In this paper we propose tests for hypotheses regarding the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data and they are robust to strong serial correlation. The data can contain a unit root and the tests still have the correct size asymptotically. The tests we analyze are standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametric kernel variance estimators. We analyze these tests using the …xed-b asymptotic framework recently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the power properties of the tests with regards to bandwidth and kernel choices. Our analysis shows that among popular kernels, there are speci…c kernel and bandwidth choices that deliver tests with maximal power within a speci…c class of tests. Based on the theoretical results, we propose a data dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang (1998). We apply the recommended test to the logarithm of a net barter terms of trade series and we …nd that this series has a statistically signi…cant negative slope. This …nding is consistent with the well known Prebisch-Singer hypothesis.
In this paper we propose tests for hypotheses regarding the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data and they are robust to strong serial correlation. The data can contain a unit root and the tests still have the correct size asymptotically. The tests we analyze are standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametric kernel variance estimators. We analyze these tests using the …xed-b asymptotic framework recently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the power properties of the tests with regards to bandwidth and kernel choices. Our analysis shows that among popular kernels, there are speci…c kernel and bandwidth choices that deliver tests with maximal power within a speci…c class of tests. Based on the theoretical results, we propose a data dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang (1998). We apply the recommended test to the logarithm of a net barter terms of trade series and we …nd that this series has a statistically signi…cant negative slope. This …nding is consistent with the well known Prebisch-Singer hypothesis.
We conduct a thorough statistical analysis of the empirical foundations for the existence of a Taylor rule. Inflation, the output gap and the federal funds rate appear to be non-stationary variables that are not cointegrated. Although this lack of cointegration could be caused by missing variables or structural breaks, we are unable to 'salvage' the rule using several plausible candidate variables and break dates. We also investigate the possibility that the Taylor rule should be modeled as a nonlinear relationship. We find that a simple threshold model makes significant progress towards rectifying some of the shortcomings of the standard model.
Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is also anticipated to exhibit better coverage performance. Its nonstandard blocking scheme, however, induces nonstandard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1174 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org
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