---
title: "Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models"
authors:
  - "Pablo Morales-Mombiela"
  - "Daniel Hernández-Lobato"
  - "Alberto Suárez"
doi: ""
url: "https://ijcai.org/proceedings/2013/230"
pdf: "https://ijcai.org/proceedings/2013/0230.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "1544-1549"
track: ""
keywords:
---

# Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models

Pablo Morales-Mombiela, Daniel Hernández-Lobato, Alberto Suárez

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 1544-1549.

## Abstract

The problem of detecting the direction of time in vector Autoregressive (VAR) processes using statistical techniques is considered. By analogy to causal AR(1) processes with non-Gaussian noise, we conjecture that the distribution of the time reversed residuals of a linear VAR model is closer to a Gaussian than the distribution of actual residuals in the forward direction. Experiments with simulated data illustrate the validity of the conjecture. Based on these results, we design a decision rule for detecting the direction of VAR processes. The correct direction in time (forward) is the one in which the residuals of the time series are less Gaussian. A series of experiments illustrate the superior results of the proposed rule when compared with other methods based on independence tests.