1.2 Detecting distributional differences between temporal granularities for exploratory time series analysis

Chapter 3 is a natural extension of Chapter 2. Many, many displays might be built using cyclic granularities. However, only a handful of them may reveal major patterns of interest. Identifying the displays which exhibit “significant” distributional differences and plotting only these would allow for more efficient exploration. Furthermore, a few of the displays in this collection will be more engaging than others. Chapter 3 provides a new distance metric for selecting and ranking the multiple granularities. The statistical significance of potential visual discoveries is aided by selecting a threshold for the proposed numerical distance measure. The distance measure is computed for a single or pairs of cyclic granularities, and it can be compared across different cyclic granularities as well as a collection of time series. This chapter also includes a case study using residential smart meter data from Melbourne to demonstrate how the suggested methodology may be utilized to automatically find temporal granularities with significant distributional differences. The methods are implemented in the open-source R package hakear.