Descriptive Statistics of Energy Prices and Returns

Abstract

Descriptive statistics are those statistical methods that are used to summarize the characteristics of a sample. The main purpose of descriptive statistics is to reduce the original sample into a handful of more understandable metrics without distorting or losing too much of the valuable information contained in the individual observations. We begin by collecting N observations {r ₁, r ₂,…,r _N} on the price return random variable R. These measurements are then organized and summarized using techniques of descriptive statistics described in this chapter. In most cases we can compactly describe the characteristics of a sample using three distinctive classes of descriptive statistics. The first class summarizes the center of the distribution and are known as measures of central tendency. The second class summarizes the spread or dispersion of the sample and are commonly known as measures of dispersion. The third class known as shape statistics summarizes important elements of the shape of the underlying probability distribution implied by the sample. Our objective in using descriptive statistics is to describe as compactly as possible the key properties of empirical data. This information will then be used to assist us in selecting an appropriate probability model for modeling price risk.