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Dickey–Fuller, Lagrange Multiplier and Combined Tests for a Unit Root in Autoregressive Time Series
Author(s) -
Oya Kosuke,
Toda Hiro
Publication year - 1998
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 - 10.1111/1467-9892.00095
Subject(s) - unit root , mathematics , autoregressive model , lagrange multiplier , unit root test , augmented dickey–fuller test , series (stratigraphy) , monte carlo method , statistics , multiplier (economics) , null hypothesis , statistical hypothesis testing , sample size determination , score test , econometrics , mathematical optimization , cointegration , paleontology , macroeconomics , economics , biology
In this paper we investigate (augmented) Dickey–Fuller (DF) and Lagrange multiplier (LM) type unit root tests for autoregressive time series through comprehensive Monte Carlo simulations. We consider two sorts of null and alternative hypotheses: a unit root without drift versus level stationarity and a unit root with drift versus trend stationarity. The DF‐type coef ficient tests are found to show the best overall performance in both cases, at least if the sample size is sufficiently large. How ever, it is also found that the DF and LM tests are roughly complementary with regard to their finite‐sample power. We therefore consider combining these two types of unit root tests to obtain ( ad hoc ‘but’) ‘robust’ test procedures. Critical values for the proposed tests are provided