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Tests against stationary and explosive alternatives in vector autoregressive models
Author(s) -
Ahlgren Niklas,
Nyblom Jukka
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2007.00560.x
Subject(s) - mathematics , autoregressive model , companion matrix , explosive material , rank (graph theory) , unit root , statistics , econometrics , statistical hypothesis testing , eigenvalues and eigenvectors , limiting , augmented dickey–fuller test , likelihood ratio test , mathematical analysis , combinatorics , mechanical engineering , chemistry , physics , organic chemistry , matrix polynomial , polynomial matrix , quantum mechanics , polynomial , engineering
Abstract. The article proposes new tests for the number of unit roots in vector autoregressive models based on the eigenvalues of the companion matrix. Both stationary and explosive alternatives are considered. The limiting distributions of test statistics depend only on the number of unit roots. Size and power are investigated, and it is found that the new test against some stationary alternatives compares favourably with the widely used likelihood ratio test for the cointegrating rank. The powers are prominently higher against explosive than against stationary alternatives. Some empirical examples are provided to show how to use the new tests with real data.