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Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of particular importance in economic applications that currently use only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. Therefore, we propose a procedure for discriminating between causality and noncausality. The methods are illustrated with an application to interest rate data.<\/jats:p>","DOI":"10.1017\/s0266466612000448","type":"journal-article","created":{"date-parts":[[2012,11,12]],"date-time":"2012-11-12T09:26:53Z","timestamp":1352712413000},"page":"447-481","source":"Crossref","is-referenced-by-count":68,"title":["NONCAUSAL VECTOR AUTOREGRESSION"],"prefix":"10.1017","volume":"29","author":[{"given":"Markku","family":"Lanne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pentti","family":"Saikkonen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2012,11,12]]},"reference":[{"key":"S0266466612000448_ref8","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1093\/biomet\/93.1.221","article-title":"A note on time-irreversibility of multivariate linear processes","volume":"93","author":"Chan","year":"2006","journal-title":"Biometrika"},{"key":"S0266466612000448_ref24","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0304-3932(79)90029-1","article-title":"A note on maximum likelihood estimation of the rational expectations model of the term structure","volume":"5","author":"Sargent","year":"1979","journal-title":"Journal of Monetary Economics"},{"key":"S0266466612000448_ref17","doi-asserted-by":"crossref","DOI":"10.2202\/1941-1928.1080","article-title":"Noncausal autoregressions for economic time series","volume":"3","author":"Lanne","year":"2011","journal-title":"Journal of Time Series Econometrics"},{"key":"S0266466612000448_ref10","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1111\/1540-6261.00426","article-title":"Term premia and interest rate forecasts in affine models","volume":"57","author":"Duffee","year":"2002","journal-title":"Journal of Finance"},{"key":"S0266466612000448_ref13","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316429","volume-title":"Multiple Time Series","author":"Hannan","year":"1970"},{"key":"S0266466612000448_ref25","doi-asserted-by":"crossref","DOI":"10.1017\/CCOL0521252806","volume-title":"Estimation, Inference and Specification Analysis","author":"White","year":"1994"},{"key":"S0266466612000448_ref6","doi-asserted-by":"crossref","first-page":"495","DOI":"10.2307\/2298008","article-title":"Yield spreads and interest rate movements: A bird\u2019s eye view","volume":"58","author":"Campbell","year":"1991","journal-title":"Review of Economic Studies"},{"key":"S0266466612000448_ref26","first-page":"265","article-title":"Moments for elliptically countered random matrices","volume":"54","author":"Wong","year":"1992","journal-title":"Sankhy"},{"key":"S0266466612000448_ref16","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.ijforecast.2011.08.003","article-title":"Optimal forecasting of noncausal autoregressive time series","volume":"28","author":"Lanne","year":"2012","journal-title":"International Journal of Forecasting"},{"key":"S0266466612000448_ref1","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/j.1751-5823.2011.00131.x","article-title":"Non-fundamentalness in structural econometric models: A review","volume":"79","author":"Alessi","year":"2008","journal-title":"International Statistical Review"},{"key":"S0266466612000448_ref23","doi-asserted-by":"crossref","first-page":"577","DOI":"10.2307\/1913267","article-title":"Identification in parametric models","volume":"39","author":"Rothenberg","year":"1971","journal-title":"Econometrica"},{"key":"S0266466612000448_ref21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1093\/biomet\/67.1.31","article-title":"Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations","volume":"67","author":"Muirhead","year":"1980","journal-title":"Biometrika"},{"key":"S0266466612000448_ref7","unstructured":"Chan, K.S. & Ho, L. (2004) On the Unique Representation of Non-Gaussian Multivariate Linear Processes. Technical report 341, University of Iowa, http:\/\/www.stat.uiowa.edu\/techrep\/."},{"key":"S0266466612000448_ref11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2937-2","volume-title":"Symmetric Multivariate and Related Distributions","author":"Fang","year":"1990"},{"key":"S0266466612000448_ref18","article-title":"Noncausality and asset pricing","author":"Lof","year":"2012","journal-title":"Studies in Nonlinear Dynamics and Econometrics"},{"key":"S0266466612000448_ref12","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1198\/016214504000001510","article-title":"Diagnostic checking in ARMA models with uncorrelated errors","volume":"100","author":"Francq","year":"2005","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466612000448_ref22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1262-1","volume-title":"Gaussian and Non-Gaussian Linear Time Series and Random Fields","author":"Rosenblatt","year":"2000"},{"key":"S0266466612000448_ref9","unstructured":"Davis, R.A. & Song, L. 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