Estimation of Right-censored SETAR-type Nonlinear Time-series Model

¹ Department of Mathematics and Statistics, Faculty of Mathematics and Science, Brock University, St. Catharines, ON, L2S 3A1, Canada
² Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, 48000, Mugla, Turkey

^* e-mail: ersinyilmaz@mu.edu.tr

Abstract

This paper focuses on estimating the Self-Exciting Threshold Autoregressive (SETAR) type time-series model under right-censored data. As is known, the SETAR model is used when the underlying function of the relation-ship between the time-series itself (Y_t), and its p delays ${(Y_{t-j})}_{j=1}^p$ violates the lin-earity assumption and this function is formed by multiple behaviors that called regime. This paper addresses the right-censored dependent time-series problem which has a serious negative effect on the estimation performance. Right-censored time series cause biased coefficient estimates and unqualified predictions. The main contribution of this paper is solving the censorship problem for the SETAR by three different techniques that are kNN imputation which represents the imputation techniques, Kaplan-Meier weights that is applied based on the weighted least squares, synthetic data transformation which adds the effect of censorship to the modeling process by manipulating dataset. Then, these solutions are combined by the SETAR-type model estimation process. To observe the behavior of the nonlinear estimators in practice, a simulation study and a real data example are carried out. The Covid-19 dataset collected in China is used as real data. Results prove that although the three estimators show satisfying performance, the quality of the estimate SETAR model based on the kNN imputation technique dominates the other two estimators.