A unified perspective on some autocorrelation measures in different fields: A note

Abstract

Using notions from linear algebraic graph theory, this article provides a unified perspective on some autocorrelation measures in different fields. They are as follows: (a) Orcutt’s first serial correlation coefficient, (b) Anderson’s first circular serial correlation coefficient, (c) Moran’s r11{r}_{11}, and (d) Moran’s II. The first two are autocorrelation measures for one-dimensional data equally spaced, such as time series data, and the last two are for spatial data. We prove that (a)–(c) are a kind of (d). For example, we show that (d) such that its spatial weight matrix equals the adjacency matrix of a path graph is the same as (a). The perspective is beneficial because studying the properties of (d) leads to studying the properties of (a)–(c) at the same time. For example, the bounds of (a)–(c) can be found from the bounds of (d).

Keywords

• orcutt’s first serial correlation coefficient
• anderson’s first circular serial correlation coefficient
• moran’s r 11
• moran’s i
• path graph
• cycle graph
• two-dimensional lattice graph
• serial correlation
• spatial autocorrelation
• 62m10
• 62h11
• 05c50