Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis

We propose tests for hypotheses on 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 still have the c...

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Bibliographic Details
Published in:Journal of business & economic statistics 2005-10, Vol.23 (4), p.381-394
Main Authors: Bunzel, Helle, Vogelsang, Timothy J
Format: Article
Language:English
Subjects:
Asymptotic value
Bandwidths
Bartering
Correlation analysis
Correlations
Critical values
Data-dependent bandwidth
Determinism
Deterministic trend
Economic models
Economic statistics
Economic theory
Estimators
Fixed-b asymptotics
Heteroscedasticity autocorrelation estimator
Hypotheses
Hypothesis testing
Linear trend
Nearly integrated
Partial sum
Power
Power envelope
Studies
Terms of trade
Time series
Unit root
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Summary:We propose tests for hypotheses on 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 still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze these tests using the fixed-b asymptotic framework recently proposed by Kiefer and Vogelsang. This analysis allows us to analyze the power properties of the tests with regard to bandwidth and kernel choices. Our analysis shows that among popular kernels, specific kernel and bandwidth choices deliver tests with maximal power within a specific 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. We apply the recommended test to the logarithm of a net barter terms of trade series and we find that this series has a statistically significant negative slope. This finding is consistent with the well-known Prebisch-Singer hypothesis.
ISSN:0735-0015
1537-2707
DOI:10.1198/073500104000000631