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Perron and Yabu (2009a) consider the problem of testing for a break occurring at an unknown date in the trend function of a univariate time series when the noise component can be either stationary or integrated. This article extends their work by proposing a sequential test that allows one to test the null hypothesis of, say, l breaks versus the alternative hypothesis of (l + 1) breaks. The test enables consistent estimation of the number of breaks. In both stationary and integrated cases, it is shown that asymptotic critical values can be obtained from the relevant quantiles of the limit distribution of the test for a single break. Monte Carlo simulations suggest that the procedure works well in finite samples. Copyright Copyright 2010 Blackwell Publishing Ltd

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This paper empirically examines the time series behavior of primary commodity prices relative to manufactures with reference to the nature of their underlying trends and the persistence of shocks driving the price processes. The direction and magnitude of the trends are assessed employing a set of econometric techniques that is robust to the nature of persistence in the commodity price shocks, thereby obviating the need for unit root pretesting. Specifically, the methods allow consistent estimation of the number and location of structural breaks in the trend function as well as facilitate the distinction between trend breaks and pure level shifts. Further, a new set of powerful unit root tests is applied to determine whether the underlying commodity price series can be characterized as difference or trend stationary processes. These tests treat breaks under the unit root null and the trend stationary alternative in a symmetric fashion thereby alleviating the procedures from spurious rejection problems and low power issues that plague most existing procedures. Relative to the extant literature, we find more evidence in favor of trend stationarity suggesting that real commodity price shocks are primarily of a transitory nature. We conclude with a discussion of the policy implications of our results.

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Saikkonen (1991, Econometric Theory 7, 1–21) developed an asymptotic optimality theory for the estimation of cointegrated regressions. He proposed the dynamic ordinary least squares (OLS) estimator obtained by augmenting the static cointegrating regression with leads and lags of the first differences of the I(1) regressors. However, the assumptions imposed preclude the use of information criteria such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC) to select the number of leads and lags. We show that his results remain valid under weaker conditions that permit the use of such data dependent rules. Simulations show that, relative to sequential general to specific testing procedures, the use of such information criteria can indeed produce estimates with smaller mean squared errors and confidence intervals with better coverage rates.

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null.These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi…cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.