In this paper, we study travel time and energy cost prediction at any future departure time for a targeted road segment and vehicle. These two prediction tasks play an important part in the design of advanced driver-assistance systems (ADAS) that can automatically manage battery charging, energy saving, and route planning for fully electric vehicles. Compared with the fundamental problem of travel time prediction, which usually learns from the historical and current data of travel time itself, energy cost prediction is a more complex problem that involves multiple context conditions and vehicle status measured by various time-invariant and time-variant data. We define a general learning problem based on multiple time-invariant and time-variant inputs to unify these two prediction tasks. To solve the defined learning problem, we propose heterogeneous delay embedding (HDE), which extracts an informative feature space for regression analysis and aims at achieving satisfactory prediction for any future departure time. The proposed HDE first categorizes the historical and current data of a time-variant measurement into different types, then incorporates different delay settings for embedding multiple types of time-series data, and finally removes redundant information and noise from the generated features using orthogonal locality preserving projection. Experimental results demonstrate the effectiveness of the proposed method for both short- and long-term predictions of travel time and energy cost.