A Suggested Estimator for AR(1) Model with Missing Observations - Abdelsamie Enany, Mohamed; Khalifa Ahmed Issa, Mohamed; Abdelfatah Gad, Ahmed (Thailand Statistician, 2023)
The paper considers estimation of stationary first-order autoregressive model AR(1) with missing observations. The maximum likelihood method is used to estimate the autoregressive parameter for AR(1) with missing observations. The efficiency of the estimation is affected by treating the initial value required to compute the first value of residuals. The conventional methods treat the initial value as fixed. Therefore, we present new method to estimate AR(1) with missing observations based on treating the initial value as random. The likelihood function is uniquely maximized and a new closed-form estimator for AR(1) in case of missing observations is developed. Monte Carlo simulation studies and a real data analysis showed that the bias and efficiency of the new estimators are more reliable than the conventional estimators. Moreover, the proposed method provides better estimates of missing values than the existing methods.