Three classes of metrics: centrality, volatility, and bumpiness

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introduz uma nova classe de estatísticas para séries cronológicas: bumpiness

All statistical textbooks focus on centrality (median, average or mean) and volatility (variance). None mention the third fundamental class of metrics: bumpiness.

Here we introduce the concept of bumpiness and show how it can be used. Two different datasets can have same mean and variance, but a different bumpiness. Bumpiness is linked to how the data points are ordered, while centrality and volatility completely ignore order. So, bumpiness is useful for datasets where order matters, in particular time series. Also, bumpiness integrates the notion of dependence (among the data points), while centrality and variance do not. Note that a time series can have high volatility (high variance) and low bumpiness. The converse is true.

The attached Excel spreadsheet shows computations of the bumpiness coefficient r for various time series. It is also of interest to readers who wish to learn new Excel concepts such a random number generation with Rand, indirect references with Indirect, Rank, Large and other powerful but not well known Excel functions. It is also an example of a fully interactive Excel spreadsheet driven by two core parameters.

Finally, this article shows (1) how a new concept is thought of, (2) then a robust, modern definition materialized, and (3) eventually a more meaningful definition created based on, and compatible with previous science.

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