A dynamical system produces a dependent multivariate sequence called dynamical time series, developed with an evolution function. As variables in the dynamical time series at the current time-point usually depend on the whole variables in the previous time-point, existing studies forecast the variables at the future time-point by estimating the evolution function. However, some variables in the dynamical time-series are missing in some practical situations. In this study, we propose an autoregressive with slack time series (ARS) model. ARS model involves the simultaneous estimation of the evolution function and the underlying missing variables as a slack time series, with the aid of the time-invariance and linearity of the dynamical system. This study empirically demonstrates the effectiveness of the proposed ARS model.

翻译：动力系统产生的多变量依赖序列称为动态时间序列，其发展由演化函数驱动。由于动态时间序列在当前时间点的变量通常依赖于前一时刻的所有变量，现有研究通过估计演化函数来预测未来时间点的变量。然而，实际情境中动态时间序列的部分变量有时会缺失。本研究提出带松弛变量的自回归时间序列（ARS）模型。该模型借助动力系统的时间不变性与线性特性，同步估计演化函数与作为松弛变量的潜在缺失变量。本研究通过实证验证了所提出ARS模型的有效性。