Fully Modified Least Squares and Vector Autoregression

1995 The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contact information may be found at the website http://www.econometricsociety.org or in the back cover of Econometrica). This statement must be included on all copies of this Article that are made available electronically or in any other format. shown to involve a linear combination of independent chi-squared variates. This limit distribution is bounded above by the conventional chi-squared distribution with degrees of freedom equal to the number of restrictions. Thus, conventional critical values can be used to construct valid (but conservative) asymptotic tests in quite general FM time series regressions. This theory applies to causality testing in VAPR's and is therefore potentially useful in empirical applications.