Importance sampling for signal extraction model in time series analysis

Abstract

In time series analysis, signal extraction model (SEM) is used to estimate unobserved signal component from observed time series data. Since parameters of the components in SEM are often unknown in practice, a commonly used method is to estimate unobserved signal component using the maximum likelihood estimates (MLEs) of parameters of the components. This paper explores an alternative way to estimate unobserved signal component when parameters of the components are unknown. The suggested method makes use of importance sampling (IS) with Bayesian inference. The basic idea is to treat parameters of the components in SEM as a random vector and compute a posterior probability density function of the parameters using Bayesian inference. Then IS method is applied to integrate out the parameters and thus estimates of unobserved signal component, unconditional to the parameters, can be obtained. This method is illustrated with a real time series data. Then a Monte Carlo study with four different types of time series models is carried out to compare a performance of this method with that of a commonly used method. The study shows that IS method with Bayesian inference is computationally feasible and robust, and more efficient in terms of mean square errors (MSEs) than a commonly used method.