-type approximation of the likelihood function defined in the frequency domain. The main reasons for using such a likelihood approximation is that i) it has substantially lower computational cost and better scalability to long time series compared to the time domain likelihood, particularly when used for Bayesian inference via Markov Chain Monte Carlo (MCMC), ii) convenience when the model itself is specified in the frequency domain, and iii) it provides access to bootstrap and subsampling MCMC which exploits the asymptotic independence of Fourier transformed data. Most of the existing literature compares the asymptotic performance of the maximum likelihood estimator (MLE) from such frequency domain likelihood approximation with the exact time domain MLE. Our article uses three simulation studies to assess the finite-sample accuracy of several frequency domain likelihood functions when used to approximate the posterior distribution in time-varying parameter models. The methods are illustrated on an application to egg price data.

翻译：针对局部平稳过程的推断通常基于频域中定义的似然函数的某种局部Whittle型近似。使用此类似然近似的主要原因是：i) 与时间域似然相比，其计算成本显著降低，且对长时序具有更好的可扩展性，特别是在通过马尔可夫链蒙特卡洛（MCMC）进行贝叶斯推断时；ii) 当模型本身在频域中定义时更为便利；iii) 它为利用傅里叶变换数据渐近独立性的自助法和子抽样MCMC提供了途径。现有文献大多比较此类频域似然近似的最大似然估计量（MLE）与精确时间域MLE的渐近性能。本文通过三项模拟研究，评估了多种频域似然函数在近似时变参数模型后验分布时的有限样本精度。这些方法通过鸡蛋价格数据的应用实例加以说明。