Author Archives: Xiaochen Xian

Stationary time series and its properties

Author: Xiaochen Xian

In this article, I would like to introduce stationary time series and its properties. Stationary time series is one whose properties do not depend on the time at which the series is observed. It has been widely applied and shows strong power in statistical analysis. The time series with any trends, seasonal patterns, or both, are not stationary. These types of time series, however, can often be converted to stationary time series using techniques like de-trending or differencing.

1. What is time series?

Time series, as its name says, is a sequence labeled by time. We denote the time series variable as ${Y_t: t=\cdots, -1, 0, 1 \cdots}$.… Read more