Forecasting of the development of a partially-observed dynamical time series with the aid of time-invariance and linearity

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.