{"type":"ScholarlyArticle","title":"Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models","authors":[{"name":"Pablo Morales-Mombiela","slug":"pablo-morales-mombiela","given":"Pablo","family":"Morales-Mombiela","affiliation":""},{"name":"Daniel Hernández-Lobato","slug":"daniel-hernandez-lobato","given":"Daniel","family":"Hernández-Lobato","affiliation":""},{"name":"Alberto Suárez","slug":"alberto-suarez","given":"Alberto","family":"Suárez","affiliation":""}],"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.","doi":null,"url":"https://ijcai.org/proceedings/2013/230","pdf":"https://ijcai.org/proceedings/2013/0230.pdf","markdown":"https://ijcai.org/proceedings/2013/230.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/230","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":230,"pages":{"first":1544,"last":1549},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}