Stationary processes

Properties of data such as central tendency, dispersion, skewness, and kurtosis are called sample statistics. Mean and variance are two of the most commonly used sample statistics. In any analysis, data is collected by gathering information from a sample of the larger population. Mean, variance, and other properties are then estimated based on the sample data. Hence these are referred to as sample statistics.

An important assumption in statistical estimation theory is that, for sample statistics to be reliable, the population does not undergo any fundamental or systemic shifts over the individuals in the sample or over the time during which the data has been collected. This assumption ensures that sample statistics do not alter and will hold for entities that are outside the sample used for their estimation.

This assumption also applies to time series analysis so that mean, variance and auto-correlation estimated from the simple can be used as a reasonable estimate for...