Constructing Optimal Tests on a Lagged Dependent Variable
Via the leading unit root case, the problem of testing on a lagged dependent variable is characterized by a nuisance parameter which is present only under the alternative (see Andrews and Ploberger (1994)). This has proven a barrier to the construction of optimal tests. Moreover, in their absence it is impossible to objectively assess the absolute power properties of existing tests. Indeed, feasible tests based upon the optimality criteria used here are found to have numerically superior power properties to both the original Dickey and Fuller (1981) statistics and the efficient detrended versions suggested by Elliott, Rothenberg and Stock (1996) and analysed in Burridge and Taylor (2000).
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- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
- Giovanni Forchini & Patrick Marsh, "undated". "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
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"Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative,"
Econometric Society, vol. 62(6), pages 1383-1414, November.
- Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
- Tom Doan, "undated". "APGRADIENTTEST: RATS procedure to perform Andrews-Ploberger Structural Break Test for GARCH/Maximum Likelihood," Statistical Software Components RTS00007, Boston College Department of Economics.
- Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
- Tom Doan, "undated". "APBREAKTEST: RATS procedure to implement Andrews-Ploberger Structural Break Test," Statistical Software Components RTS00006, Boston College Department of Economics.
- Tom Doan, "undated". "REGHBREAK: RATS procedure to perform structural break test with bootstrapped p-values," Statistical Software Components RTS00176, Boston College Department of Economics.
- Serena Ng & Pierre Perron, 2001.
"LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power,"
Econometric Society, vol. 69(6), pages 1519-1554, November.
- Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
- Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992.
"Efficient Tests for an Autoregressive Unit Root,"
NBER Technical Working Papers
0130, National Bureau of Economic Research, Inc.
- Burridge, Peter & Taylor, A M Robert, 2000. " On the Power of GLS-Type Unit Root Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(5), pages 633-645, December.
- Dufour, Jean-Marie & King, Maxwell L., 1991. "Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary or nonstationary AR(1) errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 115-143, January.
- Forchini, Giovanni, 2005. "Optimal weighted average power similar tests for the covariance structure in the linear regression model," Journal of Econometrics, Elsevier, vol. 124(2), pages 253-267, February.
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