A Likelihood Ratio Test of Stationarity Based on a Correlated Unobserved Components Model
AbstractWe propose a likelihood ratio (LR) test of stationarity based on a widely-used correlated unobserved components model. We verify the asymptotic distribution and consistency of the LR test, while a bootstrap version of the test is at least first-order accurate. Given empirically-relevant processes estimated from macroeconomic data, Monte Carlo analysis reveals that the bootstrap version of the LR test has better small-sample size control and higher power than commonly used bootstrap Lagrange multiplier (LM) tests, even when the correct parametric structure is specified for the LM test. A key feature of our proposed LR test is its allowance for correlation between permanent and transitory movements in the time series under consideration, which increases the power of the test given the apparent presence of non-zero correlations for many macroeconomic variables. Based on the bootstrap LR test, and in some cases contrary to the bootstrap LM tests, we can reject trend stationarity for U.S. real GDP, the unemployment rate, consumer prices, and payroll employment in favor of nonstationary processes with volatile stochastic trends.
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Bibliographic InfoPaper provided by The George Washington University, Department of Economics, Research Program on Forecasting in its series Working Papers with number 2008-011.
Length: 36 pages
Date of creation: Oct 2008
Date of revision: Sep 2011
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Stationarity Test; Likelihood Ratio; Unobserved Components; Parametric Bootstrap; Monte Carlo Simulation; Small-Sample Inference;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
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