Alzheimer's disease (AD) is known as one of the major causes of dementia and is characterized by slow progression over several years, with no treatments or available medicines. In this regard, there have been efforts to identify the risk of developing AD in its earliest time. While many of the previous works considered cross-sectional analysis, more recent studies have focused on the diagnosis and prognosis of AD with longitudinal or time-series data in a way of disease progression modeling (DPM). Under the same problem settings, in this work, we propose a novel computational framework that forecasts the phenotypic measurements of MRI biomarkers and predicts the clinical statuses at multiple future time points. However, in handling time series data, it generally faces with many unexpected missing observations. In regard to such an unfavorable situation, we define a secondary problem of estimating those missing values and tackle it in a systematic way by taking account of temporal and multivariate relations inherent in time series data. Concretely, we propose a deep recurrent network that jointly tackles the three problems of (i) missing value imputation, (ii) phenotypic measurements forecasting, and (iii) clinical status prediction of a subject based on his/her longitudinal imaging biomarkers. Notably, the learnable model parameters of our network are trained in an end to end manner with our circumspectly defined loss function. In our experiments over TADPOLE challenge cohort, we measured performance for various metrics and compared our method to competing methods in the literature. Exhaustive analyses and ablation studies were also conducted to better confirm the effectiveness of our method.