Time Series Analysis under Not Missing at Random

Abstract

Time series data often include missing values, and statistical modeling that deals with missing values is needed. Typically, a state-space model is used to impute missing values. However, this approach implicitly assumes that the missing mechanism is missing at random; thus, the estimator may be biased when the missing mechanism is not missing at random. In this study, we construct and incorporate the missing mechanism to reduce the bias of the estimator. The model parameter is estimated by the Monte Carlo Expectation-Maximization (MCEM) algorithm. Monte Carlo simulation is conducted to investigate the effectiveness of our proposed procedure.