Market analysis is a representative data analysis process with many applications. In such an analysis, critical numerical measures, such as profit and sales, fluctuate over time and form time-series data. Moreover, the time series data correspond to market segments, which are described by a set of attributes, such as age, gender, education, income level, and product-category, that form a multi-dimensional structure. To better understand market dynamics and predict future trends, it is crucial to study the dynamics of time-series in multi-dimensional market segments. This is a topic that has been largely ignored in time series and data cube research. In this study, we examine the issues of anomaly detection in multi-dimensional time-series data. We propose timeseries data cube to capture the multi-dimensional space formed by the attribute structure. This facilitates the detection of anomalies based on expected values derived from higher level, "more general" time-series. Anomaly detection in a time-series data cube poses computational challenges, especially for high-dimensional, large data sets. To this end, we also propose an efficient search algorithm to iteratively select subspaces in the original high-dimensional space and detect anomalies within each one. Our experiments with both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed solution.