The dimension reduction of the interval-valued data is one of the active research topics in symbolic data analysis (SDA). The main thread has been focused on the extensions of the principal component analysis (PCA) though. Instead of using PCA, the sliced inverse regression can be employed as the alternative to reduce the dimensionalities of the interval-valued data. In many real-life situations, it happened that some of the interval data were time oriented (or dependent). That is, the interval is described by a starting value and an ending value of a time period, and the starting value may be larger or less than an ending value. The classical interval DR methods that ignored the time features of the intervals may cause a loss of information. In this study, we are motivated to use SIR as a base algorithm to develop sliced-based SDR methods for time dependent the interval-valued data. In addition of the symbolic-numericalsymbolic approaches, we utilize the linear interpolation and the cubic spline interpolation for sufficient dimension reduction and visualization of the time dependent interval data. The proposed method considers the time dependency in intervals that can provide the appropriate interpretations of results than those based on the single-valued or the classical interval-valued data. We conducted a study on a microarray data of a yeast cell cycle. The results have shown that the proposed method can reveal the insight structure of genes in the 2D factorial axis. We discussed the statistical properties of the proposed method. We also investigated the further applications of the found features for the classification, clustering and regression problems to the real world data and microarray gene expression data. The comparisons with those obtained with PCA will be also examined.