Censored time series analysis with autoregressive moving average models

Time Series of Counts under Censoring: A Bayesian Approach

Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit. Ignoring censoring produces biased estimates and unreliable statistical inference. The aim of this work is to contribute to the modelling of time series of counts under censoring using convolution closed infinitely divisible (CCID) models. The emphasis is on estimation and inference problems, using Bayesian approaches with Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms.

Right-Censored Time Series Modeling by Modified Semi-Parametric A-Spline Estimator

This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan-Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data's structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.

Nonparametric autocovariance estimation from censored time series by Gaussian imputation

One of the most frequently used methods to model the autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an autocovariance structure via nonparametric estimation of the autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.